© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS
0100-1*
ICS 91.080.40
ISBN 0-626-12497-2
SABS 0100-1
Ed. 2.2
*This standard references other standards
Edition 2.2
2000
SOUTH AFRICAN STANDARD
Code of practice
The structural use of concrete
Part 1: Design
Amendments issued since publication
Amdt No.
Date
Text affected
Consolidated edition incorporating amendment No. 1 : 11 April 1994
technical corrigendum No. 1 : 26 September 1994
amendment No. 2 : 31 March 2000
Published by
THE SOUTH AFRICAN BUREAU OF STANDARDS
Gr 20
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
ICS 91.080.40
SOUTH AFRICAN BUREAU OF STANDARDS
CODE OF PRACTICE
SABS 0100-1
Ed. 2.2
Notice
|
|
THE STRUCTURAL USE OF CONCRETE
This part of SABS 0100 was approved in accordance with SABS procedures on 13 August 1992.
Amendment No. 2 was approved in accordance with SABS procedures on 31 March 2000.
Amdt 2, March 2000
NOTE 1 In terms of the Standards Act, 1993 (Act 29 of 1993), no person shall claim or declare that he or any other
person complied with an SABS standard unless
a) such claim or declaration is true and accurate in all material respects, and
b) the identity of the person on whose authority such claim or declaration is made, is clear.
PART 1: DESIGN
NOTE 2 It is recommended that authorities who wish to incorporate any part of this standard into any legislation in the
manner intended by section 31 of the Act consult the SABS regarding the implications.
This part of SABS 0100 will be revised when necessary in order to keep abreast of progress. Comment
will be welcome and will be considered when this part of SABS 0100 is revised.
Foreword
|
Edition 2.2 cancels and replaces all previous editions
Amdt 2, March 2000
Annex A (Methods of checking for compliance with serviceability criteria by direct calculation), annex B
(Movement joints), annex C (Elastic deformation of concrete), annex D (The design of deep beams)
and annex E (Bibliography) are for information only.
SABS 0100 consists of the following parts, under the general title The structural use of concrete:
- Part 1: Design
- Part 2: Materials and workmanship
A vertical line in the margin shows where the text has been modified by amendment Nos. 1 and 2.
Introduction
Obtainable from the
The Council of the South African Bureau of Standards decided that the South African code of practice
for the structural use of concrete should be based on the British Standards Institution codes of practice
BS 8110-1:1985 and BS 8110-2:1985. It should be emphasized, however, that the South African code
uses different loading procedures (compatible with section 4 of SABS 0160:1989) and introduces a few
minor changes on account of South African conditions.
South African Bureau of Standards
Private Bag X191
Pretoria
Republic of South Africa
0001
Telephone : (012) 428-7911
Fax
: (012) 344-1568
E-mail
: sales@sabs.co.za
Website : http://www.sabs.co.za
Attention is drawn to the normative references given
in clause 2 of this standard. These references are
indispensable for the application of this standard.
COPYRIGHT RESERVED
Printed in the Republic of South Africa by the
South African Bureau of Standards
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
ISBN 0-626-12497-2
ii
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
Contents
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
4.3.3
4.3.4
4.3.5
4.3.6
4.3.7
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.4.6
4.4.7
4.5
4.5.1
4.5.2
4.5.3
4.5.4
4.5.5
4.5.6
4.5.7
4.6
4.6.1
4.6.2
4.6.3
4.6.4
4.6.5
4.7
4.7.1
4.7.2
4.7.3
4.7.4
4.7.5
4.7.6
4.7.7
4.8
4.8.1
4.8.2
4.8.3
4.8.4
4.8.5
4.8.6
4.8.7
4.9
4.9.1
4.9.2
4.10
4.10.1
4.10.2
4.10.3
4.10.4
4.11
4.11.1
4.11.2
Page
Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1
Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2
Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3
Limit states design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3.1
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.4
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
3.4.6
4
General objectives and recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Limit states requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Ultimate limit state (ULS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Serviceability limit states (SLS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Loads and strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Values for the ultimate limit state (loads and materials) . . . . . . . . . . . . . . . . . . . . . . . 8
Values for serviceability limit states (loads and materials) . . . . . . . . . . . . . . . . . . . . . 9
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Properties of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Analysis (ultimate limit state) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Analysis (serviceability limit states) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Model analysis and testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Experimental development of analytical procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Reinforced concrete (design and detailing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.1.5
4.1.6
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.3
4.3.1
4.3.2
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Basis of limit states design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Durability and fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Analysis of structures and structural frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Analysis of complete structures and complete structural frames . . . . . . . . . . . . . . . . 17
Analysis of structural frames supporting vertical loads only . . . . . . . . . . . . . . . . . . . . 17
Analysis of structural frames supporting vertical and lateral loads . . . . . . . . . . . . . . . 18
Redistribution of moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Column and beam construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Continuous beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
iii
Moments of resistance at ultimate limit state for beams . . . . . . . . . . . . . . . . . . . . . . . 22
Shear resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Torsional resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Deflection of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Crack control in beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Design of solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Moments and forces in solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
One-way spanning slabs of approximately equal span . . . . . . . . . . . . . . . . . . . . . . 42
Solid slabs spanning in two directions at right angles (uniformly distributed loads)
43
Shear resistance of solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Deflection of solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Crack control in solid slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Ribbed slabs (with solid or hollow blocks or with voids) . . . . . . . . . . . . . . . . . . . . . 55
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Analysis of structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Moments of resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Arrangement of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Flat slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Shear in flat slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Deflection of panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Crack control in panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Analysis and design of flat slab structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Moments and forces in columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Moments induced by deflection in solid slender columns . . . . . . . . . . . . . . . . . . . . 76
Design of column section for ULS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Deflection of columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Crack control in columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Special creep and shrinkage conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Reinforced concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
General definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Structural stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Forces and moments in reinforced concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Short reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Slender reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Deflection of reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Crack control in reinforced walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Staircases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Design of staircases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Moments and forces in bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Design of pad footings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Design of pile caps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Considerations affecting design details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Constructional deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Concrete cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
iv
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
4.11.3 Reinforcement (general considerations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11.4 Minimum areas of reinforcement in elements . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11.5 Maximum areas of reinforcement in element . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11.6 Bond, anchorage, bearing, laps, joints and bends in bars . . . . . . . . . . . . . . . . . . .
4.11.7 Curtailment and anchorage of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11.8 Spacing of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11.9 Ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12
Additional considerations when low density aggregate concrete is used . . . . . . .
4.12.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.2 Durability and fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.3 Characteristic strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.4 Shear resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.5 Torsional resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.6 Deflection of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.7 Shear resistance of slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.8 Deflection of slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.9 Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.10 Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.11 Local bond, anchorage bond and laps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12.12 Bearing stress inside bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
92
93
96
96
101
106
108
110
110
110
110
110
111
111
111
112
112
112
112
112
SABS 0100-1
Ed. 2.2
5.9.5
5.9.6
5.9.7
5.9.8
6
5.1
5.1.1
5.1.2
5.1.3
5.1.4
5.1.5
5.2
5.2.1
5.2.2
5.3
5.3.1
5.3.2
5.3.3
5.3.4
5.3.5
5.3.6
5.4
5.5
5.6
5.7
5.8
5.8.1
5.8.2
5.8.3
5.8.4
5.8.5
5.9
5.9.1
5.9.2
5.9.3
5.9.4
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Basis of design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Durability and fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stability and other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Strength of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structures and structural frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis of structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Redistribution of moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Serviceability limit state (cracking) for beams . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ultimate limit state for beams in flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shear resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Torsional resistance of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Deflection of beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tension members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Low density aggregate prestressed concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prestressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maximum initial prestress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loss of prestress other than frictional losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loss of prestress due to friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transmission length in pre-tensioned elements . . . . . . . . . . . . . . . . . . . . . . . . . . .
End blocks in prestressed elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Considerations affecting design details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Size and number of prestressing tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cover to prestressing tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spacing of prestressing tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
113
113
113
113
113
114
114
114
114
115
115
116
118
122
125
126
126
126
126
126
127
127
127
130
132
133
135
135
135
135
137
v
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
Precast, composite and plain concrete constructions (design and detailing) . . . . . . . . . . . . 140
6.1
6.1.1
6.1.2
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.2.5
6.3
6.3.1
6.3.2
6.3.3
6.3.4
6.4
6.4.1
6.4.2
6.4.3
6.4.4
6.4.5
6.5
6.5.1
6.5.2
6.5.3
Prestressed concrete (design and detailing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7
Curved tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Longitudinal reinforcement in prestressed concrete beams . . . . . . . . . . . . . . . . . . 139
Links in prestressed concrete beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Shock loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Limit states design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Precast concrete construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Framed structures and continuous beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other precast units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bearings for precast units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Joints between precast units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structural connections between units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Continuity of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Connections with structural steel inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other types of connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Composite concrete construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Serviceability limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ultimate limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thickness of structural topping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plain concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structural stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design of plain concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
140
140
140
142
142
142
143
143
147
150
150
152
153
153
154
154
154
154
156
158
158
158
158
158
Fire resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.1
7.2
7.3
7.4
7.5
7.6
7.6.1
7.6.2
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional protection to floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concrete walls containing at least 1,0 % of vertical reinforcement . . . . . . . . . . . . .
Plain concrete walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
162
164
169
169
170
172
172
172
Annexes
A
Methods of checking for compliance with serviceability criteria by direct calculation . . . . . . 173
A.1 Analysis of structure for serviceability limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
A.2 Calculation of deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
A.3 Calculation of crack width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
B
Movement joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
B.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
vi
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
B.2 Need for movement joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
B.3 Types of movement joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
B.4 Provision of joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
B.5 Design of joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
C
Elastic deformation of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
C.1 Modulus of elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
C.2 Creep and shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
C.3 Drying shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
D
The design of deep beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
D.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
D.2 Design and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
E
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Tables
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Values for modulus of elasticity of concrete, Ec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Strength of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Characteristic strength of reinforcement, fy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Ultimate bending moments and shear forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Values of the factor f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Maximum design shear stress vc for grade 25 concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Values of coefficient
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Minimum and ultimate torsional shear stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Reinforcement for shear and torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Basic span/effective depth ratios for rectangular beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Modification factors for tension reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Modification factors for compression reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Ultimate bending moments and shear forces in one-way spanning slabs . . . . . . . . . . . . . . 42
Bending moment coefficients for slabs spanning in two directions at right
angles, simply supported on four sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Bending moment coefficients for rectangular panels supported on four sides
with provision for torsional reinforcement at the corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Bending moments and shear force coefficients for flat slabs of three or more
equal spans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Distribution of moments in panels of flat slabs designed as continuous frames . . . . . . . . . . 68
Values of for braced columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Values of for unbraced columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Values of a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Values of coefficient b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Bar schedule dimensions: deductions for tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Minimum percentage of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Ultimate anchorage bond stress fbu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Maximum clear distance between bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Maximum design shear stress vc in low density aggregate concrete beams . . . . . . . . . . . . 111
Minimum and ultimate torsional shear stress in low density aggregate concrete beams . . . 111
Strength of concrete fcu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Compressive stresses fcu in concrete for serviceability limit states . . . . . . . . . . . . . . . . . . . . 116
Flexural tensile stresses for class 2 elements (serviceability limit state (cracking)) . . . . . . . 117
Depth factors for tensile stresses for class 3 elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
vii
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
32 Conditions at the ultimate limit state for rectangular beams with pre-tensioned tendons or
with post-tensioned tendons having an effective bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
33 Conditions at the ultimate limit state for post-tensioned rectangular beams
having unbonded tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
34 Values of Vco /bh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
35 Shrinkage of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
36 Transmission lengths for small diameter strand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
37 Design bursting tensile forces in end blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
38 Nominal cover to all steel to meet specified periods of fire resistance . . . . . . . . . . . . . . . . . 136
39 Minimum cover to curved ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
40 Minimum distance between centre-lines of ducts in plane of curvature . . . . . . . . . . . . . . . . 139
41 Deleted by amendment No. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
42 Design ultimate horizontal shear stresses at interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
43 Fire resistance of reinforced concrete beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
44 Fire resistance of prestressed concrete beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
45 Fire resistance of reinforced concrete floors (siliceous or calcareous aggregate) . . . . . . . . 167
46 Fire resistance of prestressed concrete floors (siliceous or calcareous aggregate) . . . . . . . 168
47 Effect of soffit treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
48 Fire resistance of concrete columns (all faces exposed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
49 Fire resistance of concrete columns (one face exposed) . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
50 Fire resistance of siliceous aggregate concrete walls containing at least
1,0 % of vertical reinforcement and exposed to fire on one face only . . . . . . . . . . . . . . . . . . 172
C.1 Modulus of elasticity of normal-density concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Figures
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Short-term design stress strain curve for normal density concrete . . . . . . . . . . . . . . . . . . . . 13
Short-term design stress strain curve for reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Short-term design stress strain curve for prestressing reinforcement . . . . . . . . . . . . . . . . . . 14
Ultimate forces, stresses and strains in reinforced concrete sections at the ultimate
limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Single system of bent-up bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Shear failure near supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Definition of panels and bays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Effective width of solid slab carrying a concentrated load near an unsupported edge . . . . . 42
Division of slab into middle and edge strips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Apportionment of load for determining the bearing reactions . . . . . . . . . . . . . . . . . . . . . . . . 48
Definition of a shear perimeter for typical cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Punching shear zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Openings in slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Shear perimeters with loads close to free edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Types of column heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Division of flat slab panels into columns and middle strips . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Sections of shear check for flat slabs with drops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Shear at slab internal column connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Definition of breadth of effective moment transfer strip be for various typical cases . . . . . . . 69
Effective length charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Braced slender columns - Bending moments chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Unbraced slender columns - Bending moments chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Critical section of shear check in a pile cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Simplified detailing rules for beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Simplified detailing rules for slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Determination of le . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
viii
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SABS 0100-1
Ed. 2.2
27 Schematic arrangement of allowance for bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.1 Assumptions made in calculating curvatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
A.2 Values of K for various bending moment diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
C.1 Effects of relative humidity, age of concrete at loading
and section thickness upon creep factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
C.2 Drying shrinkage of normal-density concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
D.1 Equivalent truss resisting point loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
D.2 Equivalent arch resisting UD load and self-weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
D.3 Equivalent truss resisting unequal point loads A > B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
D.4 Loaded area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
ix
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SABS 0100-1
Ed. 2.2
Committee
South African Bureau of Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VJ Woodlock
(Chairman)
I Jablonski
(Standards writer)
E Coetzee
(Committee clerk)
CSIR
Division of Building Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
BG Lunt
Concrete Society of Southern Africa
A Jones
............................
Department of Public Works and Land Affairs . . . . . . . . . . . . . . . . . . . . .
DA Payne
Portland Cement Institute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
JM Clifford
South African Federation of Civil Engineering Contractors . . . . . . . . . . .
HH Meier
The South African Association of Consulting Engineers . . . . . . . . . . . . .
GJ de Ridder
The South African Institution of Civil Engineers . . . . . . . . . . . . . . . . . . . .
AE Goldstein
PC Pretorius
H Scholz
x
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CODE OF PRACTICE
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Edition 2.2
SABS 920, Steel bars for concrete reinforcement.
SABS 0100-2, The structural use of concrete - Part 2: Materials and execution of work.
SABS 0144, Detailing of steel reinforcement for concrete.
SABS 0160 (as amended), The general procedures and loadings to be adopted in the design of
buildings.
3 Limit states design
The structural use of concrete
3.1 General objectives and recommendations
The objective of design by the limit states method is to achieve reasonable probabilities that the
structure being designed will not reach a limit state (i.e. will not become unfit for use) and that the
structure will be durable. To achieve this objective, the factors given below should be taken into
consideration.
Part 1:
Design
3.1.1 The characteristic values of strengths and the nominal values of loads should be considered
in the initial stages of design, in order to take into account the variations in the strengths and properties
of the materials to be used and the variations in the loads to be supported. Where the necessary data
are available, the values should be based on statistical evidence (characteristic values) and where the
data are not available, the values should be based on an appraisal of experience (nominal values).
1 Scope
1.1 This part of SABS 0100 establishes principles for the structural use of concrete under the
following stipulations:
3.1.2 Two sorts of partial safety factors are to be used, one for material strength and the other for
loads. In the absence of special considerations, these partial safety factors should have the values
given in 3.3, appropriate to the limit state being considered, the type of loading and the material being
used.
a) method of design: limit states classified as ultimate limit state and serviceability limit states;
3.2 Limit states requirements
b) material: ordinary concrete of normal and low density, used in reinforced, prestressed and precast
structures or elements and in plain concrete walls;
3.2.1 General
c) types of structures: buildings and structures in which all load-bearing elements (e.g. slabs,
columns, walls, etc.) are of concrete.
All relevant limit states should be considered in the initial stages of the design so as to ensure an
adequate degree of safety and serviceability. The general rule, however, will be to design on the basis
of the expected critical limit state and then to check that the remaining limit states will not be reached.
NOTE -The rules for stability (see clause 3) also apply to structures in which concrete elements such as floor slabs and
walls are used in conjunction with load-bearing elements made of other materials.
3.2.2 Ultimate limit state (ULS)
1.2 This part of SABS 0100 does not cover the structural use of concrete for structures that are the
subject of specialist literature (shells, folded plates, bridges, tunnels, retaining walls, water-retaining
structures, chimneys, and other specialized elements).
3.2.2.1 General
Ultimate limit states are those concerning safety, and they correspond to the maximum load-carrying
capacity of a structure. An ultimate limit state is reached when the structure is not strong enough to
withstand the design loads, i.e. when the resistance of a critical section (or sections) to compression,
tension, shear or torsion is insufficient. This will result in loss of equilibrium of the whole or of a part
of the structure regarded as a rigid body, with the following symptoms being likely to occur:
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions
of this part of SABS 0100. All standards are subject to revision and, since any reference to a standard
is deemed to be a reference to the latest edition of that standard, parties to agreements based on this
part of SABS 0100 are encouraged to take steps to ensure the use of the most recent editions of the
standards indicated below. Information on currently valid national and international standards may be
obtained from the South African Bureau of Standards.
a) the rupture of one or more critical sections (due to overloading, fatigue, fire or deformation);
b) overturning or buckling caused by elastic or plastic instability, sway, wind flutter or ponding; and
c) very large deformation, e.g. transformation of the structure into a mechanism.
SABS 82, Bending dimensions and scheduling of steel reinforcement for concrete.
|
Reference deleted by amendment No. 1.
1
2
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SABS 0100-1
Ed. 2.2
3.2.2.2 Stability
Structures should be so designed that adequate means exist to transmit the design ultimate self-weight
load, wind load and imposed loads safely from the highest supported level to the foundations. The
layout of the structure and the interaction between the structural elements should be such as to ensure
a stable design. The engineer responsible for the overall stability of the structure should ensure the
compatibility of the design and details of parts and components, even where all or part of the design
and details thereof were undertaken by someone else.
3.2.2.3 Robustness
Structures should be so designed that they are not unreasonably susceptible to the effects of
accidents. In particular, situations should be avoided where damage to a small area of a structure or
failure of a single element could lead to the collapse of major sections of the structure. In general, if
any failure were to occur, it should be in the beams and not in the columns. Unreasonable susceptibility
to the effects of accidents may generally be prevented if the factors given below are taken into
consideration.
3.2.2.3.1 Structures should be capable of safely resisting the design ultimate horizontal load, as given
in 4.1.2, applied at each floor or roof level simultaneously.
3.2.2.3.2 Structures should have effective horizontal ties (see 4.11.9)
SABS 0100-1
Ed. 2.2
is a reasonable probability that the structure will not collapse disastrously as a result of misuse or
accident.
Consider whether, due to the nature of a particular occupancy or use of a structure (e.g. flour mill,
chemical plant, etc.), it will be necessary in the design concept or during a design reappraisal to
consider the effect of a particular hazard, to ensure that, in the event of an accident, there is a
reasonable probability that the structure will withstand the accident, even if damage does occur. In
such cases, partial safety factors greater than those given in 3.3.1.2 may be required.
NOTE - No structure can be expected to withstand the excessive loads or forces that could arise owing to an extreme
cause (such as an explosion), but the structure should not be damaged to an extent that is disproportionate to the original
cause.
3.2.2.5 Loads and strength of materials
Use the design strength of materials and the design loads appropriate for the ultimate limit state
(see 3.3).
3.2.3 Serviceability limit states (SLS)
3.2.3.1 General
Serviceability limit states are those that restrict
a) around the periphery,
a) excessive deformation (deflection, rotation);
b) internally, and
b) excessive local damage (cracking, splitting, spalling);
c) to columns and walls.
c) excessive displacement (slip of connections);
3.2.2.3.3 The layout of buildings of five storeys or more should be checked to identify any key
elements whose failure would cause the collapse of more than a limited portion close to these key
elements. Where such elements are identified and the layout cannot be revised to avoid them, the
design should take their importance into account. The likely consequences of a failure of a key element
should be considered when appropriate design loads are chosen. In all cases, an element and its
connections should be capable of withstanding a design ultimate load of 34 kN/m2 (to which no partial
safety factor should be applied) from any direction. The area to which this load is applied will be the
projected area of the element (i.e. the area of the face presented to the load). A horizontal element,
or part of a horizontal element that provides lateral supports vital to the stability of a vertical key
element, should also be considered a key element.
3.2.2.3.4 Buildings of five storeys or more should be so detailed that any vertical load-bearing element
other than a key element can be removed without causing the collapse of more than a limited portion
close to that element. This is generally achieved by providing vertical ties (see 4.11.9) in addition to
satisfying 3.2.2.3.1 to 3.2.2.3.3. There may, however, be cases where it is inappropriate or impossible
to provide effective vertical ties in all or even in some of the vertical load-bearing elements.
When this occurs, the removal of each such load-bearing element should be considered, in turn, and
the elements normally supported by such load-bearing element should be designed to "bridge" the gap,
possibly with the use of catenary action or non-linear deflection effects, and allowing for considerable
deflection.
3.2.2.4 Special hazards
In designing a structure to support loads occurring in the course of normal function, ensure that there
3
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d) excessive vibration; and
e) corrosion.
The above effects are likely to impair the normal use, occupancy, appearance or durability of the
structure or of its structural or non-structural elements, or they might affect the operation of equipment.
Effects such as temperature, creep, shrinkage, sway, settlement, and cyclic loading should be
considered, when relevant.
The design strength of materials and the design loads appropriate for serviceability limit states should
be used (see 3.3).
3.2.3.2 Deflection
3.2.3.2.1 The deflection of the structure or of any part thereof should not exceed the permissible
value. Permissible values of deflection should comply with the requirements of the particular structure,
taking the efficient functioning of the structure, possible damage to adjacent structures or aesthetic
considerations into account.
As a guide, the limits given below can be regarded as reasonable.
3.2.3.2.1.1 The final deflection (including the effects of temperature, creep and shrinkage), measured
below the as-cast level of the support of floors, roofs and all other horizontal members, should not
exceed span/250.
4
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SABS 0100-1
Ed. 2.2
3.2.3.2.1.2 Partitions and finishes will be affected only by that part of the deflection (including the
effects of temperature, creep and shrinkage) that takes place after the construction of the partitions
or the application of the finishes. Information is lacking, but it is suggested that such deflection in the
case of flexible partitions (e.g. dry-wall) be limited to the lesser of span/350 or 20 mm. In the case of
rigid brick walls or other brittle partitions, this deflection should be limited to the lesser of span/500 or
10 mm. Investigation is required in more complicated cases.
3.2.3.2.1.3 If finishes are to be applied to prestressed concrete elements, the total upward deflection
of the elements should not exceed span/300, unless uniformity of camber between adjacent elements
can be ensured.
3.2.3.2.2 Consider the effects of lateral deflections, particularly for tall slender structures. The
acceleration associated with the deflections may be more critical than the deflection itself (see 3.2.3.4).
3.2.3.2.3 In any calculation of deflections, take the design strength of materials and the design loads
given in 3.3, as appropriate for a serviceability limit state.
3.2.3.3 Cracking
3.2.3.3.1 The permissible width of cracks should be determined taking into account the requirements
(e.g. tightness, aesthetic appearance, etc.) of the particular structure.
As a guide, the limits given below can be regarded as reasonable.
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SABS 0100-1
Ed. 2.2
3.2.3.3.4 Sufficient non-prestressed reinforcement should be provided to control cracking adequately.
3.2.3.4 Vibration
Where a structure is likely to be subjected to vibration from causes such as wind forces or machinery,
take measures to prevent discomfort or alarm, damage to the structure, or interference with its proper
function. (Limits to the level of vibration that may be acceptable are described in specialist literature.)
NOTE - In certain circumstances, it could be necessary to isolate the source of vibration or, alternatively, to isolate a part
or the whole of the structure. Special consideration could be necessary for flexible elements of structure.
3.2.3.5 Other serviceability limit states
Ensure that structures designed for unusual or special functions comply with any relevant additional
limit states considered necessary by the engineer.
3.2.4 Other considerations
3.2.4.1 Fatigue
When the imposed load on a structure is predominantly cyclic in character, take the effects of fatigue
into consideration in satisfying limit state requirements.
3.2.4.2 Durability
3.2.3.3.1.1 Reinforced concrete
An assessment of the likely behaviour of a reinforced concrete structure enables identification of the
sections where the effect of cracking should be considered. In general, the surface width of cracks
should not exceed 0,3 mm. Where elements are exposed to particularly aggressive environments (see
SABS 0100-2), the surface width of cracks at points nearest the main reinforcement should not, in
general, exceed 0,004 times the nominal cover to the main reinforcement. In a reinforced concrete
structure under the effects of load and environment, the actual widths of cracks will vary considerably;
the prediction of an absolute maximum width is therefore not possible, since the possibility of some
cracks being even wider must be accepted unless special precautions are taken.
The recommendations in this part of SABS 0100 regarding concrete cover to the reinforcement and
acceptable crack widths (see 3.2.3.3) in association with the cement content and cement/water ratios
specified in SABS 0100-2, are intended to meet the durability requirements of almost all structures.
Where exceptionally severe environments are encountered, consider any additional precautions that
may be necessary and consult specialist literature with respect to each particular environment.
3.2.4.3 Fire resistance
Consider the following three conditions for structural elements that may be subjected to fire:
3.2.3.3.1.2 Prestressed concrete
a) retention of structural strength;
In the assessment of the likely behaviour of a prestressed concrete structure, the flexural tensile stress
for structures of different classes should be limited as follows:
b) resistance to penetration of flames; and
- class 1: no tensile stresses;
c) resistance to heat transmission.
NOTE - The minimum requirements for different elements for various periods of fire resistance are given in clause 7.
- class 2: tensile stresses, but no visible cracking; and
- class 3: tensile stresses, but surface width of cracks do not exceed 0,1 mm for elements exposed
to a particularly aggressive environment (see SABS 0100-2) and do not exceed 0,2 mm for all other
elements.
3.2.3.3.2 In either tall or long buildings, the effects of temperature, creep and shrinkage could, unless
otherwise catered for, require the provision of movement joints both within the structure and between
the structure and the cladding.
3.2.4.4 Lightning
Reinforcement may be used as part of a lightning protection system, but safeguards such as the
provision of bonding and the use of a resistance check after the completion of the building are
required.
3.2.3.3.3 In any calculations of crack widths (see annex A), take the design strength of the materials
and the design loads given in 3.3, as appropriate for a serviceability limit state.
5
6
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
3.3 Loads and strength of materials
b) the yield or proof stress of reinforcement fy, and
3.3.1 Loads
c) the ultimate strength of a prestressing tendon fpu below which not more than 5 % of the test results
fall.
3.3.1.1 Nominal load
3.3.2.2 Partial safety factors for strength of materials
The following nominal loads should be used in the design of a structure:
m
a) nominal self-weight load Gn (i.e the weight of the structure complete with finishes, fixtures and
partitions);
For the analysis of sections, the design strength for a given material and limit state is derived from the
characteristic strength divided by m, where m is the appropriate partial safety factor for material
strength given in 3.3.3 and 3.3.4. Factor m takes account of
b) nominal imposed load Qn;
a) differences between actual and laboratory values of strength,
b) local weakness,
c) nominal wind load W n; and
c) inaccuracies in the assessment of the resistance of sections, and
d) earth and water pressure.
The nominal load values should be taken as defined in and calculated in accordance with SABS 0160.
3.3.1.2 Partial safety factors for load
3.3.3.1 Design loads
f
The design load for a given type of limit state and loading is obtained from:
3.3.3.1.1 Take the design loads for the ultimate limit state (referred to in clauses 4 and 5 as the
ultimate loads) in accordance with clause 4 of SABS 0160 (as amended).
- Gn. f = design self-weight load,
3.3.3.1.2 The design load effect may be adjusted, at the discretion of the designer, by multiplying the
design load as in 3.3.3.1.1 by an importance factor c to allow for the consequences of failure. In the
case of critical structural elements for structures in which large crowds gather and where there would
be very serious consequences in the event of a failure, a value of c in the range 1,1 to 1,2 should be
used. For structures with a very low degree of hazard to life and with less serious consequences of
failure, a value of c of 0,9 would be appropriate.
- Qn. f = design imposed load,
-
Wn. f = design wind load,
where
f
d) the importance of the limit state that is being considered.
3.3.3 Values for the ultimate limit state (loads and materials)
is the appropriate partial safety factor for load, which is introduced to take account of
a) possible unusual increases in load beyond those considered in the derivation of the nominal loads,
b) inaccurate assessment of the effects of loading,
c) unforeseen stress redistribution within the structure,
d) the variations in dimensional accuracy achieved in construction, and
e) the importance of the limit state that is being considered.
3.3.3.1.3 In assessing the effect of loads on the whole structure or on any part of the structure, so
arrange the loads as to cause the most severe stresses. It will only be necessary to use the factor 0,9
if the self-weight load is an essential factor in the stability, e.g. for cantilevers or for wind forces. If a
critical stability condition results in the case of self-weight and wind loads combined and when (on
selected parts of the structure) the self-weight load is increased, adopt the higher figure for the
self-weight load, i.e. 1,2 Gn. Generally, in the case of self-weight, imposed and wind loads combined,
assume that no variations in f factors need be considered.
3.3.3.1.4 Since the design of the whole or of any part of a structure may be controlled by any of the
load combinations, consider each in design, and adopt the most severe.
3.3.1.3 Load during construction
The loading conditions during erection and construction should be considered in design and should
be such that the structure's subsequent compliance with the limit state requirements is not impaired.
3.3.2 Strength of materials
3.3.3.1.5 If the probable effect of excessive loads caused by misuse or accident has to be considered
in the design, take the f factor for the overload as 1,05, and consider this only in conjunction with the
sustained loads at the ULS. When considering the continued stability of the structure after it has
sustained localized damage, consider only the sustained portion of the loads at the ULS.
3.3.2.1 Characteristic strength of materials
NOTE In general, the effect of creep, shrinkage and temperature will be of secondary importance for the ULS, and no
specific calculations will be necessary.
Unless otherwise stated, the characteristic strength of materials means
3.3.3.2 Materials
a) the cube strength of concrete fcu,
When assessing the strength of a structure or of any part thereof, take the appropriate values of m
as follows:
7
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SABS 0100-1
Ed. 2.2
a) reinforcement: m = 1,15
b) concrete in flexure or axial load: m = 1,50
c) shear strength without shear reinforcement and shear taken by concrete in combination with shear
reinforcement: m = 1,40
d) bond strength: m = 1,40
e) others (e.g. bearing stresses):
m
> 1,50
NOTE When considering the effects of excessive loads or localized damage, take values of
1,0 for steel.
m
as 1,3 for concrete and
3.3.4 Values for serviceability limit states (loads and materials)
3.3.4.1 Design loads
3.3.4.1.1 Take the design loads for SLS in accordance with clause 4 of SABS 0160 (as amended).
3.3.4.1.2 When assessing the deflection of a structure or of any part thereof, so arrange the imposed
load as to cause the largest deflection.
3.3.4.1.3 The design loads given above apply when the immediate deflections of a structure
(see 3.2.3.2) are being estimated, but in most cases it is also necessary to estimate the additional
time-dependent deflections due to creep, shrinkage and temperature.
3.3.4.1.4 The deflection due to creep depends on the self-weight load and those imposed loads of
long duration. Where the full imposed load is unlikely to be permanent, calculate the deflection due
to creep on the assumption that only the self-weight load and that part of the imposed load likely to
be permanent are effective. This deflection could be upward. Consider the effects of temperature,
including temperature gradients within the elements, when these effects exceed those known from
experience to be inconsequential.
3.3.4.1.5 When an imposed load is predominantly cyclic in character, give special attention to the
assessment of the deflections.
3.3.4.1.6 When assessing crack widths (see 3.2.3.3) or other forms of local damage in a structure
subjected to temperature, creep or shrinkage effects exceeding those known from experience to be
inconsequential, consider the resulting internal forces and their effect on the structure as a whole.
3.3.4.2 Materials
When assessing the deflections of a structure or of any part thereof, take the appropriate values of
m as 1,0 for both concrete and steel. Thus, take the properties of the materials relevant to deflection
assessment, i.e. moduli of elasticity, creep, shrinkage, etc., as those associated with the characteristic
strength of the materials (see 3.4.2.2 to 3.4.2.4). When assessing the cracking strength of prestressed
concrete elements by tensile stress criteria, m should be taken as 1,3 for concrete in tension due to
flexure and 1,0 for steel.
D
D
9
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SABS 0100-1
Ed. 2.2
a) for normal density concrete, from figure 1 with
b) for reinforcement, from figure 2 with
m
m
having the relevant value given in 3.3.3.2;
having the relevant value given in 3.3.3.2;
c) for prestressing reinforcement, from figure 3, with
m
having the relevant value given in 3.3.3.2.
The strain distribution in concrete and the strains in reinforcement are derived from the assumption
that plain sections remain plain. The tensile strength of concrete is ignored.
For prestressing tendons, make appropriate allowance for relaxation; for concrete, make appropriate
allowance for shrinkage and creep.
3.4.4 Analysis (serviceability limit states)
3.4.4.1 Analysis of structures
When elastic analysis is used to determine force distribution throughout the structure, base the relative
stiffness on the concrete section, the gross section or the transformed section (see 3.4.3.1).
3.4.4.2 Analysis of cross-sections
When assessing the deflections of a structure, calculate the curvature at any section, taking into
account the influence of creep, shrinkage and cracking.
3.4.5 Model analysis and testing
Deem a design to be satisfactory on the basis of satisfactory results from an appropriate model test
coupled with the use of model analysis to predict the behaviour of the actual structure, provided the
work has been carried out by engineers with the relevant experience and using suitable equipment.
3.4.6 Experimental development of analytical procedures
Deem a design to be satisfactory if the analytical or empirical basis of the design has been justified
by development testing of prototype units and structures, relevant to the particular design under
consideration.
12
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
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Amdt 1, Apr. 1994
NOTE – fy is in megapascals.
Figure 2 — Short-term design stress strain curve for reinforcement
Amdt 1, Apr. 1994
NOTES
1 The coefficient 0,67 takes into account the difference between laboratory and site strength of concrete.
2 fcu is in megapascals.
3 For non-linear analysis, specialist literature should be consulted.
Figure 1 — Short-term design stress strain curve
for normal density concrete
Figure 3 — Short-term design stress strain curve for
prestressing reinforcement
13
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4 Reinforced concrete (design and detailing)
4.1.4 Loads
4.1 General
In this clause, the design load for the ultimate limit state is referred to as the ultimate load or the
maximum design load, to avoid confusion with the service load, which is the design load for the
serviceability limit states.
This clause gives methods of analysis and design that will, in general, ensure that for reinforced
concrete structures, the objectives set out in clause 3 are achieved. Other methods may be used,
provided that they can be shown to be satisfactory for the type of structure or element under
consideration. In certain cases, the assumptions made in this clause may be inappropriate and the
engineer will have to adopt a more suitable method, bearing in mind the nature of the structure in
question.
4.1.1 Basis of limit states design
This subclause follows the limit states principles set out in clause 3. It is assumed that for reinforced
concrete structures, the critical limit state will be the ultimate limit state (see 3.2.2). The design
methods therefore take into account the partial safety factors appropriate to the ultimate limit state,
and are followed by recommendations to ensure that the serviceability limit states of deflection,
cracking or vibration are not reached. The serviceability limit states of deflection and cracking will not
normally be reached if the recommendations given for span/effective depth ratios and reinforcement
spacings are followed. The engineer may alternatively calculate deflections and crack width to prove
compliance with clause 3. (Suitable methods are described in annex A.)
In design, use the values of the ultimate loads given in 3.3.3.1, and the values of the service loads
given in 3.3.4.1.
4.1.5 Strength of materials
In this clause, the design strengths of materials for the ultimate limit state are expressed (in all the
tables and equations) in terms of the characteristic strength of the material. Unless specifically stated
otherwise, all equations and tables include allowances for m, the partial safety factor for material
strength.
4.1.5.1 Characteristic strength of concrete
The values of the 28 d characteristic strength of concrete, fcu, and the required strength of concrete
at ages exceeding 28 d, for various grades of concrete, are given in table 2.
Table 2 Strength of concrete
4.1.2 Stability
1
2
Apart from the considerations given in 3.2.2, cognizance should also be taken of those given below:
4.1.2.1 Ultimate horizontal load
Grade
All structures should be capable of resisting an ultimate horizontal load applied at each floor and roof
level simultaneously, of at least 1,5 % of the nominal self-weight of the structure between mid-height
of the storey below and either mid-height of the storey above or the roof surface. This force could be
shared by the parts of the structure, depending on their stiffness and strength.
4.1.2.2 Safeguarding against vehicular impact
In order to obviate the possibility of vehicles running into and damaging or destroying vital load-bearing
elements in the ground floor of a structure, the provision of elements such as bollards, walls and
retaining earthbanks should be considered.
4.1.2.3 Provision of ties
In structures where all load-bearing elements are of concrete, horizontal and vertical ties should be
provided in accordance with 4.11.9.
4.1.3 Durability and fire resistance
The durability and the fire resistance of reinforced concrete depend on the amount of concrete cover
to reinforcement. Guidance on the minimum cover to reinforcement that is necessary to ensure
durability is given in 4.11.2. Fire test results or other evidence may be used to ascertain the fire
resistance of an element or, alternatively, reference could be made to clause 7.
15
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3
4
5
Required strength at other ages
Characteristic
strength, fcu
MPa
MPa
months
Age
3
6
12
20
25
30
20,0
25,0
30,0
23
29
34
24
30
35
25
31
36
35
40
45
50
35,0
40,0
45,0
50,0
39
44
49
54
40
46
51
56
42
48
53
58
Design consideration should be based on the characteristic strength fcu, or, if relevant, on the
appropriate strength given in table 2 for the age at loading.
For reinforced concrete, the lowest grade that should be used is 20 for concrete made with
normal-weight aggregates and 15 for concrete made with lightweight aggregates.
4.1.5.2 Characteristic strength of reinforcement
Base the design on the appropriate characteristic strength of reinforcement given in table 3. (If
necessary, a lower design stress may be used to help control deflection or cracking, and possibly a
different grade of reinforcement may be used.)
16
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SABS 0100-1
Ed. 2.2
beam under consideration may generally be assumed to be fixed, unless the assumption of pinned
ends is clearly more reasonable. The stiffness of the beams on either side of the beam under
consideration should be taken as half their actual stiffness values if they are taken to be fixed at their
outer ends.
The critical loading arrangements should be taken as follows:
– all spans loaded with total ultimate load (1,2Gn + 1,6Qn);
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– all spans loaded with ultimate self-weight load (1,2Gn) and alternate spans loaded with ultimate
Amdt 1, Apr. 1994
imposed load (1,6Qn).
The moments in an individual column may also be found from this simplified subframe, provided that
the subframe has at its central beam the longer of the two spans framing into the column under
consideration.
4.2.2.3 "Continuous beam" simplification
As a more conservative alternative to the preceding subframe arrangements, the moments and shear
forces in the beams at one level may also be obtained by regarding the beams as a continuous beam
over supports providing no restraint to rotation. The critical loading arrangements should be in
accordance with 4.2.2.1.
4.2.2.4 Asymmetrically loaded columns where a beam has been analysed in accordance with
4.2.2.3
In these columns, the ultimate moments may be calculated by simple moment distribution procedures,
on the assumption that the columns and beam ends remote from the junction under consideration are
fixed and that the beams possess half their actual stiffness. The arrangement of the design ultimate
imposed load should be such as to cause the maximum moment in the column.
4.2.3 Analysis of structural frames supporting vertical and lateral loads
4.2.3.1 When a frame provides lateral stability to the structure as a whole, it will be necessary to
consider the effect of lateral loads. In addition, if the columns are slender (see 4.7.1.4), it may be
necessary to consider additional moments (e.g. from eccentricity) that may be imposed on beams at
beam column junctions.
4.2.3.2 In most cases, the design of individual beams and columns may be based either on the
moments, loads and shears obtained by considering vertical loads only (as in 4.2.2) or on those
obtained by considering both vertical and lateral loads. If the moments, loads and shears obtained by
considering both types of loads are greater than those obtained by considering vertical loads only, then
the design should be based on the sum of those obtained from 4.2.3.2.1 and 4.2.3.2.2.
4.2.3.2.1 An elastic analysis of a series of subframes, each consisting of the beams at one level
together with the columns above and below. The ends of the columns remote from the beams may
generally be assumed to be fixed, unless the assumption of pinned ends is clearly more reasonable.
NOTE Lateral loads should be ignored and all beams should be considered to be loaded as in 4.2.2.
4.2.3.2.2 An analysis of the complete frame, assuming points of contraflexure at the centres of all
beams and columns, ignoring self-weight and imposed loads and considering only the design wind load
on the structure. If more realistic, instead of assuming points of contraflexure at the centres of ground
floor columns, the feet should be considered pinned.
18
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.2.4 Redistribution of moments
4.3 Beams
Redistribution of the moments obtained by elastic analysis or by the simplified methods given in 4.2.2
and 4.2.3 may be carried out, provided the following conditions are satisfied:
4.3.1 General
a)
condition 1: equilibrium between internal and external forces is maintained under all appropriate
combinations of ultimate load.
b)
condition 2: where the design ultimate resistance moment of the cross-section subjected to the
largest moment within each region of hogging or sagging is reduced, the neutral axis depth x
should not exceed
Beams of normal proportions are the subject of this subclause. In the case of beams of depth
exceeding half of their clear span, specialist literature should be consulted.
4.3.1.2 Effective span of simply supported beams
The effective span of a simply supported beam is the smaller of
( b-0,4)d
a) the distance between the centres of bearings, and
where
b) the clear distance between supports plus the effective depth.
d is the effective depth; and
b
4.3.1.1 Design limitation
=
4.3.1.3 Effective span of a continuous beam
(moment at section after redistribution)
<1
(moment at section before redistribution)
The effective span of a continuous beam is the distance between the centres of supports. In the case
of an embedded end, the centre of action of support should be taken to be half the effective depth from
the face of the support.
from the respective maximum moments diagrams.
NOTE Unless the column axial load is small, condition 2 will generally rule out reduction in column moment.
c) condition 3: the ultimate resistance moment at any section of an element complies with the
appropriate value obtained from the final envelope of redistributed elastic moments on the element,
and the ultimate resistance moment at any section is at least 75 % or 80 %, as relevant, of the
elastic moment at that particular section, obtained from elastic maximum moment diagrams
covering all appropriate combinations of ultimate loads. The value of 75 % is applicable in the case
of uniform elements (the cross-section considered does not change along the element). The value
of 80 % is applicable in the case of non-uniform elements.
d) condition 4: in structures exceeding four storeys and in which the structural frame provides the
lateral stability, the redistribution of moments is limited to 10 % and the value given in condition 3
reads 90 %.
e) condition 5: in the case of linear elastic analysis being used, the relative stiffness of the elements
is not based on the transformed sections.
4.2.5 Column and beam construction
4.3.1.4 Effective length of a cantilever
The effective length of a cantilever should be taken as its length to the face of the support plus half
the effective depth. If a cantilever forms the end of a continuous beam, the effective span should be
taken as its clear length plus the distance to the centre of the support.
4.3.1.5 Effective width of flanged beam
In the absence of a more accurate determination, ensure that the effective flange width
a) for a T-beam does not exceed the lesser of
1) the web width plus L z /5 and
2) the actual width of the flange, and
b) for an L-beam does not exceed the lesser of
1) the web width plus L z /10 and
Any structural frame in a building provided with lateral stability by walls or bracing designed to resist
all lateral forces may be considered to consist of continuous beams (see 4.3) and columns (see 4.7),
and the simplified but more conservative methods given in the appropriate subsections may be used
in design as an alternative to the methods given in 4.2.2.
2) the actual width of the flange,
where L z is the distance between points of zero moment (considering the bending moment envelope
on spans). For a continuous beam, L z may be taken as 0,7 times the effective span.
4.3.1.6 Slenderness limits for beams
To ensure lateral stability, the clear distance between lateral restraints should not exceed the following:
a) for simply-supported and continuous beams,
the lesser of 60bc and 250b c2 /d; and
b) for cantilevers with lateral restraint provided only at the support,
19
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SABS 0100-1
Ed. 2.2
Table 4 Ultimate bending moments*) and shear forces
1
2
3
Position
Moment
Shear
At outer support
0
0,45F
Near middle of end span
Fl
11
-
At first interior supports
-Fl
9
0,6F
At middle of interior spans
Fl
14
-
At interior supports
-Fl
12
0,55F
*)Do not redistribute the moments obtained from the table.
NOTE F is the total ultimate load (1,2G n + 1,6Qn) and
l is the effective span.
4.3.3 Moments of resistance at ultimate limit state for beams
4.3.3.1 Analysis of beams
When a cross-section of a beam is being analysed to determine its ultimate moment of resistance, the
following assumptions should be made:
a) the strain distribution in the concrete in compression and the strains in the reinforcement, whether
in tension or in compression, are derived from the assumption that plane sections remain plane;
b) the simplified stress diagram of concrete in compression is as shown in figure 4; alternatively, the
stresses in the concrete in compression may be derived from the stress strain curve shown in
figure 1, taking m as 1,5; in both cases,
1) the strain at the outermost compression fibre is taken as 0,003 5; and
2) where beams are reinforced for tension only, the depth of the concrete in compression is limited
to half the effective depth of the beam;
c) the tensile strength of the concrete is ignored;
d) the stress in the reinforcement is derived from the stress strain curve shown in figure 2, taking
m as 1,15;
e) where the beam is designed to resist flexure only, the lever arm is assumed not to exceed 0,95
times the effective depth. In the analysis of a cross-section of a beam that has to resist a small axial
thrust, the effect of the ultimate force may be ignored if the force does not exceed the value of 0,1fcu
multiplied by the cross-sectional area.
4.3.3.2 Design possibilities
In the actual design, in order to find the amount of reinforcement required, either the design formulae
given in 4.3.3.4, or strain compatibility together with the assumption of plane strain (in the case of
non-rectangular beams) may be used.
22
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A
As
b
b
d
d
f
f
f
f
f
h
M
x
z
K
d
K
K
K
M
bd f
K
k
z d
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x
d z
A
M
K
K
d
fz
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z
K
d
x
d z
A
K K
A
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Kf
f bd f d d
bd
A f
fz
f
f
d
x
f
M
A
f
b d
f
h
d
d
h
M
f A
M
f
b h
h
d
d
h
h
d
f bd
d
v
f
v
V
bd
V
b
d
v
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v
vc
0,75
f cu
m
25
1/3
100 A
bv d
1/3
400
d
1/4
(2)
f
A
b d
A
b
d
v
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d
without shear reinforcement
v
v
d a d
a
v
f
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G
C
G
C
C
v
C
v
h
h
NVh
AM
v
h/b
h
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N
V
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A
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N/A
h
M
Vh/M
v
v
v
v
N A v
v
v
h
h
h
h
v
v
v
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T
v
h
h
h
T
h
v
h
h
h
v
v
T
h
T
h
f
h
h
T
v
v
v
v
v
v y
v
v
v
v
v
v
v
v
v
y
y
A
s
T
x y
f
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SABS 0100-1
Ed. 2.2
A
A
f
x
partitions for beams of span up to 10 m (see 3.2.3.2). For cantilevers, add or subtract, as appropriate,
the support rotation times the cantilever span.
y
s f
Table 10 Basic span/effective
depth ratios for rectangular beams
A
1
2
Support conditions
Ratio
Truly simply supported beams
Simply supported beams with nominally restrained ends
Beams with one end continuous
Beams with both ends continuous
Cantilevers
16
20
24
28
7
A
f
f
s
4.3.6.2.2 Table 10 may be used for spans exceeding 10 m but only when it is not necessary to limit
the increase in deflection after the construction of partitions and finishes. Otherwise, in order to prevent
damage to finishes and partitions, the values given in table 10 should be multiplied by 10/span, except
for cantilevers, where the design should be justified by calculation.
x
y
4.3.6.3 Modification of span/effective depth ratios for reinforcement
s
4.3.6.3.1 Tension reinforcement
x y
|
|
Since deflection is influenced by the amount of tension reinforcement and its stresses, it is necessary
to modify the span/effective depth ratios according to the ultimate design moment and the service
stress at the centre of the span (or at the support in the case of a cantilever). Therefore, values of
span/effective depth ratio obtained from table 10 should be multiplied by the appropriate factor
Amdt 1, Apr. 1994
obtained from table 11.
v
36
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f
f x
x
A
A
x
f
f
A
A
f
f
M
bd
M
b
d
f
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SABS 0100-1
Ed. 2.2
4.4 Solid slabs
4.4.1 Design of solid slabs
In general, the recommendations given in 4.3 for beams will apply also to solid slabs, but take 4.4.2
to 4.4.7 into account.
As
bd
4.4.2 Moments and forces in solid slabs
4.4.2.1 General
In solid slabs, the moments and shear forces resulting from both distributed and concentrated loads
may be found as for beams. They may also be determined by elastic analyses such as those of
Pigeaud and Westergaard. Alternatively, Johansen's yield-line method or Hillerborg's strip method may
be used, provided that the ratios between support and span moments are similar to those obtained by
the use of the elastic theory. Values in the range 1,0 to 1,5 are recommended.
4.4.2.2 Resistance moments of solid slabs
The ultimate moment of resistance of a cross-section in a solid slab may be determined by using the
methods given in 4.3.3 for beams.
4.4.2.3 Simplification of load arrangements
A
A continuous slab will be able to withstand the most unfavourable arrangements of design loads if it
is designed to resist the moments and forces arising from the single-load case of maximum design
load on all spans. The following conditions are to be met:
a)
in a one-way spanning slab, the area of each bay exceeds 30 m2.
NOTE In this context, a bay is a strip across the full width of a structure and supported on two sides (see figure 7).
Figure 7 — Definition of panels and bays
40
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SABS 0100-1
Ed. 2.2
b)
the ratio of the characteristic imposed load to the characteristic self-weight load does not exceed
1,25.
c)
the characteristic imposed load does not exceed 5 kN/m2, excluding partitions.
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SABS 0100-1
Ed. 2.2
When analysis is carried out for the single-load case of maximum design load on all spans, the
resulting support moments, except those at the support of cantilevers, should be reduced by 20 %, with
a resultant increase in the span moments (see 4.2.4). When a span is adjacent to a cantilever of length
exceeding one-third of the span of the slab, the other possibility of loading arrangement should be
considered, i.e. the case of slab unloaded and the cantilever loaded.
d)
steel curtailment complies with the simplified rules for curtailment given in 4.11.7.3.
4.4.2.4 Distribution of concentrated loads on slabs
If a slab is simply supported on two opposite edges and carries one or more concentrated loads in a
line in the direction of the span, the maximum bending moments may be assumed to be resisted by
an effective width of slab (measured parallel to the supports), given below.
4.4.2.4.1 For solid slabs, the effective width may be taken as the sum of the load width plus
2,4x(1- x/l) where x is the distance from the nearer support to the section under consideration and l is
the span. For cantilever slabs the equivalent value is 2,4x.
4.4.2.4.2 For slabs other than solid slabs, the effective width will depend on the ratio of the transverse
and longitudinal flexural rigidities of the slab. The minimum value to be taken, however, is the load
width plus 4 x/l (1- x/l) metres where x and l are as defined in 4.4.2.4.1, such that, for a section at
mid-span, the effective width is equal to 1 m plus the load width.
4.4.2.4.3 Where the concentrated load is near an unsupported edge of a slab, the effective width
should not exceed the value given in 4.4.2.4.1 or 4.4.2.4.2, as appropriate, nor half that value plus the
distance of the centre of the load from the unsupported edge (see figure 8).
Figure 8 — Effective width of solid slab carrying a concentrated
load near an unsupported edge
4.4.3 One-way spanning slabs of approximately equal span
Where the length of the longer side of a slab exceeds three times the length of the shorter side, so
design the slab as to span one way only.
When the conditions of 4.4.2.3 are met, the moments and shears in continuous one-way spanning
slabs may be calculated using the coefficients given in table 13.
Table 13 Ultimate bending moments and shear forces in one-way spanning slabs
1
2
3
Position
Moment
Shear
At outer support
Near middle of end span
At first interior support
0
0,086 Fl
-0,086 Fl
0,4F
0,6F
At middle of interior spans
At interior supports
0,063 Fl
-0,063 Fl
0,5F
NOTE F is the total ultimate load (1,2Gn + 1,6Qn).
Allowance has been made in these coefficients for 20 % redistribution. No further redistribution should
be carried out. (See also 4.2.4 (d).)
41
42
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SABS 0100-1
Ed. 2.2
Table 14 Bending moment coefficients
for slabs spanning in two directions
at right angles, simply supported on four sides
M
M
l
M
l
2
M
l
l
1
2
ly
lx
sx
3
sy
1,0
1,1
1,2
0,045
0,061
0,071
0,045
0,038
0,031
1,3
1,4
1,5
0,080
0,087
0,092
0,027
0,023
0,020
1,6
1,7
1,8
0,097
0,100
0,102
0,017
0,015
0,016
1,9
2,0
2,5
3,0
0,103
0,104
0,108
0,111
0,016
0,016
0,016
0,017
4.4.4.2 Restrained slabs
n
g
q
l
Both in continuous and in discontinuous slabs where the corners are prevented from lifting and
provision for torsion is made, the maximum moments per unit width are given by the following
equations:
l
l
l
nl2x
(3)
nl2x
(4)
Msx =
sx
Msy =
sy
where
Msx, Msy
are the maximum bending moments at mid-span on strips of unit width spanning lx and
ly, respectively;
n
is the total ultimate load per unit area (1,2 gn + 1,6 qn);
lx
is the length of shorter side;
is the length of larger side; and
ly
sx
,
sy
are the bending moment coefficients given in table 15.
44
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
Table 15 Bending moment coefficients for rectangular panels
supported on four sides with provision for torsional reinforcement
at the corners
1
2
3
4
5
6
Short-span coefficients
Case
Type of panel and
moments considered
7
8
9
sx
Values of ly/lx
10
Long-span
coefficients, sy
for all values of
ly/lx
1,0
1,1
1,2
1,3
1,4
1,5
1,75
2,0
1
Interior panels
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,031
0,024
0,037
0,028
0,042
0,032
0,046
0,036
0,050
0,039
0,053
0,041
0,059
0,045
0,063
0,049
0,032
0,024
2
One short edge discontinuous
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,039
0,029
0,044
0,033
0,048
0,036
0,052
0,039
0,055
0,041
0,058
0,043
0,063
0,047
0,067
0,050
0,037
0,028
3
One long edge discontinuous
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,039
0,030
0,049
0,036
0,056
0,042
0,062
0,047
0,068
0,051
0,073
0,055
0,082
0,062
0,089
0,067
0,037
0,028
Two adjacent edges
discontinuous
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,047
0,036
0,056
0,042
0,063
0,047
0,069
0,051
0,074
0,055
0,078
0,059
0,087
0,065
0,092
0,070
0,045
0,034
5
Two short edges discontinuous
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,046
0,034
0,050
0,038
0,054
0,040
0,057
0,043
0,060
0,045
0,062
0,045
0,067
0,047
0,070
0,053
0,034
6
Two long edges discontinuous
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,034
0,046
0,056
0,065
0,072
0,078
0,091
0,100
0,045
0,034
Three edges discontinuous (one
long edge continuous)
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,057
0,043
0,065
0,048
0,071
0,053
0,076
0,057
0,080
0,060
0,084
0,063
0,092
0,069
0,098
0,074
0,044
8
Three edges discontinuous (one
short edge continuous)
Negative moment at continuous
edge . . . . . . . . . . . . . . . . . . . . . .
Positive moment at mid-span . . .
0,042
0,054
0,063
0,071
0,078
0,084
0,096
0,105
0,058
0,044
9
Four edges discontinuous
Positive moment at mid-span . . .
0,055
0,065
0,074
0,081
0,087
0,092
0,103
0,111
0,056
4
7
Figure 9 — Division of slab into middle and edge strips
Where these equations are used, the conditions given below apply.
4.4.4.2.1 In the case of continuous slabs
The nominal self-weight and imposed loads on adjacent slabs should be approximately the same as
those on the slab under consideration, and the spans of all adjacent slabs should be approximately the
same in each of the two directions of the lines of the supports. (See also 4.4.4.2.2.)
a) tension reinforcement at mid-span: extend at least 50 % of the tension reinforcement provided
at mid-span in the middle strip in the lower part of the slab to within 0,15l of the continuous edge
axis, and to within 50 mm of the discontinuous edge axis; extend the remaining part of the
reinforcement to within 0,25l of a continuous edge axis, and to within 0,15l of the discontinuous
edge axis;
b) tension reinforcement over the continuous edges: extend at least 50 % of the tension
reinforcement provided in the upper part of a middle strip to a distance 0,3l from the face of the
support; extend the remaining part of the reinforcement to a distance of 0,15l from the face of the
support;
c) tension reinforcement over the discontinuous edge: at a discontinuous edge, negative
moments may arise, depending on the degree of fixity of the edge of the slab; in general, tension
reinforcement equal to 50 % of that provided at mid-span extending 0,1l into the span (from the
face of the support) will be sufficient;
d) tension reinforcement in an edge strip, parallel to the edge: the reinforcement need not exceed
the minimum given in 4.11.4 and the minimum given in the rules for torsional reinforcement given
in (e), (f) and (g) below;
e) torsional reinforcement at any corner where the slab is simply supported on both edges
meeting at that corner: the reinforcement should comprise top and bottom reinforcement, each
with layers of bars placed parallel to the sides of the slab and extending from the external faces of
the edges a minimum distance of one-fifth of the shorter span; the area of reinforcement in each
of these four layers should be three-quarters of the area required for the maximum mid-span
moment in the slab;
4.4.4.2.2 In the case of continuous and discontinuous slabs
f) torsional reinforcement at any corner contained by edges over only one of which the slab
is continuous: reinforcement equal to half of that described in (e) above should be provided;
Regard slabs as divided in each direction into middle strips and edge strips as shown in figure 9, the
middle strip being three-quarters of the width and each edge strip one-eighth of the width;
g) torsional reinforcement need not be provided at any corner contained by edges over both
of which the slab is continuous: where ly /lx exceeds 3, so design slabs as to span one way only.
The maximum moments calculated as in 4.4.4.2 apply to the middle strips only and no redistribution
is permitted.
45
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SABS 0100-1
Ed. 2.2
4.4.4.2.3 In the case of a restrained slab with unequal conditions at adjacent panels
If the support moments for adjacent panels (calculated using table 15) differ significantly, they may
be adjusted as follows:
a) calculate the sum of the moments at mid-span and supports (ignoring signs);
b) treat the values from table 15 as fixed end moments;
c) distribute these fixed end moments across the supports according to the relative stiffness of
adjacent spans, giving new support moments;
d) adjust the mid-span moment; this should be such that when it is added to the support moments as
in (c) above (ignoring signs), the total should equal that obtained in (a) above;
if, for a given panel, the resulting support moments now significantly exceed the values given by
equations (3) and (4), the tension steel over the supports will need to be extended beyond the
provisions of 4.11.7.3. The procedure is as follows:
1) the span moment is taken as parabolic between supports; its maximum value is as found in (d)
above;
2) the points of contraflexure of the new support moments (as in (c) above) and the span moment
(as in (1) above) are determined;
3) at each end, half the support tension steel is extended to at least an effective depth or 12 bar
diameters beyond the nearest point of contraflexure; and
v
v
4) at each end, the full area of the support tension steel is extended to half the distance obtained
in (3) above.
4.4.4.3 Loads on supporting beams
f
v
The design loads on beams supporting solid slabs spanning in two directions at right angles and
supporting uniformly distributed loads may be assumed to be in accordance with figure 10. If the edges
of two slabs having the same support meet at a corner, the dividing angle is 45 If a fully restrained
edge meets a freely supported edge, the dividing angle on the restrained side is 60 . With partial
restraint, the angles may be assumed to lie between 45 and 60
igure 10(b)).
v
V
bd
v
V
b
d
v
v
v
v
v
47
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SABS 0100-1
Ed. 2.2
The enhancement in design shear strength close to supports (as described in 4.3.4.2) may also be
applied to solid slabs.
4.4.5.2 Shear stresses in solid slabs under concentrated load
4.4.5.2.1 The following terms specific to perimeters are used in this subclause:
a) perimeter: a boundary of the smallest rectangle (or square) that can be drawn around a loaded
area and that nowhere comes closer to the edges of the loaded area than some specified distance
lp (a multiple of 0,75d) (see figure 11).
NOTE See 4.4.5.2.8 for loading close to a free edge.
b) failure zone: an area of slab bounded by perimeters 1,5d apart (see figure 12);
c) effective length of a perimeter: the length of the perimeter reduced, where appropriate, for the
effects of openings or external edges;
d) effective depth d: the average effective depth for all effective reinforcement passing through a
perimeter; and
e) effective steel area: the total area of all tension reinforcement that passes through a zone and that
extends at least one effective depth (see above) or 12 times the bar size beyond the zone on either
side.
NOTE The reinforcement percentage used to calculate the design ultimate shear stress vc is given by:
100 x effective steel area
ud
where
u is the outer perimeter of zone concerned; and
d is the effective depth (as defined above).
v
f
v
V
u d
V
u
d
d
v
49
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SABS 0100-1
Ed. 2.2
d
Equations 7(a) and 7(b) should not be applied where the shear stress v exceeds 2vc.
Where v>2vc and a reinforcing system is provided to increase the shear resistance, justification should
be provided to demonstrate the validity of the design.
In the above equations:
d
d
d
Asv
is the area of shear reinforcement;
fyv
is the characteristic strength of shear reinforcement (but not exceeding 450 MPa);
u
is the effective length of the outer perimeter of the zone;
d
is the effective depth of slab; and
v - vc > 0,4 MPa.
v
V
ud
v
V d
u
v
v
A bd
A
b
v
d
d v
v
A
v
v
v
v ud
a
v
v
f
v
A
v
d/a
v
v
v
v ud
f
52
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
|
4.4.5.2.7 When openings in slabs and footings (see figure 13) are located at a distance of less than
six times the thickness of the slab from the edge of a concentrated load or reaction, then that part of
the periphery of the critical section that is enclosed by radial projections of the openings to the centroid
of the loaded area is to be considered ineffective.
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Figure 13 — Openings in slabs
Where an opening is adjacent to the loaded area and its greatest width is less than the lesser of onequarter of the loaded area side or one-half of the slab depth, its presence may be ignored.
|
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|
|
4.4.5.2.8 Where a concentrated load is located close to a free edge, the effective length of a
perimeter should be taken as the lesser of the two illustrated in figure 14. The same principle may be
adopted for corner columns.
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Amdt 1, Apr. 1994
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NOTE – d is the average effective depth for all effective reinforcement passing through a perimeter.
Figure 14 — Shear perimeters with loads close to free edge
Figure 12 — Punching shear zones
53
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
containing permanent blocks;
4.4.6 Deflection of solid slabs
d) the greater of 50 mm or one-tenth of the clear distance between the ribs, for all other slabs without
permanent blocks.
Deflections may be calculated and compared with the serviceability provisions given in 3.2.3.2 but,
in all normal cases, it will be sufficient to restrict the span/effective depth ratio. The appropriate ratio
for a solid slab may be obtained from table 10, modified by tables 11 and 12. The reinforcement at the
middle of the span in the width of the slab under consideration should be considered to influence
deflection.
4.5.1.3 Size, spacing and position of ribs
The minimum width of ribs, whether they are rectangular or tapered, should be at least 65 mm and
their depth, excluding any topping, should not exceed four times their width.
In the case of a two-way spanning slab, the ratio should be based on the shorter span and its amount
of reinforcement in that direction.
In-situ ribs should be spaced at centres not exceeding 1,5 m and the edge rib that bears along its
length on a beam or wall shall be at least as wide as the bearing, i.e. the block or void shall not be on
the bearing.
4.4.7 Crack control in solid slabs
In general, compliance with the reinforcement spacing rules given in 4.11.8 will be an acceptable
method of controlling flexural cracking in slabs but, in certain cases, advantage may be gained from
calculating crack widths (see annex A) and comparing them with the recommended values given in
clause 3.
4.5.1.4 Hollow blocks and formers
4.5.1.4.1 Blocks and formers may be of any suitable material but, when required to contribute to the
structural strength of a slab, they should be made of
4.5 Ribbed slabs (with solid or hollow blocks or with voids)
a) concrete or burnt clay and have a crushing strength of at least 14 MPa measured on the net section
when axially loaded in the direction of compressive stress in the slab, or
4.5.1 General
|
4.5.1.1 Construction
This subclause refers to in-situ slabs constructed in one of the following ways:
a) where topping is considered to contribute to structural strength:
1) as a series of concrete ribs cast in situ between blocks that remain part of the completed
structure; the tops of the ribs are connected by a topping of concrete of the same strength as that
used in the ribs;
2) as a series of concrete ribs with topping cast on forms that may be removed after the concrete
has set;
3) with a continuous top and bottom face but containing voids of rectangular, oval or other shape.
b) where topping is not considered to contribute to structural strength: as a series of concrete
ribs cast in-situ between blocks that remain part of the completed structure; the tops of the ribs may
be connected by a topping of concrete but not necessarily of the same strength as that used in the
ribs.
4.5.1.2 Thickness of topping
When a topping is used to contribute to the structural strength, ensure that its thickness, after any
necessary allowance has been made for wear, is at least
a) 30 mm for slabs that have permanent blocks as described in 4.5.1.4 and have a clear distance of
not more than 500 mm between the ribs;
b) 25 mm for slabs as in (a) above but with each row of blocks jointed in mortar having a cement-sand
mixture not weaker than 1:3, or having a cube strength of 11 MPa;
b) fired briquettes, clay or shale.
Amdt 1, Apr. 1994
4.5.1.4.2 When a slab is constructed in accordance with 4.5.1.2(a) but the topping is not used to
contribute to structural strength, the blocks should comply with 4.5.1.4.1(a) or (b). In addition, the
thickness of the block material above its void shall be the greater of at least 20 mm or one-tenth of the
clear distance between the ribs. The overall thickness of the block and topping (if any) should be not
less than one-fifth of the clear distance between the ribs.
4.5.2 Analysis of structure
The moments and forces due to ultimate loads on continuous slabs may be obtained by any of the
methods given in 4.4.2 for solid slabs. Alternatively, the slabs may be designed as a series of simply
supported spans, provided that they will not be exposed to weather or corrosive conditions. Wide
cracks may develop at the supports and the engineer shall satisfy himself that these will not impair
finishes or lead to corrosion of the reinforcement.
Rules for the arrangement of reinforcement are given in 4.5.6.
4.5.3 Moments of resistance
The methods given in 4.3.3 for determining the ultimate moment of resistance of beams may be used.
When sections are being analysed, the stresses in burnt clay blocks in the compression zone may be
taken as 0,25 times the strength as determined in 4.5.1.4.1(a). However, when evidence is available
to show that not more than 5 % of the blocks have a strength below a specified crushing strength, the
stress may be taken as 0,3 times that strength.
4.5.4 Shear
In one-way or two-way spanning slabs, the design shear stress v should be calculated from the
following equation:
c) the greater of 40 mm or one-tenth of the clear distance between the ribs, for all other slabs
55
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SABS 0100-1
Ed. 2.2
v
If a slab has been designed as simply supported but is continuous over supports, the reinforcement
provided in the top of the slab should be at least one-quarter of that required in the middle of adjoining
spans. This reinforcement shall extend by at least one-tenth of the clear span into adjoining spans.
V
b d
4.5.6.2.2 A single layer of mesh should be provided in the topping of all ribbed and hollow block slabs.
The mesh should have a cross-sectional area in each direction of at least 0,12 % of the topping. The
spacing of wires should not exceed half the centre-to-centre distance between ribs.
V
4.5.7 Cover to reinforcement
b
The side cover to reinforcement in slabs that have permanent blocks shall be at least 10 mm .
Similarly, for slabs that have slip tiles under the ribs at least 10 mm thick, the cover to the bars shall
be at least 10 mm above the tiles. In all other cases, provide cover in accordance with 4.11.2.
d
b
4.6 Flat slabs
b
4.6.1 General
b
4.6.1.1 Construction
b
v
v
v
A flat slab is a reinforced concrete slab with or without drops and supported, generally without beams,
by a rectangular arrangement of columns with or without flared column heads (see figure 15). A flat
slab may be solid or may have recesses formed on the soffit such that the soffit comprises a series
of ribs in two directions.
v
v
v
A panel is the area within the lines joining the centres of the columns.
f
4.6.1.2 Symbols
For the purposes of 4.6.1 to 4.6.5 (inclusive), the following symbols apply:
d
I
l1
panel length, measured from centres of columns, in direction of span under consideration
l2
panel width, measured from centres of columns at right angles to direction of span under
consideration
lm
average of l1 and l2
hc
diameter of column or of column head (see figure 15) (which shall be taken as the diameter of a
circle of the same area as the cross-section of the head (see 4.6.1.3))
n
total ultimate load per unit area of panel (1,2gn + 1,6qn)
58
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.6.1.3 Column heads
Ensure that where column heads are provided, the heads of interior columns and such portions of the
heads of exterior columns as will lie within the structure, meet with the following conditions:
a)
the angle of greatest slope of the head, for the purposes of analysis, does not exceed 45 from
the vertical; and
b)
the diameter of the column head hc is taken as its diameter measured at a distance of 40 mm
below the soffit of the slab (or the soffit of the drop, where provided), as shown in figure 15, but
does not exceed 0,25lm.
4.6.1.4 Division of panels
Flat slab panels should be assumed to be divided into column strips and middle strips (see figure 16),
as follows:
a)
take the width of the column strip as one-half of the width of the panel, except that where drops
are used, the width may be taken as the width of the drop; and
b)
take the width of the middle strip as the difference between the width of the panel and that of the
column strip.
Drops should be ignored if their smaller dimension is less than one-third of the shorter span of the
surrounding panels. Smaller drops may still be taken into account in assessing the resistance to
punching shear.
In the case of unalike panels: if there is a support common to two panels that are of such dimensions
that the strips in one panel do not match those in the other, the division of the panels over the region
of the common support should be taken as that calculated for the panel giving the wider column strip.
4.6.1.5 Thickness of panels
The thickness of the slab will generally be controlled by considerations of deflection (see 4.6.3). In no
case, however, should the thickness of the slab be less than 125 mm.
The minimum thickness required when shear reinforcement is provided, is 150 mm.
Figure 15 — Types of column heads
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.6.1.6 Openings in panels
Openings, excluding those that comply with the conditions given in 4.6.1.6.1 to 4.6.1.6.3, shall be
completely framed on all sides by beams that carry the loads to the columns, and an opening shall not
encroach upon a column head. (But see also 4.4.5.2.)
4.6.1.6.1 Openings in the area common to two intersecting middle strips
The greatest dimension in a direction parallel to a centre-line of the panel should not exceed 0,4l, and
the total positive and negative moments specified in 4.6.5.1 or 4.6.5.2 should be redistributed between
the remaining principle design sections to meet the changed conditions.
4.6.1.6.2 Openings in the area common to two column strips
Aggregate length and aggregate width should not exceed one-tenth of the width of the column strip;
the reduced sections should be capable of resisting the appropriate moments specified in 4.6.5.1 or
4.6.5.2, and the perimeter for calculating shear stress should be reduced as appropriate (see 4.4.5.2).
4.6.1.6.3 Openings in the area common to one column strip and one middle strip
Aggregate length and aggregate width should not exceed one-quarter of the width of the column strip,
and the reduced sections should be capable of resisting the appropriate moments specified in 4.6.5.1
or 4.6.5.2.
4.6.2 Shear in flat slabs
4.6.2.1 General
|
|
Punching shear around the columns is the critical consideration for shear in flat slab structures. The
design effective shear force should be found in the subclauses given below and then the procedure
given in 4.4.5.2 should be followed. For flat slabs between 150 mm and 200 mm thick, the allowable
stress in the shear reinforcement should be reduced from the full value at 200 mm of thickness to zero
at 150 mm of thickness, with intermediate values being interpolated linearly. Edges of the drop should
be considered the consecutive perimeter on which the shear stress is to be checked (see figure 17).
Amdt 1, Apr. 1994
If the ratio of spans exceeds 2, specialist literature should be consulted.
Figure 16 — Division of flat slab panels into columns and middle strips
Figure 17 — Sections of shear check for flat slabs with drops
61
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SABS 0100-1
Ed. 2.2
V
V
V
V
V
M
V
V
V x
V
V
V
M
x
M
V
V
Figure 18 — Shear at slab internal column connection
V
V
V
V
V
63
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V
V
M
V
V M
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Vx
x
M
l
f
G
Q
G
Q
G
Q
h
n l
l
h
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
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SABS 0100-1
Ed. 2.2
EI/l
Table 17 Distribution of moments in panels
of flat slabs designed as continuous frames
EI/l
1
Moments
Negative
Positive
2
3
Apportionment between column
and middle strips expressed as a
percentage of the total negative or
positive moment*)
Column strips
Middle strip
75
55
25
45
)
Fl
Fl
F
F
Fl
F
Fl
F
Fl
* Where the column strip is taken as equal to the width of
the drop, and the middle strip is thereby increased in
width to a value exceeding half the width of the panel,
increase the moments to be resisted by the middle strip
in proportion to its increased width. The moments to be
resisted by the column strip may then be decreased by
an amount such that there is no reduction in either the
total positive or the total negative moments resisted by
the column strip and middle strip together.
Fl
Fl
Fl
Fl
F
G
l
l
Q
4.6.5.3.2 Design moments transferable between a slab and the edge or corner columns will only be
able to be transferred by a column strip considerably narrower than in the case of an internal column.
The breadth of this strip be for various typical cases is shown in figure 19. The value of be should never
be taken as exceeding the column strip width appropriate for an internal panel. The maximum design
moment Mt,max that can be transferred to a column by the appropriate strip may be calculated from the
following equation:
Mt,max = 0,15 be d 2 fcu
h
where
be is the breadth of strip;
d is the effective depth for the top reinforcement in the column strip; and
fcu is the characteristic strength of concrete.
The value of Mt,max should exceed half the design moment obtained from an equivalent frame analysis
or it should exceed 70 % of the design moment if a grillage or finite element analysis has been used.
If the value of Mt,max is less than this, the structural arrangements should be changed.
68
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SABS 0100-1
Ed. 2.2
EI/l
EI/l
l
A
A
a
b
Figure 19 — Definition of breadth of effective moment transfer
strip be for various typical cases
h
d
4.6.5.3.3 Where analysis of the structure indicates a design column moment that exceeds Mt,max, the
design edge moment in the slab should be reduced to a value not exceeding Mt,max and the positive
design moments in the span should be adjusted accordingly. The normal limitations on redistributions
and neutral axis depth may be ignored in this case. Moments in excess of Mt,max may only be
transferred to a column if an edge beam or strip of slab along the free edge is so reinforced as to carry
the extra moment into the column by torsion. In the absence of an edge beam, an appropriate breadth
of slab may be assessed using the principles illustrated by figure 19. Alternatively, the method of
taking the stiffness of edge columns into account may be used.
d
e
f
f
m
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SABS 0100-1
Ed. 2.2
4.7.1.2.3 If a column has a large enough section to withstand the design maximum loads without the
addition of reinforcement, it may be designed in the same way as a plain concrete wall (see 6.5).
h
I
4.7.1.3 Braced and unbraced columns
l
A column may be considered braced in a given plane if lateral stability to the structure as a whole is
provided by walls, bracing or buttressing designed to resist all lateral forces in that plane. It should
otherwise be considered unbraced. If the degree of lateral restraint is in doubt, the stiffness of the
bracing system should be evaluated from the ratio Sb/Su. If the ratio exceeds 5, the frame can be
considered fully braced.
l
M
M
4.7.1.4 Short and slender columns
M
A column may be considered slender in a particular plane if its slenderness ratio in that plane (lex/h or
ley/b) exceeds 10 for unbraced columns and 17-7M1/M2 for braced columns. It should otherwise be
considered short. It is therefore possible that a column may be slender in one plane and short in the
other plane and it should be treated accordingly.
M
M
4.7.1.5 Slenderness limits for columns
M
Generally, the clear height lo should satisfy the following:
M
lo < 60b and b > 0,25h (see also note to 4.7.1)
M
If, in any given plane, one end of an unbraced column is unrestrained (e.g. a cantilever column), its
clear height lo should satisfy the following:
M
lo < 25b and b > 0,25h (see also note to 4.7.1)
M
For unbraced columns, the considerations of deflection (see 4.7.5) may introduce further limitations.
M
f A
d d
4.7.1.6 Effective height of a column
f bd
4.7.1.6.1 Effective height of a column: general method
N
The effective height le of a column in a given plane may be obtained from the following equation:
N
f bd
N
n
S
S
le = lo
Values of are given in tables 18 and 19 (for braced and unbraced columns, respectively) as a
function of the end conditions of the column. Figure 20 may be used to obtain an approximate
assessment of the effective height, if desired. It should be noted that the effective height of a column
in the two plane directions may be different.
In tables 18 and 19, the end conditions are defined in terms of a scale of 1 to 4. An increase in this
scale corresponds to a decrease in end fixity. An appropriate value can be assessed from the following
four end conditions:
a) end condition 1: the end of the column is connected monolithically to beams on either side that
are at least as deep as the overall dimension of the column in the plane under consideration. Where
the column is connected to a foundation structure, this should be of a form specifically designed to
carry moment.
b) end condition 2: the end of the column is connected monolithically to beams or slabs on either side
that are shallower than the overall dimensions of the column in the plane under consideration.
72
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SABS 0100-1
Ed. 2.2
c) end condition 3: the end of the column is connected to members that, while not specifically
designed to provide restraint to rotation of the column, will nevertheless provide some nominal
restraint.
d) end condition 4: the end of the column is unrestrained against both lateral movement and rotation
(e.g. the free end of a cantilever column in an unbraced structure).
Table 18 Values of
1
End condition
at top
1
2
3
for braced columns
2
3
3
0,75
0,80
0,90
0,80
0,85
0,95
0,90
0,95
1,00
c,min
is the lesser of
c
and
.
c2
The stiffness of a member should be obtained by dividing the second moment of area of its
concrete section by its actual length, which is the distance centre-to-centre of restraints. When c
is being calculated, only elements properly framed into the end of the column in the appropriate
plane of bending should be considered. In cases of relative stiffness, the following simplifying
assumptions may be made:
2) simply supported beams framing into a column:
c
may be taken as 0;
3) connection between column and base design to resist nominal moment only:
taken as 0;
End condition at bottom
2
SABS 0100-1
Ed. 2.2
) flat slab construction: the stiffness of an equivalent beam that has the width and thickness of
the slab forming the column strip should be assumed; (For edge columns, see 4.6.5.3.2.)
4
1
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4) connection between column and base design to resist column moment:
as ,0.
c
c
may be
may be taken
4.7.1.6.3 Columns effective length charts
NOTE Figure 20 should be used only for the purposes of this subclause.
Table 19 Values of
1
End condition
at top
1
2
3
4
for unbraced columns
2
3
In the absence of more detailed information, the recommended practical stiffness ratios at the base
are:
4
= 0 for columns designed as "pinned" at the base; and
=
End condition at bottom
1
2
3
1,2
1,3
1,6
2,2
1,3
1,5
1,8
-
1,6
1,8
-
for columns rigidly connected to the base.
Where ideal conditions prevail, the ratio as above can be obtained as equal to infinity and as zero
respectively but should be justified by analysis.
4.7.1.6.2 Effective height of a column: more rigorous method
It is recommended that calculations be based on I/l for columns and 0,5 times I/l for beams, where I
may be based on the concrete section only and l is the distance between centres of restraints. To
account for different far end conditions of beams, a further factor can be applied to the beam stiffness
as follows:
For a framed structure, effective height may be obtained from the following equations:
Braced column
a) for a braced column, the lesser of
Far end of beam is hinged
Far end of beam is fixed against rotation
le = lo [0,7 + 0,05 ( c1 +
le = lo (0,85 + 0,05
c,min
c2
)] < lo and
Unbraced column
) < lo
Far end of beam is hinged
Far end of beam is fixed against rotation
b) for an unbraced column, the lesser of
le = lo [1,0 + 0,15 ( c1 +
le = lo (2,0 + 0,3
c,min
c2
: ,5
: 2,0
: 0,5
: 0,67
)] and
)
where
is the clear height between end restraints;
lo
is the ratio of sum of column stiffnesses to sum of beam stiffnesses at one end of column;
c1
is the ratio of sum of column stiffnesses to sum of beam stiffnesses at other end of
column; and
c2
73
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l
(EI)i/(EI)
n
l
l
n
n
e
l
l
n
n
i i)
a
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SABS 0100-1
Ed. 2.2
a
If calculations show that the primary moment in one or both planes is less than the nominal eccentricity
moment (see 4.7.2.3), the primary moment in the relevant plane(s) should be based on the eccentricity
moment.
Kh
K
K
N
N
N
N
The critical section is designed to withstand the design ultimate axial load N, plus the total design
moment in either of the two directions.
4.7.3.2.1 Slender braced columns bent uni-axially
K
N
Figure 21 shows the distribution of moments assumed over the height of a typical braced column. It
may be assumed that the initial moment at the point of maximum additional moment (i.e. near
mid-height of the column) is given by:
N
M
K
M
Mi = 0,4 M1 + 0,6 M2
N
f A
f A
where
M1 is the smaller initial end moment due to design ultimate vertical loads; and
M2 is the larger initial end moment due to design ultimate vertical loads.
Assuming the column is bent in double curvature, M1 should be taken as negative and M2 as positive.
If a column is bent in a single curvature, both terms are assumed positive.
l
It can be seen from figure 21 that the maximum design moment will be the greatest of (a), (b) or (c)
below.
a) M2;
b) Mi + Madd; and
c) eminN.
4.7.3.2.2 Slender unbraced columns bent uni-axially
The distribution of moments assumed over the height of an unbraced column is indicated in figure 22.
The additional moment referred to in 4.7.3.1 may be assumed to occur at whichever end of the column
has the stiffer joint (i.e. where the largest primary moment occurs).
K
K
The additional moment is to be based on the unbraced effective length. The additional moment at the
other end of the column may be reduced in proportion to the ratio of the joint stiffness. The moment
will act in a direction such that it increases the absolute magnitude at the critical section. The
maximum design moment for the column will therefore be the greater of (a) and (b) below.
l
h
a) M2 = Mv + MH [1 + Madd,unbr /(Mv + MH)]; or
h
b) 0,6 M2 + 0,4 M1 + Madd, braced
M
where M1 and M2 are the smaller and larger column end moment respectively, after including for the
sway effect as illustrated in figure 22, and Madd, braced from equation (13), using the braced effective
length.
Na
If calculations show that the total primary moments at both ends Mv + MH are less than the nominal
eccentricity moment eminN, MH shall be taken as eminN about each axis separately.
78
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
Figure 22 — Unbraced slender columns — Bending moments chart
4.7.3.3 Additional moments in members attached to a slender column
Where le/h exceeds 10 for unbraced columns and 17-7M1/M2 for braced columns in one or both
principal planes, members monolithically connected to such columns at either end should be designed
to withstand the additional design moments in the plane(s) where the slenderness limits are exceeded,
in addition to those moments calculated using normal analytical methods. Where there are columns
both above and below a joint, the beams or slabs should be designed to withstand the sum of the
additional design moments at the ends of the two columns.
Figure 21 — Braced slender columns — Bending moments chart
79
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N
f A
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A f
M/N
h
f
M h
M h
M b
M b
M
M
M
h
M
b
M
b
M
h
l h
h
M
b
M
M
l
h
f A
M
M
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SABS 0100-1
Ed. 2.2
l
4.8.2.3 Forces in lateral supports
h
4.8.2.3.1 A lateral support is an element (a prop, a buttress, a floor, cross-wall or other vertical or
horizontal element) able to transmit lateral forces from a braced wall to the principal structural bracing
or to the foundations.
4.8.2.3.2 The forces that lateral supports should be able to transmit are assumed to be equal in
magnitude to the sum of the following:
a) the simple static reactions to the sum of the applied maximum design horizontal forces at the point
of lateral support; and
b) 2,5 % of the total maximum design vertical load that the wall or column is designed to carry at the
point of lateral support.
4.8.2.4 Resistance of lateral supports to rotation
Resistance of lateral supports to rotation should only be considered to exist in the following cases:
a) where both the lateral support and the braced wall are concrete walls that are adequately detailed
to provide bending restraint; or
b) where precast or in-situ concrete floors (irrespective of the direction of span) have a bearing on at
least two-thirds of the thickness of the wall, or where there is a connection that provides adequate
bending restraint.
l h
4.8.3 Forces and moments in reinforced concrete walls
4.8.3.1 Axial forces
l
The axial force in a reinforced wall may be calculated on the assumption that the beams and slabs that
transmit force into the wall are simply supported.
4.8.3.2 Design transverse moments
4.8.3.2.1 Design transverse moments, where derived from beams or other constructions designed to
frame monolithically at right angles into the wall, should be calculated using elastic analysis.
4.8.3.2.2 When a construction is designed to be simply supported by a wall, the eccentricity may be
assessed as for plain walls (see 6.5.3.5) and the resultant moment calculated. Except for short-braced
walls (see 4.8.4.1 and 4.8.4.2) that are loaded almost symmetrically, the moment per unit length in the
direction at right angles to a wall should be taken as the greater of 0,05nw x h, or nw x 15 mm, where
nw is the axial load per unit length and h is the thickness of the wall.
4.8.3.2.3 In a slender wall, significant additional moments may be induced by lateral deflections of
the wall under load. To make appropriate allowance for this, such a wall may be considered a slender
column bent about the minor axis (see 4.7.3.2), except that where a wall is reinforced with only one
central layer of reinforcement, the additional moments should be doubled.
4.8.3.3 Design in-plane moments
Moments in the plane of a single wall, due to horizontal forces, can be calculated from statics. When
a horizontal force is resisted by several walls, the proportion allocated to each wall should be
proportional to its stiffness. When a shear connection is assumed between vertical edges of adjacent
walls, an appropriate elastic analysis may be used, provided the shear connection is designed to
withstand the design force.
84
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SABS 0100-1
Ed. 2.2
4.8.4 Short reinforced walls
Short braced axially loaded reinforced walls that by the nature of the structure cannot be subjected
to significant moments, may be designed in the presence of the nominal eccentricity moment by the
following equation:
N < 0,40 fcuAc + 0,67Ascfy
.
At various points along the wall, effects (a) and (b) above are combined and checked, using the
assumptions given in 4.7.4.
The slenderness ratio is the ratio of the effective height of the wall le to its thickness h. The following
limitations of the slenderness ratio shall be observed:
a) in the case of a braced wall reinforced as in 4.11.4 but less than 1 %, the ratio le/h shall not exceed
40;
is the total design axial load on the wall due to maximum design loads;
fcu is the characteristic strength of concrete;
b) in the case of a braced wall reinforced as in 4.11.4 but exceeding 1 %, the ratio le/h sha ll not exceed
45;
Ac is the net cross-sectional area of concrete in wall;
Asc is the area of vertical reinforcement; and
fy
b) transverse moments: the transverse moments are calculated (see 4.8.3.2).
4.8.5.2 Limits of slenderness
m
where
N
SABS 0100-1
Ed. 2.2
a) in-plane moments and axial forces: the distribution of force along the wall is calculated by elastic
analysis, assuming no tension in the concrete (see 4.8.3.3);
4.8.4.1 Short braced axially loaded reinforced walls
NOTE This includes an allowance for
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c) in the case of an unbraced wall reinforced as in 4.11.4, the ratio le/h shall not exceed 30.
is the characteristic strength of compression reinforcement.
4.8.6 Deflection of reinforced walls
4.8.4.2 Walls subjected to transverse moments and to uniformly distributed axial forces
When the only eccentricity of force derives from the transverse moments, the design axial load may
be assumed to be distributed uniformly along the length of the wall. The cross-section of the wall
should be designed to resist the appropriate design ultimate axial load and transverse moment. The
assumptions made in the analysis of beam sections apply (see 4.3.3).
4.8.4.3 Walls subjected to in-plane moments and to axial forces
The cross-section of the wall should be designed by application of the assumptions given in 4.3.3.
4.8.4.4 Walls subjected to axial forces and to significant transverse and in-plane moments
The deflection of a reinforced concrete wall will be within reasonable limits if the preceding provisions
are followed and if, in the case of a cantilever shear wall, the total height of the wall does not exceed
12 times its length.
4.8.7 Crack control in reinforced walls
Cracks in a reinforced concrete wall will be within reasonable limits if the reinforcement is arranged
in two layers and each layer complies with the bar spacing rules given in 4.11.8.2.
4.9 Staircases
4.9.1 General
The assessment of the effects should comprise three stages, as follows:
a) in-plane moments and axial forces: the distribution of force along the wall is calculated by elastic
analysis, assuming no tension in the concrete (see 4.8.3.3);
b) transverse moments: the transverse moments are calculated (see 4.8.3.2).
At various points along the wall, effects (a) and (b) above are combined and checked, using the
assumptions given in 4.3.3.
4.8.5 Slender reinforced walls
4.9.1.1 Distribution of loading
4.9.1.1.1 Assume the ultimate load to be uniformly distributed over the plan area of the staircase.
When, however, staircases surrounding open wells include two spans that intersect at right angles, the
load on the areas common to both spans may be assumed to be divided equally between the two
spans.
4.9.1.1.2 When staircases or landings that span in the direction of the flight are built at least 110 mm
into walls along part or all of their length, a 150 mm strip adjacent to the wall may be deducted from
the loaded area.
4.8.5.1 Design procedure
4.9.1.2 Effective width of staircases
The assessment of the effects should comprise three stages, as follows:
Take the effective width of a staircase without stringer beams as the actual width of the staircase.
When a staircase is built into a wall along part or all of its span, include two-thirds of the embedded
width up to a maximum of 80 mm, in the effective width.
85
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SABS 0100-1
Ed. 2.2
4.9.1.3 Effective span of staircases
4.9.1.3.1 When a staircase without stringer beams is built monolithically at its ends into structural
elements spanning at right angles to the span of the staircase, take the effective span as the sum of
the clear horizontal distance between the supporting elements plus half the widths of the supporting
elements, subject to maximum additions of 900 mm at both ends.
4.9.1.3.2 When a staircase without stringer beams is simply supported, take the effective span as the
horizontal distance between the centre-lines of the supports.
4.9.1.3.3 For the purposes of this subclause, a staircase may be taken to include a section of landing
spanning in the same direction and continuous with the stair flight.
4.9.1.4 Depth of section
Take the depth of the section as the minimum thickness perpendicular to the soffit of the staircase.
4.9.2 Design of staircases
4.9.2.1 Loading
Staircases should be designed to support the ultimate design load in accordance with the load
arrangements given in 3.3.3.1.
4.9.2.2 Strength, deflection and crack control
A
The provisions given in 4.3 and 4.4 for beams and slabs may be used except for the span/effective
depth ratio of a staircase without stringer beams, where 4.9.2.3 applies.
A
4.9.2.3 Permissible span/effective depth ratio for staircases without stringer beams
Provided the stair flight occupies at least 60 % of the span, the ratio calculated in accordance with
4.3.6.2 may be increased by 15 %.
4.10 Bases
l
l
c
d
c
4.10.1 General
d
d
l
This subclause covers the design of pad footings and pile caps.
4.10.2 Moments and forces in bases
4.10.2.1 Except where the reactions to the applied design ultimate loads and moments are derived
by more accurate methods, e.g. an elastic analysis of a pile group or the application of established
principles of soil mechanics, make the following assumptions:
a) when the base is axially loaded, assume the reactions to ultimate design loads to be uniformly
distributed per unit area or per pile; and
b) when the base is eccentrically loaded, assume the reactions to vary linearly across the base or
across the pile system.
4.10.2.2 The critical section for bending moment in the design of an isolated base may be taken at
the face of the column or wall.
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.10.3.4 Bond and anchorage
The provisions given in 4.11.6 apply to reinforcement in bases.
The critical sections for local bond stress are
a) the critical sections described in 4.11.6, and
b) sections at which the depth changes or any reinforcement ends.
4.10.3.5 Limit state of deflection
This limit state may be ignored for bases.
4.10.3.6 Crack control in bases
The provisions given in 4.11.8.2 concerning the maximum distance between bars in tension apply to
bases, but reinforcement need not be provided in the side of bases to control cracking.
4.10.4 Design of pile caps
4.10.4.1 General
Pile caps are designed either by the bending theory or by truss analogy; if the latter is used, the truss
should be of triangulated form, with a node at the centre of the loaded area.
Figure 23 — Critical section of shear check in a pile cap
The lower nodes of the truss lie at the intersections of the centre-lines of the piles with the tensile
reinforcement.
4.10.4.4 Punching shear
4.10.4.2 Shear forces
The design shear stress calculated at the perimeter of the column should not exceed the maximum
value of shear stress (see 4.3.4.1).
The design shear strength of a pile cap is normally determined by the shear along a vertical
cross-section of the full width of the cap. Critical sections for the shear should be assumed to be
located at 20 % of the diameter of the pile inside the face of the pile, as indicated in figure 23. The
whole of the force from the piles with centres lying outside this line should be considered to be applied
outside this line.
In addition, if the spacing of the piles exceeds 3 pile diameters, punching shear should be checked in
accordance with 4.6.2 on a perimeter as indicated in figure 23.
|
The maximum shear capacity may also be limited by the provisions of 4.4.5.2.6.
Amdt 1, Apr. 1994
4.11 Considerations affecting design details
4.10.4.3 Design shear resistance
The design shear resistance of pile caps may be determined in accordance with 4.4.5, subject to the
Amdt 1, Apr. 1994
limitations given below.
|
|
4.10.4.3.1 Where the spacing of the piles is less than or equal to 3 pile diameters, the enhancement
of the shear strength may be applied over the whole of the critical section.
Where the spacing is greater, the enhancement may only be applied to strips of width equal to 3 pile
diameters, centred on each pile. Minimum stirrups are not required in pile caps where v < vc (enhanced
if appropriate).
4.10.4.3.2 The tension reinforcement should be provided with a full anchorage, in accordance with
4.11.6.
4.11.1 Constructional deviations
4.11.1.1 Sizes of elements
When deciding on the nominal overall size of a reinforced concrete element, take account of the
principles of dimensional co-ordination. Bear in mind that absolute accuracy exists only in theory and
that tolerable degrees of inaccuracy have to be accepted in practice. Specify as large a degree of
tolerance as possible, without rendering the finished structure or any part thereof unacceptable for the
purpose for which it is intended.
4.11.1.2 Dimensional tolerance
The partial safety factor for loads will, on a design based on nominal dimensions, provide for all normal
tolerances. However, when large tolerances are being specified for small highly stressed elements,
it may, in exceptional cases, be necessary to base the design on net dimensions after making
allowance for the maximum specified tolerance.
89
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.11.1.3 Tolerance on position of reinforcement
4.11.2 Concrete cover to reinforcement
4.11.1.3.1 In all normal cases, the design may be based on the assumption that the reinforcement is
in its nominal position. However, when reinforcement is located in relation to more than one face of
an element (e.g. a link in a beam in which the nominal cover for all sides is given), the actual concrete
cover on one side may be greater and can be derived from consideration of certain other tolerances
appropriate to
4.11.2.1 Nominal cover is that dimension used in design and indicated on the drawings.
4.11.2.2 Determine the concrete cover to reinforcement by consideration of fire resistance and
durability under the envisaged conditions of exposure.
b) stiffness, straightness, and accuracy of cutting, bending and fixing of bars or reinforcement cage;
4.11.2.3 Cover is not required to the end of a straight bar in a floor or roof unit when the end of the
unit is not exposed to the weather. However, the ends of simply supported beams not directly exposed
to the weather may be liable to condensation with the consequent need to protect the reinforcement
against corrosion. Regard the following as subject to moderate exposure: roofs, balconies, washeddown floors, car parks, or any other construction that, although nominally protected from water, might
become moist as a result of deterioration of finishes or for other reasons.
c) accuracy of formwork in both dimension and plan (this includes permanent forms such as blinding
or brickwork); and
4.11.2.4 Always make the nominal cover at least equal to the diameter of the bar and, in the case of
bundles of three or more bars, equal to the diameter of a single bar of equivalent area.
a) dimensions and spacing of cover blocks, spacers or chairs or both (including the compressibility of
these items and the surfaces they bear on);
d) the size of the structural part and the relative size of the bars or reinforcement cage.
4.11.1.3.2 In certain cases where bars or reinforcement cages are positioned accurately on one face
of a structural element, this may lead to an accumulation of tolerances affecting the position of highly
stressed reinforcement at the opposite face of the element. The consequent possible reduction in
effective depth to this reinforcement may exceed the percentage allowed for in the normal value of
the partial safety factor for loads. In the design of a particularly critical element, therefore, appropriate
adjustment to the effective depth assumed may be necessary.
4.11.1.4 Construction and movement joints
4.11.2.5 Concrete cover to all reinforcement, including links, should be at least equal to the maximum
nominal size of the aggregate.
4.11.2.6 Where a surface treatment (such as bush hammering) cuts into the face of the concrete, add
the expected depth of treatment to the nominal cover.
4.11.2.7 Where, owing to its particular situation, an element is required to resist the action of fire for
a specified period, the nominal cover may need to be increased or, alternatively, the concrete cover
to the main bars may need to be reinforced to prevent premature spalling.
4.11.1.4.1 Construction joints
4.11.2.8 Take special care in conditions of extreme exposure or where low density or porous
aggregates are used. (See the appropriate clause of SABS 0100-2, and 4.12.2.)
The number of construction joints should be kept to the necessary minimum. Their exact location
should be indicated on a drawing or agreed on with the contractor. Generally, construction joints should
be at right angles to the direction of the element.
4.11.2.9 Take account of possible deviations in reinforcement fitting between two concrete faces
(see 4.11.3.2).
The concrete at the joint should be bonded with the concrete subsequently placed against it to such
degree that the load-bearing capacity of the concrete in the area of the joint is not impaired. If it is
necessary for a joint to transfer tensile or shear stresses, the surface of the first pour should be
roughened to increase the bond strength and to provide aggregate interlock. (For details, see
SABS 0100-2.)
4.11.1.4.2 Movement joints
Movement joints are those specifically designed and provided to allow relative movement of adjacent
parts of an element or structure to occur without impairment of the functional integrity of the element
or structure. They may also act as connection joints between several parts of an element or structure,
or they may be provided solely to permit translocation or rotation or both.
Careful consideration should be given to the location of movement joints and their position should be
clearly indicated on the drawings, both for the individual elements and for the structure as a whole. In
general, movement joints in the structure should pass through the whole structure in one plane. If
special preparation of the joint faces is required, this should be specified.
Further information on various types of movement joints is given in annex B.
4.11.2.10 Minimum concrete cover for reinforcement is given in SABS 0100-2. For fire-resistant
covering, see clause 7.
4.11.3 Reinforcement (general considerations)
4.11.3.1 Groups of bars
Bars may be arranged in pairs in contact or in groups of three-bar or four-bar bundles in contact. Each
pair or bundle should be treated as a single bar of equivalent area for all the purposes of clause 4.
Terminate bars in a bundle at different points spaced at least 40 times the bar size apart except for
bundles that stop at a support. Laps may be made to one bar in a bundle at a time. Never, even at
laps, should more than four bars be arranged in contact.
Do not use bundles in an element without links.
4.11.3.2 Bar schedule dimensions
4.11.3.2.1 Schedule bars in accordance with the requirements of SABS 82.
4.11.3.2.2 Where reinforcement is to fit between two concrete faces, determine the dimensions of the
reinforcement on the bending schedule as the nominal dimension of the concrete less the nominal
cover on each face and less the total deduction for tolerance on element size and on bending given
in table 22.
91
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92
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SABS 0100-1
Ed. 2.2
Table 22
ar schedule dimensions: Deductions for tolerance
1
2
Distance between
concrete faces
Type of bar
m
0-1
1-2
Over 2
Any length
3
Total
deduction
mm
Links and other bent bars
Links and other bent bars
Links and other bent bars
Straight bars
10
15
20
40
4.11.3.2.3 These deductions will apply to most reinforced concrete constructions but if the tolerance
on element size for the four categories in table 22 exceeds 5 mm, 5 mm, 10 mm and 10 mm
respectively, make larger deductions or increase the cover.
4.11.4 Minimum areas of reinforcement in elements
4.11.4.1 Symbols
For the purposes of this subclause, the following symbols apply:
Ac
total area of concrete
Acc area of concrete in compression
As
minimum recommended area of reinforcement
Asc area of steel in compression
Ast area of transverse steel in a flange
s bf
b
width of section
bw
width or effective width of the rib (for a box, T-section or I-section, bw is taken as the average
width of the concrete below the flange)
fy
characteristic strength of reinforcement
h
overall depth of the cross-section of a reinforced element
hf
depth of flange
l
span of beam
s
b
93
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A
b
S
A
b
S
A
b
s
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SABS 0100-1
Ed. 2.2
4.11.6.2 Anchorage bond stress
Anchorage bond stress is assumed to be constant over the effective anchorage length. It may be
calculated as the force in the bar divided by its effective surface anchorage area (see 4.11.6.3). It
should not exceed the values for ultimate anchorage bond stress fbu given in table 24. In beams where
minimum links in accordance with 4.3.4 have not been provided, the anchorage bond stresses used
should be those appropriate to plain bars, irrespective of the type of bar provided. This does not apply
to slabs.
Table 24 Ultimate anchorage bond stress fbu
1
2
Bar type
3
4
SABS 0100-1
Ed. 2.2
a) it passes round another bar of at least its own diameter, through an angle of 90 , and continues for
a minimum length of eight times its own diameter; or
b) it passes round another bar of at least its own diameter, through an angle of 180 , and continues
for a minimum length of four times its own diameter.
4.11.6.5 Anchorage of column starter bars in bases
The compression bond stresses that develop on starter bars within bases or pile caps do not need to
be checked, provided that
a) the starters extend to the level of the bottom reinforcement, and
5
b) the base or pile cap has been designed for moments and shears in accordance with 4.10.
Ultimate anchorage bond stress fbu
4.11.6.6 Laps and joints
MPa
Concrete grade
Plain bar in tension
Plain bar in compression
Deformed bar*) in tension
Deformed bar*) in compression
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20
25
30
40 or more
1,2
1,5
2,2
2,7
1,4
1,7
2,5
3,1
1,5
1,9
2,9
3,5
1,9
2,3
3,4
4,2
4.11.6.6.1 General
Connections transferring stress may be lapped, welded, or joined by mechanical devices. They should,
if possible, occur away from points of high stress and should, preferably, be staggered. Do not use
welded joints where the imposed load is predominantly cyclic in nature.
4.11.6.6.2 Minimum laps
*)As defined in SABS 920.
The minimum lap length for bar reinforcement should be at least the greater of 15 times the bar
diameter or 300 mm, and for mesh reinforcement should be at least 250 mm.
NOTE Reduce the values by 30 % for deformed top bars and by 50 % for plain
top bars in elements of depth exceeding 300 mm.
4.11.6.6.3 Design of tension laps
4.11.6.3 Design anchorage bond stress
The design anchorage bond stress is assumed to be constant over the anchorage length and is given
by the following equation:
fb = Fs/
e
a) where a lap occurs at the top of a section as cast and the minimum cover is less than twice the size
of the lapped reinforcement, the lap length should be increased by a factor of 1,4;
l < fbu
where
fb
is the bond stress;
Fs
is the force in bar or group of bars;
l
e
fbu
The lap length for a tension lap should be at least equal to the design tension anchorage length
(see 4.11.6.2). The lap length for bars (or wires in fabric) of unequal diameter may be based upon the
smaller bar (or wire). The following should also apply:
b) where a lap occurs at a corner of a section and the minimum cover to either face is less than twice
the size of the lapped reinforcement or, where the clear distance between adjacent laps is less than
the greater of 75 mm or six times the size of the lapped reinforcement, the lap length should be
increased by a factor of 1,4; and
is the anchorage length;
c) in cases where both preceding conditions apply, the lap length should be increased by a factor of
2,0.
is the effective bar diameter (for a single bar, the actual bar diameter and for a group
of bars in contact, equal to the diameter of a bar of equal total area); and
Values for lap length are given in SABS 0144.
is the ultimate anchorage bond stress given in table 24.
4.11.6.6.4 Design of compression laps
4.11.6.4 Anchorage of links
The lap length for a compression lap should exceed the compression anchorage length (see 4.11.6.3)
by at least 25 %. Lap length for bars (or wires in fabric) of unequal diameter may be based upon the
smaller bar (or wire).
A link may be considered to be fully anchored if it complies with the following:
Values for lap length are given in SABS 0144.
NOTE Values for anchorage lengths are given in SABS 0144.
97
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SABS 0100-1
Ed. 2.2
4.11.6.6.5 Laps in beams and columns with limited cover
Where the diameter of both bars at a lap exceed 20 mm and the cover is less than 1,5 times the
diameter of the smaller bar, transverse links should be provided throughout the lap length. At the lap,
the diameter of the links should be at least one-quarter of the diameter of the smaller bar and the
spacing should not exceed 200 mm.
4.11.6.6.6 Maximum amount of reinforcement in a layer
At laps, the sum of the reinforcement diameters in a particular layer should not exceed 40 % of the
width of the section at that level.
4.11.6.6.7 Joints with compressive bars
Where the stress in a bar at a joint is entirely compressive, the load may be transferred by an end
bearing of square-sawn ends held in concentric contact by a suitable sleeve or mechanical device
(see 6.3.2.3). The concrete cover for the sleeve should be at least that specified for normal
reinforcement.
4.11.6.7 Welded joints in bars
4.11.6.7.1 Welding of cold-worked bars is not permissible.
4.11.6.7.2 Ensure that welded joints do not occur at bends in reinforcement. Where possible, stagger
joints in parallel bars of the principal tensile reinforcement in the longitudinal direction.
NOTE Joints may be considered staggered if the distance between them is not less than the end anchorage length for
the bar. (See also the appropriate clause of SABS 0100-2.)
4.11.6.7.3 Where the strength of the weld has been proved by tests to be at least equal to that of the
parent bar, the strength of joints may be based on 80 % of the specified characteristic strength of the
joined bars for joints in tension and 100 % for joints in compression, divided, in each case, by the
appropriate m factor. However, the strength of welded joints in tension may be based on 100 % of the
specified characteristic strength of the bars if the welding operations are carried out under strict
supervision and if, at any cross-section of the element, not more than 20 % of the tensile
reinforcement is welded.
4.11.6.7.4 In the welds of a lapped joint, take the shear strength of the filler material as 0,38 times its
yield or proof stress. Make the length of weld sufficient to transmit the design load in the bar, i.e. make
the bar cross-sectional area times 0,87 fy equal to the effective length of weld times the throat
thickness times the shear strength of filler material. Ensure that the length of a run of weld does not
exceed five times the diameter of the bar. If a longer length of weld is required, divide it into sections
and make the space between runs at least five times the diameter of the bar.
F
r
f
a
F
r
4.11.6.8 Hooks and bends
4.11.6.8.1 General
f
Reinforcement end anchorages such as hooks and bends should be so formed, dimensioned and
arranged as to avoid overstressing the concrete and should only be used to meet specific design
requirements as specified in SABS 82.
a
a
99
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.11.7 Curtailment and anchorage of reinforcement
4.11.7.2.1 Simply supported beams
4.11.7.1 General recommendations for curtailment and anchorage of bars
Extend at least 50 % of the tension reinforcement provided at midspan to the supports and give it an
effective anchorage of 12 past the centre of the support. Extend the remaining part of the
reinforcement to within 0,08l of the centre of the support.
4.11.7.1.1 In any element subject to bending, extend every bar, except at end supports, beyond the
point at which it is no longer needed, for a distance equal to the greater of the effective depth of the
elements or 12 times the diameter of the bar. A point at which a bar is no longer required is where the
resistance moment of the section, considering only the continuing bars, is equal to the required
moment. In addition, do not stop any bar in a tension zone unless one of the following conditions is
satisfied:
4.11.7.2.2 Cantilever beams
Extend at least 50 % of the tension reinforcement provided at the support to the end of the cantilever.
Extend the remaining part of the reinforcement a distance of the greater of l/2 or 45 times the bar
diameter from the face of the support.
a) the bar extends an anchorage length appropriate to its design strength (0,87 fy) from the point at
which it is no longer required to resist bending; or
4.11.7.2.3 Continuous beams of approximately equal spans under substantially uniformly
distributed loads and that are designed in accordance with 4.3.2.2
b) the shear capacity at the section where the bar stops exceeds twice the shear force actually
present; or
The rules are as follows:
a) top reinforcement: make at least 20 % of the reinforcement in tension over the supports
effectively continuous through the spans; of the remainder, extend half to a point at least 0,25l
from the face of the support, and the other half to a point at least 0,15l from the face of the
support, but do not stop any bar at a point less than 45 times its own diameter from the face of the
support;
c) the continuing bars at the section where the bar stops provide double the area required to resist
the moment at that section.
NOTE Satisfy any one of these conditions for all arrangements of ultimate load considered.
4.11.7.1.2 At a simply supported end of an element, anchor each tension bar by one of the following:
b) bottom reinforcement: extend at least 30 % of the reinforcement in tension at midspan to the
centre of the supports; extend the remainder to within 0,15l of the centre of interior supports, and
to within 0,1l of the centre of an exterior support;
a) an effective anchorage length equivalent to 12 times the bar diameter beyond the centre-line of
the support; no bend or hook should begin before the centre of the support;
b) an effective anchorage length equivalent to 12 times the bar diameter plus d/2 from the face of
the support, where d is the effective depth of element; no bend or hook should begin before d/2
from the face of the support; or
c) at a simply supported end: use the detailing given in 4.11.7.2.1.
|
Table moved by Amendment No. 1.
c) for slabs, provided that the design ultimate shear stress at the face of the support is less than half
the appropriate value vc given in 4.3.4, a straight length of bar beyond the centre-line of the
support equal to the greater of one-third of the support width or 30 mm.
4.11.7.1.3 As curtailment of substantial areas of reinforcement at a single section can lead to the
development of large cracks at that point, in the case of curtailment of a large number of bars, it is
advisable to stagger the curtailment points in heavily reinforced elements.
4.11.7.1.4 Where a cantilever forms an extension beyond the end support of a continuous beam or
slab, the top steel in the adjacent span should be extended beyond the point of contraflexure.
4.11.7.1.5 To satisfy the requirements for ties, the provisions of 4.11.9 should be observed in addition
to the rules given in this clause.
4.11.7.2 Simplified rules for curtailment of bars in beams
In the case of beams that support substantially uniformly distributed loads, the simplified rules given
below may be applied as an alternative to the provisions given in 4.11.7.1. (See also figure 24.) The
rules do not apply to doubly reinforced elements or haunched elements.
101
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.11.7.3 Simplified rules for curtailment of bars in slabs
In the case of solid slabs spanning one way and that support substantially uniformly distributed loads,
the following simplified rules given below may be applied as an alternative to the provisions given in
4.11.7.1. (See also figure 25.)
4.11.7.3.1 Simply supported slabs
For bottom reinforcement, extend at least 50 % of the tension reinforcement provided at midspan to
the supports and give it an effective anchorage of 12 past the centre of the supports. Extend the
remaining part of the reinforcement to within 0,08l of the supports.
4.11.7.3.2 Cantilever slabs
Extend at least 50 % of the tension reinforcement provided at the support to the end of the cantilever.
Extend the remaining part of the reinforcement a distance of the greater of l/2 or 45 times the bar
diameter, from the face of the support.
4.11.7.3.3 Continuous slabs of approximately equal spans under substantially uniformly
distributed loads and that are designed in accordance with 4.3.2.2
The rules are as follows:
a) top reinforcement: extend all tension reinforcement over supports a distance of the greater of
0,15l or 45 times the bar diameter, from the face of the support, and extend at least 50 % of the
reinforcement a distance of 0,3l from the face of the support into the spans.
b) bottom reinforcement: extend the tension reinforcement provided at midspan of a slab to within
0,2l from the centre of the internal support and to within 0,1l from the centre of the external
support, and extend at least 40 % into the support.
c) where, at an end support, there is a monolithic connection between the slab and its
supporting beam or wall: make provision for the negative moment that may arise. The negative
moment to be assumed in this case depends on the degree of fixity, but it will generally be
sufficient to provide tension reinforcement equal to half that provided at midspan, extending a
distance of the greater of 0,1l or 45 times the bar diameter, from the face of the support into the
span.
d) for solid slabs spanning in two directions at right angles: see 4.4.4, where simplified rules
for curtailment are given in connection with the simplified methods of analysis used. When other
methods of analysis are used to obtain the moments in slabs, base the detailing of the
reinforcement on similar principles.
NOTE Recommendations for the arrangement of reinforcement in flat slabs are given in 4.6 and for that in ribbed slabs
(with solid or hollow blocks or with voids) in 4.5.
Figure 24 — Simplified detailing rules for beams
103
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
4.11.8 Spacing of reinforcement
4.11.8.1 Minimum distances between bars
4.11.8.1.1 When the diameter of a bar exceeds the maximum size of coarse aggregate by more than
5 mm, a spacing smaller than the bar diameter should be avoided. A pair of bars in contact or a bundle
of three or four bars in contact should be regarded as a single bar of equivalent area when the spacing
is being assessed.
4.11.8.1.2 The spacing of bars should be made suitable for the proper compaction of concrete, and
when an internal vibrator is likely to be used, adequate spacing should be provided in the
reinforcement to enable the vibrator to be inserted. Minimum reinforcement spacing is best determined
by experience or proper work tests, but in the absence of better information, the distances given below
may be used.
4.11.8.1.2.1 Individual bars
Except where bars form part of a pair or bundle (see 4.11.8.1.2.2 and 4.11.8.1.2.3), the horizontal
distance between bars should be at least (hagg + 5) mm, where hagg is the maximum size of the coarse
aggregate. Where there are two or more rows,
a) the gaps between corresponding bars in each row should be vertically in line; and
b) the vertical distance between bars should be at least 2/3hagg.
4.11.8.1.2.2 Pairs of bars
Bars may be arranged in pairs either touching or closer than in 4.11.8.1.2.1, in which case
a) the gaps between corresponding pairs in each row should be vertically in line and of width at least
(hagg + 5) mm;
b) when the bars forming the pair are one above the other, the vertical distance between pairs should
be at least 2/3hagg; and
c) when the bars forming the pair are side by side, the vertical distance between pairs should be at
least (hagg + 5) mm.
4.11.8.1.2.3 Bundled bars
Horizontal and vertical distances between bundles should be at least (hagg + 15) mm and the gaps
between the rows or bundles should be vertically in line.
4.11.8.2 Maximum distances between bars in tension
4.11.8.2.1 Beams
4.11.8.2.1.1 The rules given below for beams may apply in normal internal or external conditions of
exposure (but see 4.11.8.2.1.6) where a crack width limited to 0,3 mm is appropriate, unless the
calculations of crack width (see A.3 in annex A) show that greater spacing is acceptable.
4.11.8.2.1.2 In the application of these rules in the case of bars of mixed sizes, any bar of diameter
less than 0,45 times the diameter of the maximum bar in the section should be ignored, except when
those near the side faces of beams are being considered.
Figure 25 — Simplified detailing rules for slabs
105
106
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
4.11.8.2.1.3 Bars placed near the side faces of beams to control cracking should comply with 4.11.4.4.
b) where the reinforcement percentage is less than 1 %, the bar spacing should be limited to the
values given in table 25, divided by this percentage of reinforcement.
4.11.8.2.1.4 The clear horizontal distance between adjacent bars or groups near the tension face of
a beam should not exceed the value given in table 25, depending on the amount of redistribution
carried out in analysis and the characteristic strength of reinforcement. Instead of using the values
given in table 25, assess the clear spacing from the following relationship:
300 > clear spacing <
4.11.8.2.2.3 When table 25 is used for slabs and the amount of redistribution is unknown (e.g. table 15
is used), a value of -15 % may be assumed for support moments and a value of zero may be
assumed for span moments.
4.11.8.3 Spacing of shrinkage reinforcement
47 000
fs
When it is considered necessary to provide reinforcement in an element to distribute cracking arising
from shrinkage and temperature effects, follow the provisions given in 6.5.3.17 for plain walls.
where fs is the design service stress in the reinforcement, which may be obtained from 4.3.6.3.
Table 25 Maximum clear distance between bars
1
2
3
250
450
485
5
6
7
8
9
Amdt 1, Apr. 1994
10
11
|
12
4.11.9 Ties
4.11.9.1 General
Ties provide the interaction that is necessary between elements of the structure to ensure that all
forces are distributed evenly throughout the structure. All structures are provided with the following
types of tie:
Clear distance between bars
Characteristic
strength of
reinforcement, fy
MPa
4
mm
Percentage redistribution to or from section considered
a) peripheral ties;
-30
-25
-20
-15
-10
0
+10
+15
+20
+25
+30
215
120
110
230
130
120
245
135
125
260
145
135
275
155
140
300
170
155
300
185
170
300
195
180
300
205
190
300
210
195
300
220
205
b) internal ties;
c) horizontal ties to columns and walls; and
d) for buildings of five storeys or more, vertical ties.
4.11.8.2.1.5 The clear distance from a corner of a beam to the surface of the nearest longitudinal bar
should not exceed half the clear distance given in table 25.
4.11.9.2 Proportioning of ties
4.11.8.2.1.6 The above rules are not applicable to beams subjected to particularly aggressive
environments unless, in the calculation of the resistance moment, fy has been limited to 300 MPa.
In the design of ties, it may be assumed that the reinforcement acts at its characteristic strength and
that there are no forces, other than those mentioned in 4.11.9.4 to 4.11.9.6. Reinforcement provided
for other purposes may be regarded as forming part of, or the whole of, these ties.
4.11.8.2.2 Slabs
4.11.9.3 Continuity and anchorage of ties
The clear spacing between main bars should not exceed the lesser of three times the effective depth
or 750 mm. In normal internal or external conditions, unless crack widths are checked by direct
calculations, the additional rules given below ensure adequate control of cracking.
Bars should be lapped, welded or mechanically joined, in accordance with 4.11.6.6. A tie may be
considered anchored to another tie at right angles if the bars of the first tie extend
a) 12 times the bar diameter or an equivalent anchorage beyond all the bars of the other tie, or
4.11.8.2.2.1 No additional check is required on bar spacing if
b) an effective anchorage length (based on the force in the bars) beyond the centre-line of the bars
of the other tie. At re-entrant corners or at substantial changes in construction, ensure that the ties
are adequately anchored or otherwise made effective.
a) grade 250 steel is used and the slab depth does not exceed 250 mm;
b) grade 450 steel is used and the slab depth does not exceed 200 mm; or
c) the amount of tension reinforcement in a slab, expressed as a percentage of the cross-sectional
area (the width of section times the effective depth), is less than 0,3 % .
Where a structure is divided into structurally separated sections by means of expansion joints, there
should not be any form of tie between such sections.
4.11.9.4 Peripheral ties
4.11.8.2.2.2 When none of the conditions given in 4.11.8.2.2.1 apply, then
a) where the reinforcement percentage is more than 1 %, the bar spacing should be limited to the
values given in table 25; and
107
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At each floor and roof level, an effectively uninterrupted peripheral tie should be provided, capable of
resisting a tensile force of 1,0Ft (in kilonewtons), located within 1,2 m of the edge of the structure or
in the perimeter wall; the value of Ft is the lesser of Ft = 60 and the value obtained from
108
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SABS 0100-1
Ed. 2.2
Ft = (20 + 4 ns)
where ns is the number of storeys in the structure.
4.11.9.5 Internal ties
In addition to the peripheral tie, internal ties should be provided at each floor and roof level in two
directions approximately at right angles such that the ties will be effectively uninterrupted throughout
their length and will be anchored to the peripheral tie at both ends unless they continue as column and
wall ties. Some or all of the internal ties may be spread evenly over the width of the structure or may
be grouped at beams or walls, or at other appropriate intervals, but at spacings generally not
exceeding 1,5lr , where lr is the greater of the distances between the centres of the columns, walls or
frames supporting any two adjacent floor spans in the direction of the tie under consideration. Ties in
a wall should be located within 0,5 m of the top or bottom of the floor slab.
The ties should be capable of resisting, in each direction, a tensile force of
Ft
gn + qn
lr
7,5
5
kilonewtons per metre of width but at least Ft kilonewtons per metre of width,
where
Ft
is as in 4.11.9.4;
gn + qn is the sum of average nominal self-weight and imposed floor loads (in kilonewtons per
square metre); and
is as defined above.
lr
Where the vertical load-bearing elements are walls that, on plan, occur in one direction only
(cross-wall or spine-wall construction), the ties parallel to the walls should be capable of resisting a
tensile force of Ft kilonewtons per metre of width.
4.11.9.6 Horizontal ties to columns and walls
Each external column and each metre length of external wall should be anchored or tied horizontally
into the structure at each floor and roof level with a tie capable of developing a force equal to the
greater of the forces given in (a) and (b) below.
a) the lesser of 2,0Ft kilonewtons or
lo
2,5
Ft kilonewtons,
v
where lo is the floor-to-ceiling height, in metres; or
f
b) 3 % of the total ultimate vertical load carried by the column or wall at that level.
Where the peripheral tie is located within the wall, only such horizontal tying as is required to anchor
the internal ties to the peripheral ties need be provided (see 4.11.9.5).
Corner columns should be tied into the structure at each floor and roof level in each of two directions
approximately at right angles, with ties capable of developing a force equal to the greater of the forces
given in (a) and (b) above.
Column and wall ties may be provided partly or wholly with the same reinforcement as that provided
for the peripheral or internal ties.
109
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E
l h
l b
l h
e
l
E
f
v
f
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a
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
5 Prestressed concrete (design and detailing)
5.1.5 Strength of materials
5.1 General
5.1.5.1 Characteristic strength of concrete
This subclause gives methods of analysis and design that will in general ensure that, for prestressed
concrete structures of classes 1, 2, and 3 as given in 3.2.3.3.1.2, the criteria set out in clause 3 are
met. Other methods may be used provided that they can be shown to be satisfactory for the type of
structure or element under consideration. In certain cases, the assumptions made in this clause may
be inappropriate and the engineer will have to adopt a more suitable method, having regard to the
nature of the structure in question.
The characteristic strengths of concrete that may be specified for prestressed concrete are given in
table 28 together with their required strengths at other ages. The minimum grades recommended are
those that have characteristic compression strengths of 30 MPa and 40 MPa for post-tensioning and
pre-tensioning, respectively. The concrete strength at transfer should be at least 18 MPa for unbonded
systems and 25 MPa for bonded systems.
Table 28 — Strength of concrete fcu
For low density aggregate concrete, the prestress losses will in general exceed those for dense
aggregate concrete, and specialist literature should be consulted.
1
2
3
4
5
Characteristic strength*)
When structures are to be erected in seismic areas, the effect of adverse bending of the prestressed
elements should be considered.
5.1.1 Basis of design
MPa
Characteristic
strength, fcu
Grade
Age,
months
MPa
5.1.1.1 This subclause follows the limit states philosophy set out in clause 3, but since it is not possible
to assume that a particular limit state will always be the critical one, design methods are given for the
ultimate limit state and the serviceability limit states.
30
40
50
60
5.1.1.2 In general, the design of class 1 and class 2 elements is determined by the concrete tension
limitations for service load conditions, but check the ultimate strength in flexure, shear and torsion.
30,0
40,0
50,0
60,0
3
6
12
34
44
54
64
35
46
56
66
36
48
58
68
*)These increased strengths due to age should only be used if it has been
demonstrated to the satisfaction of the engineer that the materials to be used are
capable of producing these higher strengths.
5.1.1.3 The design of class 3 elements is usually determined by ultimate strength conditions, or by
deflection or by cracking or by both.
5.1.2 Durability and fire resistance
The design should be based on the 28 d characteristic strength or, if appropriate, on the required
strength given in table 28 for the age at loading.
For guidance on the minimum cover to reinforcement and prestressing tendons that have to be
provided to ensure durability, see 5.9.3. Use the results of fire tests or other evidence to ascertain the
fire resistance of an element or, alternatively, refer to clause 7.
5.1.5.2 Characteristic strength of steel
5.1.3 Stability and other considerations
For recommendations concerning such considerations as vibration and stability, refer to the general
provisions of clauses 3 and 4.
5.1.4 Loads
The specified characteristics of prestressing tendons and wires are not covered by this code. The
characteristic strengths of reinforcement are those given in 4.1.5.2.
5.2 Structures and structural frames
5.2.1 Analysis of structures
Complete structures and structural frames may be analysed in accordance with 3.4.3 but, when
appropriate, the methods given in 5.3, 5.4 and 5.5 may be used for individual elements.
5.1.4.1 Values of loads
The values of the design ultimate loads are those given in 3.3.3.1 and 3.3.4.1. The design loads to be
used for the serviceability limit states are given in 3.3.4. (See also 5.3.2.)
5.1.4.2 Design load arrangements
In general, when assessing any particular effect of loading, ensure that the arrangement of loads is
the one that causes the most severe effect. Consider the secondary effects due to both the
construction sequence and the prestress, particularly for the serviceability limit states.
113
Base the relative stiffness of elements on the concrete section as described in 3.4.3.1.
5.2.2 Redistribution of moments
5.2.2.1 The moments obtained by elastic analysis, for the ultimate limit state only, may be distributed,
provided that the following conditions are satisfied:
a) equilibrium between the internal forces and the external loads under each appropriate combination
of ultimate loads is maintained;
114
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
b) the ultimate resistance moment provided at any section of an element is at least 80 % of the
moment at that section, obtained from an elastic maximum moments diagram covering all
appropriate combinations of ultimate load;
5.3.1.3 Continuous beams
c) in structures exceeding four storeys, in which the structural frame provides the lateral stability, the
reduction in moment allowed by condition (b) above is not more than 10 %; and
a) only alternate spans loaded with the maximum design load; and
d) where, as a result of redistribution, the ultimate resistance moment at a section is reduced, the
neutral axis depth x of the section resisting the reduced moment does not exceed
x = (ßred - 0,5)d
is the effective depth; and
ßred
= (moment at the section after redistribution)
(maximum elastic moment at the section)
b) all spans loaded with the maximum design load.
The moments obtained by this method may be redistributed, for the ultimate limit state only, within the
conditions and limits recommended in 5.2.2.
5.3.2 Serviceability limit state (cracking) for beams
where
d
Carry out an elastic analysis with the following arrangements of load (see 3.3.3.1 and 3.3.4.1):
5.3.2.1 Section analysis
The following assumptions may be made when service loads are considered:
a) plane sections remain plane;
5.2.2.2 In general, condition 5.2.2.1(d) will limit or prevent redistribution in rectangular elements of
class 1 and class 2 (see 3.2.3.3.1.2), unless the prestress is small. Redistribution with a reduction of
moment in columns will generally be ruled out, unless the design ultimate axial load and the prestress
in the column are small.
b) for class 1 and class 2 elements (see 3.2.3.3.1.2), elastic behaviour of the concrete exists up to
stresses given in 5.3.2.2 and 5.3.2.3; for class 3 elements, elastic behaviour is deemed to exist up
to the hypothetical stresses given in 5.3.2.2 and 5.3.2.3. The modulus of elasticity may be taken
as given in 3.4.2.1;
5.3 Beams
c) in general, it may only be necessary to calculate the stresses due to the load combinations as in
3.3.3.1 immediately after the transfer of prestress and after all losses of prestress have occurred;
in both cases, the effects of self-weight load and imposed load on the strain and force in the
tendons may be ignored.
5.3.1 General
5.3.1.1 Definitions
The definitions and limitations of the geometric properties of prestressed beams are as given for
reinforced concrete beams in 4.3.1.
5.3.1.2 Slender beams
In addition to limiting the slenderness of a beam (see 4.3.1.6) when under load in its final position, the
possible instability of a prestressed beam during erection should be considered (see the appropriate
clause of SABS 0100-2). Elements may collapse by tilting about a longitudinal axis through the lifting
points. This initial tilting, which may be due to imperfections in beam geometry and in locating the
lifting points, could cause lateral bending moments and these moments, if too high, could result in
lateral instability.
5.3.2.2 Stress limitations under service conditions
5.3.2.2.1 Compressive stresses
Ensure that the compressive stresses in the concrete do not exceed the values given in table 29.
Table 29 Compressive stresses fcu in concrete for
serviceability limit states
The following factors may require consideration:
a) beam geometry, i.e. type of cross-section, span/breadth/depth ratios, etc.;
b) location of lifting points;
c) method of lifting, e.g. inclined or vertical slings, type of connection between the beam and the
slings; and
d) tolerances in construction, e.g. maximum lateral bow.
It may be necessary to assess the design stresses due to the combined effects of lateral bending,
self-weight load and pre-stress; if cracking is possible, the method of lifting should provide adequate
lateral support.
115
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1
2
Nature of loading
Allowable compressive stresses
Design load in bending
0,33 fcu
In continuous beams and other statically
indeterminate structures, this may be increased
to 0,4 fcu within the range of support moments.
Design load in direct
compression
0,25 fcu
5.3.2.2.2 Tensile stresses in flexure
Ensure that the flexural tensile stresses do not exceed the values below for the given classes of
element. These stresses are appropriate for an element or a structure that is monolithic, but tension
is not allowed at mortar or concrete joints of members made up of pre-cast units.
a) class 1 elements: no tensile stress;
116
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SABS 0100-1
Ed. 2.2
|
|
As is the area of bonded prestressed reinforcement in the tension zone and the area of
Amdt 1, Apr. 1994
unstressed reinforcement in the tension zone, in square millimetres;
b
is the width of section in tension zone, in millimetres (For sections with a flange in tension
zone, b is the width of equivalent tension zone area, assuming a neutral axis depth of h/3.);
and
h
is the height of section, in millimetres.
For deflection and cracking of class 3 elements, see the methods described in annex A.
Table 31 Depth factors for tensile stresses for class 3 elements
1
2
Depth of member
mm
Depth factor for
tensile stresses for
class 3 elements
< 200
400
600
1,1
1,0
0,9
800
> 1 000
0,8
0,7
f
f
5.3.2.3 Stress limitations at transfer for beams (SLS)
5.3.2.3.1 Compressive stresses
Design compressive stresses in the concrete at transfer should not exceed 0,45fci at the extreme fibre
(in the case of triangular or near triangular distribution of prestress) or 0,3fci for near uniform
distribution of prestress, where fci is the concrete strength at transfer.
5.3.2.3.2 Tensile stresses in flexure
Design tensile stresses in flexure in the concrete at transfer should not exceed the values given below:
a) class 1 elements: ensure that at transfer, the tensile stress does not exceed the value of 1 MPa;
b) class 2 elements: ensure that the tensile stress does not exceed the value appropriate to the
concrete strength at transfer given in table 30; ensure that elements with pre-tensioned tendons
have some tendons or unstressed reinforcement well distributed throughout the tensile zone of the
section and elements with post-tensioned tendons have unstressed reinforcement located near the
tension face of the element;
f
w
A
c) class 3 elements (see also annex A): the tensile stress should, in general, not exceed the
appropriate value for a class 2 element; where this stress is exceeded, regard the section in design
as cracked.
bh
w
5.3.3 Ultimate limit state for beams in flexure
f
5.3.3.1 Section analysis
When analysing sections under maximum design loads, make the following assumptions:
118
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
a) the strain distribution in the concrete in compression is derived from the assumption that plane
sections remain plane;
b) the stresses in the concrete in compression are either derived from the stress strain curve given
in figure 1, with a m of 1,5, or are taken as equal to 0,45fcu over the whole compression zone (see
figure 4); in both cases, the strain at the outermost compression fibre is taken as 0,0035;
c) the tensile strength of the concrete is ignored;
Mu
is the design moment of resistance of beam;
fpb
is the design tensile stress in tendons at failure;
d
is the effective depth to centroid of steel area Aps;
dn
is the depth to centre of compression zone; and
Aps
is the area of prestressing tendons in tension zone.
d) the strains in bonded prestressing tendons and in any unstressed reinforcement, whether in tension
or in compression, are derived from the assumption that plane sections remain plane;
5.3.3.2.2 For rectangular beams, and for flanged beams in which the compression block lies within
the flange, dn = 0,45x, where x is the neutral axis depth.
e) the stresses in bonded prestressing tendons, whether initially tensioned or untensioned, and in
unstressed reinforcement are derived from the appropriate stress/strain curves;
5.3.3.2.3 Values for fpb and x may be derived from table 32 for pre-tensioned elements and for
post-tensioned elements with effective bond between the concrete and tendons. The effective
prestress after all losses shall be at least 0,45fpu. Ignore prestressing tendons and unstressed
reinforcement in the compression zone in strength calculations when using this method.
NOTE The stress/strain curves for prestressing reinforcement are given in figure 3 and those for reinforcement are given
in figure 2. An empirical approach towards obtaining the stress in the tendons at failure is given in 5.3.3.2.
f) in post-tensioned elements where the tendons are unbonded, the stress in the tendons does not
exceed the values given in table 33 unless a higher stress can be justified on the basis of tests.
5.3.3.2.4 For rectangular beams, and for flanged beams in which the neutral axis lies within the
flange, the stress in the tendons at failure may be derived from table 33 for unbonded tendons.
Table 32 Conditions at the ultimate limit state for rectangular
beams with pre-tensioned tendons or with post-tensioned tendons
having an effective bond
Table 33 Conditions at the ultimate limit state for post-tensioned
rectangular beams having unbonded tendons
1
fpu Aps
2
3
4
5
6
Design stress in tendons as
a proportion of the design
strength
fpb /0,87fpu
Ratio of depth of neutral
axis to that of the centroid
of the tendons in the
tension zone
x/d
fpe /fpu
fpe/fpu
fcu bd
1
7
0,6
0,5
0,4
0,6
0,5
0,4
0,05
0,10
0,15
1,0
1,0
0,99
1,0
1,0
0,97
1,0
1,0
0,95
0,11
0,22
0,32
0,11
0,22
0,31
0,11
0,22
0,31
0,20
0,25
0,30
0,92
0,88
0,85
0,90
0,86
0,83
0,88
0,84
0,80
0,40
0,48
0,55
0,39
0,47
0,54
0,38
0,46
0,52
0,35
0,40
0,45
0,50
0,83
0,81
0,79
0,77
0,80
0,77
0,74
0,71
0,76
0,72
0,68
0,64
0,63
0,70
0,77
0,83
0,60
0,67
0,72
0,77
0,58
0,62
0,66
0,69
2
3
4
5
6
7
Stress in tendons as a
proportion of effective
prestress fpb/fpe for values of
effective span l
effective depth d
Ratio of depth of neutral axis to
that of the centroid of the
tendons in the tension zone x/d
for values of
effective span l
effective depth d
0,025
0,05
0,10
1,23
1,21
1,18
1,34
1,32
1,26
1,45
1,45
1,45
0,10
0,16
0,30
0,10
0,16
0,32
0,10
0,18
0,36
0,15
0,20
1,14
1,11
1,20
1,16
1,36
1,27
0,44
0,56
0,46
0,58
0,52
0,64
f pe Aps
fcu bd
5.3.3.2.5 In table 32, the following assumptions have been made:
a) the effective prestress after all losses have occurred (fpe) does not exceed 0,6fpu;
b) the compression block is rectangular with a uniform stress of 0,45fcu;
c) either the tendons are in ducts or, if they are free (as in hollow beams), diaphragms are provided
to prevent a reduction of the effective depth; and
5.3.3.2 Design formulae
5.3.3.2.1 In the absence of an analysis based on the assumptions given in 5.3.3.1, the moment of
resistance of any shape of beam may be obtained from the following equation:
Mu = fpbAps(d-dn)
d) the effective depth is determined by assuming that the tendons are in contact with the top of the
duct or with the soffit of the diaphragms.
5.3.3.2.6 In addition, for unbonded tendons, values of f pb and x may be obtained from equations (15)
and (16). (The value of fpb should not be taken as exceeding 0,7fpu.)
where
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f
f
l
x
f
A
f
f
bd
f
f
A
f
bd
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A
Af f
d
V
f
A
d
f
v
f
f
f
b
V
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f
x
f
V
f
V
V
bh f
f
f
f
f
f
b
b
h
l
V
bh
f
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d
A
A
M
M
f pt
Y
Y
f
I
f
f
f
f
f
A
V
A
f
f
f
V
v
V
M
b
f
l
f
l
V
bd f
V
d
f
l
l
V
V
f
f
v bd
M
V
M
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V
V
V
V
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SABS 0100-1
Ed. 2.2
5.3.6 Deflection of beams
NOTE See also annex A.
5.3.6.1 Class 1 and class 2 elements (see 3.2.3.3.1.2)
A
5.3.6.1.1 The instantaneous deflection due to service loads may be calculated with the use of elastic
analysis based on the concrete section properties and on the value for the modulus of elasticity given
in 3.4.2.1.
b
f
s
5.3.6.1.2 The total long-term deflection due to the prestressing force, self-weight load and any
sustained imposed load may be calculated with the use of elastic analysis based on the concrete
section properties and on an effective modulus of elasticity based on the creep of the concrete per unit
length for unit applied stress after the period under consideration (specific creep). The values for
specific creep given in 5.8.2.5 may in general be used unless a more accurate assessment is required.
Make due allowance for the loss of prestress after the period under consideration. Ensure that the
deflections comply with the limits given in 3.2.3.2.
f
b
A
5.3.6.2 Class 3 elements
s
V
A
V
s
Where the permanent load is less than or equal to 25 % of the imposed load, the deflection of class 3
elements may be calculated in accordance with 5.3.6.1. Where the permanent load exceeds 25 % of
the imposed load, the basic span/effective depth ratios given in 4.3.6 and table 10 should be complied
with unless more rigorous calculations based on the moment curvature relationship are made.
V
V
f
5.4 Slabs
d
The provisions given in 5.3 for beams apply also to slabs. The methods of analysis given in 4.4.2 and
4.5.2 are appropriate for the ultimate limit state. Elastic analysis should be used for the serviceability
limit states.
d
The design for shear should be in accordance with 5.3.4 except that shear reinforcement need not be
provided if v is less than vc.
The analysis and design of flat slabs should be carried out in accordance with appropriate specialist
literature.
5.5 Columns
d
V
V
Prestressed concrete columns in framed structures, where the mean stress in the concrete section
imposed by the tendons is less than 2,5 MPa, may be analysed as reinforced columns in accordance
with 4.7.
d
d
5.6 Tension members
The tensile strength of tension members should be based on the design strength of the prestressing
tendons (0,87fpu) and the strength developed by any unstressed reinforcement. The unstressed
reinforcement may usually be assumed to be acting at its design stress (0,87fy); in special cases it may
be necessary to check the stress in the reinforcement, using strain compatibility.
5.7 Low density aggregate prestressed concrete
Design of members in low density aggregate prestressed concrete should be based on the provisions
given in 4.12. For assessment of the prestress losses, which will, in general, exceed those for dense
aggregate concrete, specialist literature should be consulted.
126
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
5.8.2.3 Loss of prestress due to elastic deformation of the concrete
5.8 Prestressing
5.8.1 Maximum initial prestress
5.8.1.1 The jacking force should not normally exceed 75 % of the characteristic strength of the tendon
but may be increased to 80 %, provided that additional consideration is given to safety, to the
stress/strain characteristics of the tendon, and to the assessment of the friction losses.
5.8.1.2 In the determination of the jacking force to be used, consideration should also be given to the
gripping efficiency of the anchorage.
5.8.1.3 When deflected tendons are used in pre-tensioning, consideration should, in the determination
of the maximum initial prestress, be given to the possible influence of the size of the deflector on the
strength of the tendons. (See the appropriate clause of SABS 0100-2.)
Attention should also be paid to the effect of any frictional forces that may occur.
5.8.2.3.1 Calculation of the immediate loss of force in the tendons due to elastic deformation of the
concrete at transfer may be based on the values for the modulus of elasticity of the concrete given in
table 1 when the actual experimental values are not available (see annex C). The modulus of elasticity
of the tendons may be obtained from 3.4.2.3.
5.8.2.3.2 For pre-tensioning, calculate the loss of prestress in the tendons at transfer on a modular
ratio basis, using the stress in the adjacent concrete.
5.8.2.3.3 For elements with post-tensioning tendons that are not stressed simultaneously, there is a
progressive loss of prestress during transfer, due to the gradual application of the prestressing force.
Calculate the resulting loss of prestress in the tendons on the basis of half the product of the modular
ratio and the stress in the concrete adjacent to the tendons averaged along their length; alternatively,
the loss of prestress may be accurately calculated by basing it on the sequence of tensioning.
5.8.2.3.4 In making these calculations, it may usually be assumed that the tendons are located at their
centroid.
5.8.2 Loss of prestress other than frictional losses
5.8.2.4 Loss of prestress due to shrinkage of the concrete
5.8.2.1 General
When calculating the forces in tendons at the various stages considered in design, make allowance
for the appropriate losses of prestress resulting from
5.8.2.4.1 The shrinkage strain to be considered depends upon the following:
a) the aggregate used;
a) relaxation of steel of the tendons,
b) the original water content;
b) the elastic deformation and subsequent shrinkage and creep of the concrete,
c) the effective age of transfer;
c) slip or movement of tendons at anchorages during anchoring, and
d) the effective section thickness; and
d) other causes in special circumstances, for example when steam curing is used with pre-tensioning.
e) the ambient relative humidity.
If experimental evidence on performance is not available, take the properties of the steel and of the
concrete into account when calculating the losses of prestress from these causes. The provisions given
in the following subclauses are applicable to a wide range of structures, especially buildings. It must
be recognized, however, that these recommendations are necessarily general and approximate.
5.8.2.4.2 The loss of prestress in the tendons due to shrinkage of the concrete may be calculated as
the product of the shrinkage per unit length of the concrete (see table 35) and the modulus of elasticity
of the tendons (as in 3.4.2.3).
5.8.2.2 Loss of prestress due to relaxation of steel
5.8.2.2.1 Ensure that the loss of force in the tendon allowed for in the design is double the maximum
relaxation after 1 000 h duration, for a jacking force equal to that imposed at transfer.
5.8.2.2.2 When there is no experimental evidence available, the relaxation loss for normal
stress-relieved wire or strand may be assumed to decrease linearly from 10 % for an initial prestress
of 80 %, to 3 % for an initial prestress of 50 %. This would apply when the estimated total creep and
shrinkage strain of the concrete is less than 500 x 10-6. When the creep plus shrinkage strain exceeds
500 x 10-6, the loss for an initial stress of 80 % should be reduced to 8,5 %. Losses for low-relaxation
tendons may be assumed to be half the above values.
5.8.2.2.3 Make no reduction in the value of the relaxation loss for a tendon when a load equal to or
exceeding the relevant jacking force has been applied for a short time prior to the anchoring of the
tendon.
5.8.2.2.4 In special cases, such as tendons exposed to high temperatures or subjected to large lateral
loads, greater relaxation losses will occur. Consult specialist literature in these cases.
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SABS 0100-1
Ed. 2.2
2
3
4
Shrinkage per unit length
Relative humidity
System
80 %
60 %
35 %
e.g. coastal
towns
e.g. most
inland areas
e.g. environments of
unusually low
relative humidity
such as Windhoek
and Upington
Pre-tensioning
Transfer at 3 d to 5 d
after concreting
180 x 10-6
310 x 10 -6
420 x 10 -6
Post-tensioning
Transfer at 7 d to 14 d
after concreting
140 x 10-6
250 x 10 -6
350 x 10 -6
SABS 0100-1
Ed. 2.2
in the section at transfer is less than one-third of the cube strength of concrete. Where the maximum
stress anywhere in the section at transfer exceeds one-third of the cube strength of the concrete, the
value for the creep per unit length should be increased up to the maximum value equal to 1,25 times
the values given in 5.8.2.5.2 and 5.8.2.5.3, as relevant. This maximum value is applicable when the
maximum stress at transfer is half the cube strength. For intermediate stresses, the values for the
creep per unit length should be interpolated linearly.
Table 35 Shrinkage of concrete
1
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5.8.2.5.5 The values in the preceding subclauses relate to the ultimate creep after a period of years.
When it is necessary to determine the deformation of the concrete due to creep at some earlier stage,
it may be assumed that half the total creep takes place in the first month after transfer and that threequarters of the total creep takes place in the first 6 months after transfer.
5.8.2.5.6 When applying the provisions given above, which are necessarily general, consult specialist
literature for more detailed information on the factors affecting creep, particularly those such as
aggregates used, original water content, effective age at transfer, effective section thickness, ambient
relative humidity and ambient temperature. Care should be taken when using Reef quartzite,
aggregates of the Beaufort group of the Karoo sequence and the Lesotho basalts, since the values
may be three times bigger. (See also figure C.1.)
5.8.2.6 Draw-in during anchorage
5.8.2.4.3 Some adjustment to the figures in table 35 will be necessary for other ages of concrete at
transfer, for other conditions of exposure, or for massive structures, in which cases specialist literature
should be consulted.
5.8.2.4.4 When it is necessary to determine the loss of prestress and the deformation of the concrete
at some stage before the total shrinkage is reached, it may be assumed that half the total shrinkage
takes place during the first month after transfer and that three-quarters of the total shrinkage takes
place within the first 6 months after transfer.
5.8.2.4.5 In certain regions of South Africa, the aggregate may exhibit abnormally high shrinkage
characteristics. The fine-grained shales and sandstones of the Beaufort group of the Karoo sequence
are those most likely to lead to high dimensional changes in concrete. Seek advice when these
aggregates or others of a similar type are to be used.
5.8.2.5 Loss of prestress due to creep of the concrete
5.8.2.5.1 The loss of prestress in the tendons may be calculated on the assumption that creep is
proportional to the stress in the concrete (see 5.8.2.5.4). The loss of prestress is obtained as the
product of the creep per unit length of the concrete adjacent to the tendons and the modulus of
elasticity of the tendons (see 3.4.2.3). When calculating this loss, it is usually sufficient to assume that
the tendons are located at their centroid.
5.8.2.5.2 For pre-tensioning at between 3 d and 5 d after concreting and for humid or dry conditions
of exposure where the required cube strength at transfer exceeds 40,0 MPa, take the creep of the
concrete per unit length as 48 x 10-6 per megapascal. For lower values of cube strength at transfer,
assume the creep per unit length to be 48 x 10-6 x 40,0/fci per megapascal, where fci is the concrete
strength at transfer.
5.8.2.5.3 For post-tensioning at between 7 d and 14 d after concreting and for humid or dry conditions
of exposure where the required cube strength at transfer exceeds 40,0 MPa, take the creep of the
concrete per unit length as 36 x 10-6 per megapascal. For lower values of cube strength at transfer,
take the creep per unit length as 36 x 10-6 x 40,0/fci per megapascal.
5.8.2.5.4 The values as in 5.8.2.5.2 and 5.8.2.5.3 are applicable when the maximum stress anywhere
129
In post-tensioning systems, make allowance for any movement of the tendon at the anchorage when
the prestressing force is transferred from the tensioning equipment to the anchorage. The loss due to
this movement is particularly important in short elements and for such elements check, on site, the
allowance made by the designer.
5.8.2.7 Loss of prestress due to steam curing
Where steam curing is used in the manufacture of prestressed concrete elements, consider changes
in the behaviour of the material at temperatures higher than normal.
5.8.3 Loss of prestress due to friction
5.8.3.1 General
5.8.3.1.1 In post-tensioning systems, there will be movement of the greater part of the tendon relative
to the surrounding duct during the tensioning operation and, if the tendon is in contact with either the
duct or any spacers provided, friction will cause a reduction in the prestressing force as the distance
from the jack increases. In addition, a certain amount of friction will be developed in the jack itself and
in the anchorage through which the tendon passes.
5.8.3.1.2 In the absence of evidence established to the satisfaction of the engineer, assess, in
accordance with 5.8.3.2 to 5.8.3.4, the stress variation likely to be expected along the design profile
in order to obtain the prestressing force at the critical sections considered in design. Calculate the
extension of the tendon, allowing for the variation in tension along its length.
5.8.3.2 Friction in the jack and anchorage
This will vary considerably between systems and should be ascertained for the type of jack and the
anchorage system to be used.
5.8.3.3 Friction in the duct due to unintentional variation from the specified profile
Whether the desired duct profile is straight or curved or a combination of both, there will be slight
variations in the actual line of the duct, which may cause additional points of contact between the
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SABS 0100-1
Ed. 2.2
tendon and the sides of the duct, and so produce friction. Calculate the prestressing force Px at any
distance x from the jack, from the following equation:
Px = Poe
-Kx
SABS 0100-1
Ed. 2.2
e) 0,05 for greased strand running in plastics sleeve.
5.8.4 Transmission length in pre-tensioned elements
(where Kx < 0,2, take e-Kx as 1 - Kx)
5.8.4.1 The transmission length is defined as the length of the element required to transmit the initial
prestressing force in a tendon to the concrete.
where
5.8.4.2 The transmission length depends on a number of variables, the most important being
Po is the prestressing force in tendon at jacking end;
a) the degree of compaction of the concrete,
e
is the base of Napierian logarithms (2,718); and
b) the size and type of tendon,
K
is the constant depending on the type of duct or sheath employed, the nature of its inside
surface, the method of forming it, and the degree of vibration employed in placing the
concrete.
c) the strength of the concrete, and
Take the value of K per metre of length in the above formula as at least 33 x 10-4 but
a) K = 17 x 10-4 where strong rigid sheaths or duct formers are used so closely supported that they are
not displaced during the concreting operation; and
b) K = 25 x 10-4 for greased strands running in plastics sleeves.
Other values may be used, provided they have been established by tests to the satisfaction of the
engineer.
5.8.3.4 Friction in the duct due to curvature of the tendon
5.8.3.4.1 When a tendon is curved, the loss of tension due to friction is dependent on the angle the
tendon is turned through and on the coefficient of friction µ between the tendon and its supports.
5.8.3.4.2 Calculate the prestressing force Px at any distance x along the curve from the tangent point
from the following equation:
Px = Poe
-µx/rps
where
5.8.4.3 The transmission length can vary a great deal for different factory or site conditions, for
example it has been shown that the transmission length for wire can vary between 50 and 160 wire
diameters. As far as possible, therefore, the engineer should base the transmission length on
experimental evidence for known site or factory conditions.
5.8.4.4 Consider the following general provisions, based on research, in relation to the known site or
factory conditions:
a) for factory-produced units where plain or indented wire with a small offset crimp (e.g. 0,3 mm offset,
40 mm pitch) is used, a transmission length of 100 wire diameters may be assumed when the ends
of the units are fully compacted and the cube strength of the concrete at transfer is at least 35 MPa;
b) for units where wire of a considerable crimp (e.g. 1,0 mm offset, 40 mm pitch) is used, a
transmission length of 65 wire diameters may be assumed when the ends of the units are fully
compacted and the cube strength of the concrete at transfer is at least 35 MPa;
c) the development of stress from the end of the unit to the point of maximum stress is such that it
may be assumed that 80 % of the maximum stress is developed in a length of 70 wire diameters
for the conditions described in (a) above, and in a length of 54 wire diameters for the conditions
described in (b) above;
d) when the cube strength of the concrete at transfer is less than 35 MPa, the transmission lengths
may be greater;
Po is the prestressing force in the tendons at tangent point near jacking end;
rps is the radius of curvature; and
e
d) the deformation, e.g. crimp of the tendon and surface condition of the tendon.
e) the transmission length for tendons near the top of a beam may exceed that for identical tendons
placed lower in the beam, since the concrete near the top is less likely to be as well compacted;
is as defined in 5.8.3.3.
f) since the sudden release of tendons leads to a great increase in the transmission lengths in the
units near the releasing end of the bed, tendons shall be so cut as not to cause a sudden shock to
the concrete;
Values of µ may be taken as follows:
a) 0,55 for lightly rusted strand running in an unlined concrete duct;
c) 0,25 for strand or wire running in a steel duct;
g) from the available experimental data, the transmission length for small diameter strand is not
proportional to the diameter of the tendon, nor is the scatter of results as great as it is for wire;
table 36 gives values for the transmission lengths for small diameter strand; in the absence of more
exact data, these values may be used in design.
d) 0,17 for pulled-through oversized duct oiled with water-soluble oil; and
h) if the tendons are prevented from bonding to the concrete near the ends of the elements by the use
b) 0,30 for lightly rusted strand or wire running in a lightly rusted steel duct;
131
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SABS 0100-1
Ed. 2.2
jacking force for the strength of concrete at the time of prestressing; and
d) post-tensioning anchorage zones shall be designed to develop the guaranteed ultimate strength of
the lesser of prestressing anchorages or prestressing tendons.
5.8.5.2 Bursting tensile forces in post-tensioned elements
5.8.5.2.1 The bursting forces round individual anchorages should be assessed in the end blocks on
the basis of the tendon jacking load (for serviceability limit state) or the nominal tendon force (for
ultimate limit state). The latter is necessary only in the case of elements with unbonded tendons. For
elements with rectangular anchorages and for rectangular end blocks, the bursting tensile force Fbst
may be calculated from table 37 in relation to the value of Ypo/Yo for each direction,
l
where
l
l
Yo
is half the side of the end block;
Ypo
is half the side of the loaded area; and
Pk
is the tendon jacking force.
Circular bearing plates should be treated as square plates of equivalent area.
K
Table 37 Design bursting tensile forces in end blocks
f
1
2
Ypo/Yo
Fbst/Pk
0,2
0,3
0,4
0,23
0,23
0,20
0,5
0,6
0,7
0,17
0,14
0,11
f
K
K
K
NOTE Intermediate values
may be interpolated.
K
5.8.5.2.2 This force, Fbst, will be distributed in a region extending from 0,2 Yo to 2,0 Yo from the loaded
face and should be resisted by reinforcement in the form of spirals or closed links, uniformly distributed
thoughout this region. The reinforcement should act at a stress of 200 MPa (in the case of
serviceability limit state) or at its design strength, i.e. 0,87fy (in the case of ultimate limit state). When
the concrete cover to the reinforcement is less than 50 mm, the stress shall be limited to a value
corresponding to a strain of 0,001.
K
5.8.5.2.3 Where groups of anchorages or bearing plates are used, the end block should be divided
into a series of symmetrically loaded prisms, and each prism should be treated in the above manner.
However, additional reinforcement will be required round the groups of anchorages to ensure overall
equilibrium of the end block.
5.8.5.2.4 Special attention should also be paid to end blocks having a cross-section different in shape
from that of the general cross-section of the beam. Specialist literature should be consulted.
5.8.5.2.5 Compliance with the above requirements will generallly ensure that bursting tensile forces
along the load axis are provided for. Alternative methods of design that make allowance for the tensile
134
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
strength of the concrete may be used, in which case specialist literature should be consulted.
Table 38 Nominal cover to all steel to meet specified
periods of fire resistance
5.9 Considerations affecting design details
1
5.9.1 General
2
3
4
5
6
7
Nominal cover
The following subclauses supplement the considerations for design details for reinforced concrete as
given in 4.11.
Fire
resistance
5.9.2 Size and number of prestressing tendons
h
5.9.2.1 Ensure that the size and number of prestressing tendons are such that cracking of the concrete
would precede failure of the beam.
5.9.2.2 This requirement will be satisfied for under-reinforced beams, where failure would be due to
fracture of the tendons, if the percentage of reinforcement, calculated on an area equal to the width
of the beam soffit multiplied by its overall depth, is at least 0,15. For over-reinforced beams, where
failure would be due to crushing of the concrete, the maximum number and size of tendons will be
governed by considerations of strain compatibility (see 5.3.3.1).
5.9.3 Cover to prestressing tendons
mm
Beams
Floors
Ribs
Simply
supported
Continuous
Simply
supported
Continuous
Simply
supported
Continuous
0,5
20
20
20
20
20
20
1
20
20
25
20
35
20
1,5
35
20
30
25
45
35
2
60
35
40
35
55
45
3
70
60
55
45
65
55
4
80
70
65
55
75
65
NOTES
5.9.3.1 General
1 For the purposes of assessing a nominal cover for beams, the cover to main bars, which
would have been obtained from table 43, has been reduced by a notional allowance for stirrups
of 10 mm to cover the range 8 mm to 12 mm.
Cover to prestressing tendons will generally be governed by considerations of durability
(see SABS 0100-2) and fire resistance.
5.9.3.2 Bonded tendons
2 The nominal covers given relate specifically to the minimum element dimensions (see clause
7). Increased covers are necessary if smaller elements are used. (Specialist literature should
be consulted.)
The recommendations of 4.11.2 concerning cover to reinforcement may also be applicable to tendons.
The required nominal cover against corrosion and the associated mix limitations are given in
SABS 0100-2.
3 Cases that lie below the line require attention to the additional measures necessary
to reduce the risks of spalling (see clause 7).
The values of cover as fire protection for various structural elements may be taken from table 38. The
ends of individual pre-tensioned tendons do not normally require concrete cover and should preferably
be cut off flush with the end of the concrete element.
5.9.3.3 Cover to tendons in ducts
The cover to any duct should be at least the greater of 50 mm or the diameter of the duct. Precautions
should be taken to ensure a dense concrete cover, particularly with large or wide ducts.
5.9.3.4 Cover to external tendons
Where the tendons are located outside the structural concrete (as defined in the relevant clause of
SABS 0100-2) and are to be protected by dense concrete added subsequently, the thickness of this
cover shall be at least equal to that required for tendons inside the structural concrete under similar
conditions. The concrete cover should be anchored by reinforcement to the prestressed element, and
should be checked for crack control in accordance with clause 4.
5.9.3.5 Cover to curved tendons
For cover to curved tendons, see 5.9.5.2.
135
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
Where the curved tendons run close to, and approximately parallel with, the surface of an element and
if the tendons develop radial forces perpendicular to the exposed surface of the concrete, the duct, if
necessary, should be restrained by stirrup reinforcement anchored into the element.
5.9.4 Spacing of prestressing tendons
5.9.4.1 General
Table 39 Minimum cover to curved ducts
In all prestressed elements, there should be sufficient gaps between the tendons or groups of tendons
to allow the largest size of aggregate used to move, under vibration, to all parts of the mould.
1
5.9.4.2 Spacing of bonded tendons
2
3
4
5
6
7
8
9
10
80
90
100
Minimum cover
The provisions of 4.11.8 concerning spacing of reinforcement apply. In pre-tensioned elements, where
anchorage is achieved by bond, the spacing of the wires or strands in the ends of the elements should
be such as to allow the transmission length given in 5.8.4 to develop. In addition, if the tendons are
positioned in two or more widely spaced groups, the possibility of longitudinal splitting of the element
should be considered.
mm
Duct internal diameter
Radius of
curvature
of duct
5.9.4.3 Spacing of tendons in ducts
mm
19
m
30
40
50
60
70
Tendon force
The clear distance between ducts or between ducts and other tendons should be not less than the
greatest of the following:
kN
a) hagg + 5 mm, where hagg is the nominal maximum size of the coarse aggregate;
296
387
960
1337
1920
2640
3360
4320
5183
50
55
50
155
70
50
220
100
65
320
145
90
445
205
125
265
165
350
220
420
265
55
50
75
65
60
95
85
75
115
100
90
150
120
110
185
140
125
70
85
80
100
95
90
115
110
105
70
80
90
2
4
6
b) in the vertical direction, the vertical internal dimension of the duct; or
c) in the horizontal direction, the horizontal internal dimension of the duct.
8
10
12
Where internal vibrators are used, sufficient space should be provided between ducts to enable the
vibrator to be inserted.
14
16
18
Where two or more rows of ducts are used, the horizontal gaps between the ducts should be vertically
in line wherever possible, for ease of construction.
20
5.9.4.4 Spacing of curved tendons
40
For spacing of curved tendons, see 5.9.5.3.
100
50
50
50
50
60
100
NOTES
5.9.5 Curved tendons
1 The tendon force shown is the maximum normally available for the given size of duct (taken
as 80 % of the characteristic strength of the tendon).
5.9.5.1 General
2 Where tendon profilers or spacers are provided in the ducts, and these are of a type that will
concentrate the radial force, the values given in the table will need to be increased.
Where curved tendons are used in post-tensioning, the positioning of the tendon ducts and the
sequence of tensioning should be such as to prevent
3 The cover for a given combination of duct internal diameter and radius of curvature shown
in the table may be reduced in proportion to the square root of the tendon force when this is less
than the value tabulated, subject to the provisions of 5.9.3.3 and 5.9.3.4.
a) bursting of the cover at the sides of ducts in thin elements,
b) bursting of the cover where the tendons run close to and approximately parallel with the soffit of the
element, and
c) crushing of the concrete that separates tendons in the same vertical plane. (If necessary, provide
reinforcement between ducts.)
5.9.5.2 Cover to curved tendons
5.9.5.3 Spacing of curved tendons
In order to prevent crushing of the concrete that separates the ducts, the minimum spacing between
ducts should be as follows:
a) in the plane of curvature: the distance given in table 40; and
b) perpendicular to the plane of curvature: the distance given in 5.9.4.3.
In order to prevent bursting of the cover perpendicular to the plane of curvature, and in the plane of
curvature, the cover should be in accordance with the values given in table 39.
137
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SABS 0100-1
Ed. 2.2
Table 40 Minimum distance between centre-lines of ducts
in plane of curvature
1
2
3
4
5
6
7
8
9
5.9.6.2 Ensure that any calculation that takes unstressed reinforcement into account will still be in
accordance with 5.3.2.1 and 5.3.3.1.
5.9.6.3 Reinforcement may be necessary, particularly where post-tensioning systems are used, to
control any cracking resulting from the restraint to longitudinal shrinkage of beams that is provided by
the formwork during the time before the prestress is applied.
10
Minimum distance between centre-lines of ducts in plane of curvature
5.9.7 Links in prestressed concrete beams
mm
Radius of
curvature
of duct
m
Duct internal diameter
5.9.7.1 The number and disposition of links in rectangular beams and in the webs of flanged beams
will normally be governed by considerations of shear (see 5.3.4).
mm
19
30
40
50
60
70
80
90
100
5.9.7.2 Provide links to resist the bursting tensile forces in the end blocks of prestressed beams in
accordance with 5.8.5.
Tendon force
5.9.7.3 Provide links in the transmission length of pre-tensioned beams in accordance with the
requirements of 5.3.4 and using the information given in 5.8.4.
kN
2
4
6
296
387
960
1337
1920
2640
3360
4320
5183
110
55
38
140
70
60
350
175
120
485
245
165
700
350
235
960
480
320
610
410
785
525
940
630
90
80
125
100
175
140
60
240
195
160
305
245
205
395
315
265
470
375
315
140
175
160
225
195
180
270
235
210
140
160
180
200
8
10
12
14
16
18
5.9.8 Shock loading
When a prestressed concrete beam may be required to resist shock loading, reinforce it with closed
links and longitudinal reinforcement, preferably of mild steel. Other methods of design and detailing
may be used, provided it can be shown that the beam can develop the required ductility.
6 Precast, composite and plain concrete constructions (design and
detailing)
20
40
38
60
80
100
120
SABS 0100-1
Ed. 2.2
6.1 General
6.1.1 Design objectives
NOTES
This subclause is concerned with the additional considerations that arise in design and detailing when
precast units, including large panels, are incorporated into a structure, or when a structure in its entirety
is of precast concrete construction. It also covers the use of plain concrete for walls.
1 The tendon force shown is the maximum normally available for the given size of duct (taken
as 80 % of the characteristic strength of the tendon).
2 Values less than 2 x the internal diameter of the duct are not included.
6.1.2 Limit states design
3 Where tendon profilers or spacers are provided in the ducts, and these are of a type that will
concentrate the radial force, the values given in the table will need to be
increased. If necessary, reinforcement should be provided between ducts.
6.1.2.1 Basis of design
4 The distance for a given combination of duct internal diameter and radius of curvature shown
in the table may be reduced in proportion to the tendon force when this is less than
the value tabulated, subject to the provisions of 5.9.4.3.
5.9.5.4 Special measures to reduce spacing of ducts
As an exception, it may be possible first to tension and grout the tendon that has the least radius of
curvature, and to allow an interval of 48 h to elapse before tensioning the next tendon. In this case,
the provisions for spacing given in 5.9.4.3 apply.
The limit states philosophy set out in clause 3 also applies to precast in-situ construction and therefore,
in general, the recommended methods of design and detailing for reinforced concrete given in clause 4
and those for prestressed concrete given in clause 5 also apply to precast and composite construction.
Subsections in clauses 4 and 5 that do not apply are either specifically worded for in-situ construction
or are modified by this clause. Provisions for the design and detailing of plain concrete walls are given
in 6.5.
6.1.2.2 Handling stress
Precast units should be designed to resist, without permanent damage, all stresses induced by
handling, storage, transport and erection. (See also 5.3.1.2 and SABS 0100-2.)
5.9.6 Longitudinal reinforcement in prestressed concrete beams
5.9.6.1 Reinforcement may be used in prestressed concrete elements either to increase the strength
of sections or to comply with 5.3.4.3.
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
When necessary, specify the positions of lifting and supporting points. Consultation at the design stage
with those responsible for handling is an advantage. Ensure that the design takes into account the
effects of both snatch lifting from and placing onto supports.
element such as the length between adjacent lateral supports or between a lateral support and a free
edge. For the purposes of this definition of wall length only, a lateral support may be considered to
occur at
6.1.2.3 Connections and joints
a) a stiffened section of the wall (not exceeding 1 m in length) capable of resisting a horizontal force
of 1,5Ft kN per metre height of wall, or
6.1.2.3.1 The design of connections is of fundamental importance in precast construction and should
be carefully considered. The engineer responsible for the overall stability of the structure should ensure
the compatibility of the design and details of components. The responsibility for overall stability shall
be clearly assigned when some or all of the design and details are not worked out by the engineer.
b) a substantial partition at right angles to the wall, provided that it is tied to the wall with a tie force
equal to 0,5Ft kN per metre height of wall (a substantial partition may be taken as one having an
average mass per unit area of at least 150 kg/m2),
6.1.2.3.2 Joints to allow for movement due to shrinkage, thermal effects and possible differential
settlement of foundations are of as great importance in precast as in in-situ construction. Determine
the number and spacing of such joints (see annex B) at an early stage in the design. In the design of
beam and slab ends on corbels and nibs, take particular care to provide overlap and anchorage (in
accordance with 4.11.6 and 4.11.7) of all reinforcement adjacent to the contact faces, taking
constructional tolerances into consideration.
To comply with 6.1.2.4.8.2, ground floor columns that are exposed to the risk of impact by vehicles
and that cannot be allowed to become ineffective, should be so designed as to withstand an
appropriate impact.
6.1.2.4 Stability
6.1.2.4.1 The provisions regarding stability given in 4.1.2 apply also to precast, composite and plain
concrete construction except that, in structures of five storeys or more, supported by plain concrete
walls, it will be necessary to ensure that the area of effective vertical ties from foundation to roof level
is at least 0,2 % of the cross-sectional area of the walls.
6.1.2.4.2 The tie forces referred to in 4.1.2 should be resisted by reinforcement or prestressing
tendons embedded in precast units or in in-situ structural elements or in both, but they should be
effectively continuous.
6.1.2.4.3 Ties should be joined, generally using one of the methods described in 6.3.2, 6.3.3 or 6.3.4.
6.1.2.4.4 Ties connecting precast units should be so arranged as to minimize out-of-balance effects.
where Ft is a tie force as in 4.11.9.4.
6.1.2.4.8.2 Any vertical load-bearing element that cannot be allowed to become ineffective, together
with its connections, shall be so designed as to withstand a load of 34 kN/m2 applied to it from any
direction. Any horizontal element (or any part thereof) that provides lateral support vital to the stability
of that vertical load-bearing element shall be so designed, together with its connections, as to
withstand a load of 34 kN/m2 applied to it from any direction. Any element or lateral support so
designed should also be capable of supporting the reaction from any attached building components
also subject to a loading of 34 kN/m2 or such reaction as might reasonably be transmitted, having
regard to the strength of the attached component and the strength of its connection.
6.1.2.4.9 In order to comply with 3.3.3.2, when a structure is designed in accordance with 6.1.2.2.8.1,
or a vertical load-bearing element is designed in accordance with 6.1.2.2.8.2, take the partial safety
factor for strength m as 1,3 for concrete and 1,0 for steel. The partial safety factor for loads f is 1,05.
6.1.2.4.10 Durability should be considered in the design and detailing of connections.
6.2 Precast concrete construction
6.1.2.4.5 The minimum dimension of any in-situ concrete section in which tie bars are provided should
be not less than the sum of the bar size (or twice the bar size at laps) plus twice the maximum
aggregate size plus 10 mm.
6.2.1 Framed structures and continuous beams
6.1.2.4.6 The tie should be able to transmit the forces from the reinforcement in the precast units and
to develop the required strength at all lapped joints. If enclosing links are used, the ultimate tensile
resistance of the links should be not less than the ultimate tension in the tie.
When the continuity of reinforcement or tendons through the connections or the interaction between
units (or both) is such that the structure will behave as a frame or as a continuous beam, the analysis,
redistribution of moments, and the design and detailing of individual units may all be in accordance
with clause 4 or clause 5, as appropriate.
6.1.2.4.7 Ensure that column and wall ties do not, for their anchorage at either end, rely solely on the
bond of a straight plain bar. So bend or so hook plain bars as to provide the required anchorage in
bearing on sound concrete unless they are welded or mechanically anchored to the main reinforcement
in a precast unit.
6.1.2.4.8 As an alternative to providing the vertical ties recommended above for structures of five
storeys or more, such structures may be designed in accordance with the provisions given below.
6.1.2.4.8.1 So design the structure that, at each storey in turn, if any single vertical load-bearing
element (other than one complying with 6.1.2.4.8.2 becomes incapable of carrying its load, it does not
cause the collapse of the structure or of any significant part thereof. In designing the structure for this
condition, take into account any building components that are otherwise non-load-bearing. When
reliance is placed on catenary action, make allowance for the horizontal reactions necessary for
equilibrium. In the case of a wall, take the length under consideration to be a single load-bearing
141
6.2.2 Slabs
6.2.2.1 Slabs consisting of wide precast units or of a series of narrow precast units with effective
jointing between them capable of shear transfer, may be designed in accordance with 4.4 or 4.5 or
5.4, as appropriate.
6.2.2.2 When assessing the effect of concentrated loads (including partitions in the direction of span),
ensure that the width of slab assumed to contribute to the support of the load does not exceed the
width of the loaded area together with the width of three precast units and joints (when there is no
topping) or the width of four precast units and joints (where the topping is at least 30 mm thick), unless
test results substantiate the use of a wider area. In no case take the width as extending more than
0,25l on either side of the loaded area, where l is the span.
142
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SABS 0100-1
Ed. 2.2
6.2.3 Other precast units
Design and detail other precast concrete units, including large panels, in accordance with the
appropriate provisions of clause 4, clause 5 or subclause 6.5, and make provision for the appropriate
connections as recommended in 6.3.
SABS 0100-1
Ed. 2.2
6.2.4.2.5 Provide shear reinforcement in the form of horizontal links distributed in the upper two-thirds
of the effective depth of the corbel at the column face; ensure that this reinforcement is at least
one-half of the area of the main tension reinforcement, and anchor it adequately.
6.2.4.2.6 Corbels should be designed for shrinkage and temperature stresses.
Design precast units intended for use in composite constructions (see 6.4) as such, but also check or
design for the conditions arising during handling, transportation and erection. In a floor or roof
construction of hollow blocks supported by precast concrete ribs, pay particular attention to the bearing
of blocks on the ribs when no topping is provided.
6.2.4.3 Continuous concrete nibs
6.2.4 Bearings for precast units
6.2.4.3.1 Ensure that the projection of the nib is sufficient to provide an adequate bearing width for
the type of unit to be supported (see 6.2.4.4). Give the reinforcement in the nib and any reinforcement
in the supported unit a minimum nominal overlap in plan of 60 mm.
6.2.4.1 Terms relating to bearings for precast units
The following terms relate to bearings for precast units:
a) simple bearing: a supported unit bears directly on a support, the effect of projecting steel or added
concrete being discounted;
b) dry bearing: a bearing with no intermediate padding material;
c) bedded bearing: a bearing with contact surfaces that have an intermediate padding of
cementitious material;
d) non-isolated unit: a supported unit that, in the event of loss of an assumed support, would be
capable of carrying its load by transverse distribution to adjacent units;
e) bearing length: the length of support, supported unit or intermediate padding material (whichever
is the least) measured along the line of support (see figure 27); and
f) bearing width: the overlap of support and supported unit, measured at right angles to the line of
support (see figure 27).
6.2.4.2 Concrete corbels
6.2.4.2.1 A corbel is a short cantilever beam in which the principal load is so applied that the distance
av between the line of action of the load and the face of the supporting element is less than d (where
d is the effective depth of the corbel at the face of the supporting element), and the depth at the outer
end of the beam is at least one-half of the depth at the face of the supporting element.
6.2.4.2.2 Determine the depth at the face of the supporting element from shear conditions in
accordance with 4.3.4.2 but limit av as specified above.
6.2.4.2.3 Design the main tension reinforcement in a corbel and check the strength of the corbel on
the assumption that it behaves as a simple strut-and-tie system. Ensure that the reinforcement so
obtained is at least 0,4 % of the section at the face of the supporting element and is adequately
anchored. At the front face of the corbel, anchor the reinforcement either by welding to a transverse
bar of equal strength or by bending the bars backwards to form a loop; in the latter case, ensure that
the bearing area of the load does not project beyond the straight portion of the bars forming the main
tension reinforcement.
6.2.4.2.4 When the corbel is designed to resist a stated horizontal force, provide additional
reinforcement to transmit this force in its entirety; weld the reinforcement to the bearing plate and
anchor it adequately within the supporting element.
143
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Where a continuous nib less than 300 mm deep provides a bearing, as on a boot lintel, design the
nib as a short cantilever slab in accordance with the provisions given below:
6.2.4.3.2 Assume the line of action of the design load to occur at the outer edge of the loaded area,
i.e. at the front edge of the nib, or at the beginning of the chamfered edge, or at the outer edge of the
bearing pad, as appropriate.
6.2.4.3.3 Take the maximum design bending moment as the distance from the line of action of the
load to the nearest vertical leg of the links in the beam element from which the nib projects, times the
load. (Ensure that the tension reinforcement in the nib is at least that required by 4.11.4, and anchor
the reinforcement adequately.)
6.2.4.3.4 Extend the tension reinforcement (the area of the reinforcement being not more than that
given in 4.11.5) as near to the front face of the nib as considerations of adequate cover will allow, and
anchor it there, either by welding to a transverse bar of equal strength or by bending the bars through
180 to form loops in the horizontal or vertical plane (ensure that vertical loops are of a bar diameter
not exceeding 12 mm).
6.2.4.3.5 Provide links in the element from which the nib projects. The links should be capable of
transmitting (in addition to any other forces they resist) the load from the nib to the compression zone
of the element.
6.2.4.4 Bearings for precast units
6.2.4.4.1 General
Ensure that the bearing width (see 6.2.4.1(f)) of precast units is sufficient to provide
a) a proper anchorage of the tension reinforcement (see 4.11.7), and
b) a proper restraint against loss of bearing through movement. Do not use direct bearing connections
as column/column or wall/wall connections, either with or without flexible padding.
6.2.4.4.2 Calculation of net bearing width
For non-isolated units (see 6.2.4.1(d)), the net bearing width should be the greater of 40 mm and the
value calculated from the equation:
net bearing width =
design ultimate support reaction per unit
(design effective bearing length x design ultimate bearing stress)
where the design effective bearing length is as in 6.2.4.4.3 and the design ultimate bearing stress is
as in 6.2.4.4.4. For isolated units, the net bearing width should exceed that of non-isolated units
(see 6.2.4.1(d)) by 20 mm.
144
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
6.2.4.4.3 Design effective bearing length
In the equation given in 6.2.4.4.2, the effective bearing length is the least of
a) bearing length per element,
b) one-half of bearing length per element plus 100 mm, and
c) 600 mm.
6.2.4.4.4 Design ultimate bearing stress
The design ultimate bearing stress is based on the weaker of the bearing surfaces and has the
following value:
a) for dry bearing on concrete: 0,4 fcu (an allowance for
m
included);
b) for bedded bearing on concrete: 0,6 fcu (an allowance for
m
included);
c) for the concrete face of a steel bearing plate cast into a unit or support and not exceeding
40 % of the bearing length: 0,8 fcu (an allowance for m included).
Bearings using flexible padding may be designed using stresses intermediate between those for dry
and for bedded bearings.
6.2.4.5 Spalling at supports
The outer edges of the concrete interface of precast units and the bearings are subject to spalling.
Chamfers occurring within areas subject to spalling may be ignored when the outer edge of a
supporting unit or the end of a supported unit is being determined (see figure 27). The
recommendations for allowances for effects of spalling at supports and at the end edges of supported
units are given below.
6.2.4.5.1 The distances to be assumed ineffective as bearing surfaces for the outer edges of supports
in relation to the material of the support:
a) steel: nil;
b) concrete grade 30 or higher, plain or reinforced: 15 mm;
Figure 27 — Schematic arrangement of allowance for bearing
6.2.4.5.2 The distances to be assumed ineffective as bearing surfaces for the end edges of supported
units in relation to the reinforcement at bearing of the supported unit:
a) straight bars, horizontal loops or vertical loops not exceeding 12 mm in diameter, close to end of
element: the greater of 10 mm or cover;
c) brickwork or masonry: 25 mm;
b) tendons or straight bars exposed at end of element: nil; and
d) concrete of a grade lower than grade 30, plain or reinforced: 25 mm;
e) reinforced concrete less than 300 mm deep at the outer edge: not less than the nominal cover to
reinforcement on the outer face of the support; and
f) reinforced concrete where vertical-loop reinforcement exceeds 12 mm diameter: nominal end cover
plus inner radius of bend. Where unusual spalling characteristics are known to apply when
particular constituent materials are being used, adjustment should be made to the distances
recommended.
c) vertical-loop reinforcement of bar size exceeding 12 mm: nominal end cover plus inner radius of
bend.
6.2.4.6 Allowance for construction inaccuracies
The allowance for construction inaccuracies should cover deviations that can occur during the
assembling of components, site construction, manufacture and erection, and may be assessed from
a statistical analysis of measured or predicted deviation. Alternatively, for supported members of span
up to 15 m and with average standards of accuracy, the allowance may be taken as the greatest of:
a) 15 mm, or 3 mm per metre of distance between the faces of steel or precast concrete supports;
145
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SABS 0100-1
Ed. 2.2
b) 20 mm, or 4 mm per metre of distance between the faces of masonry supports; and
SABS 0100-1
Ed. 2.2
6.2.5.2.2 Pay particular attention to detailing the joint and joint reinforcement to prevent premature
splitting or spalling of the concrete in the ends of the precast units.
c) 25 mm, or 5 mm per metre of distance between the faces of in-situ concrete supports.
6.2.5.2.3 Where a wall or a column is subjected to lateral loads, design the horizontal joints for shear
in accordance with 6.5.3.14.
6.2.4.7 Horizontal forces or rotation at a bearing
The presence of horizontal forces at a bearing can reduce the load-carrying capacity of the supporting
unit considerably by causing premature splitting or shearing. These forces may be due to creep,
shrinkage, and temperature effects, or may result from misalignment, lack of plumb or other causes.
When they are likely to be significant, consider these forces in designing and detailing the joints by
providing
6.2.5.3 Joints transmitting shear in slabs
a) either sliding bearings or suitable lateral reinforcement in the top of the supporting unit, and
6.2.5.3.1 Floor units transmitting shear in a horizontal plane should be restrained to prevent their
moving apart horizontally, and the joints between them should be formed by grouting with a suitable
concrete or mortar mix. When the calculated shear stress in the joint under ultimate loads does not
exceed 0,23 MPa, no reinforcement need be provided in or across the joint, and the sides of the unit
forming the joint may have the normal finish.
b) continuity reinforcement to tie together the ends of the supported units.
Where, owing to large spans or other reasons, large rotations are likely to occur at the end supports
of flexural units, use bearings that are capable of accommodating these rotations.
6.2.5 Joints between precast units
6.2.5.1 General
6.2.5.1.1 Design the critical sections of precast units close to joints to resist the worst combinations
of shear, axial force and bending caused by the ultimate vertical and horizontal forces. When the
design of the units is based on the assumption that the joint between them is not capable of
transmitting moment, either design the joint to ensure that this is so (see 6.2.4.7) or take suitable
precautions to ensure that if any cracking develops, it will not be unsightly and will not excessively
reduce the unit's resistance to shear or axial force.
6.2.5.1.2 Where a space is left between two or more precast units, which is to be filled later with in-situ
concrete or mortar, make the space large enough for the filling material to be placed easily and
compacted sufficiently to fill the gap without abnormally high standards of workmanship or
supervision. The assembly instructions shall specify clearly at what stage during construction the gap
should be filled.
As the majority of joints will incorporate a structural connection (see 6.3), give consideration to this
aspect in the design of the joint.
6.2.5.2 Joints transmitting mainly compression
6.2.5.2.1 A joint that transmits mainly compression is most commonly used for horizontal joints
between load-bearing walls or columns. Design the joint to resist all the forces and moments implicit
in the assumptions made in analysing the structure as a whole and in designing the individual units to
be joined. In the absence of more accurate information derived from a comprehensive programme of
suitable tests, the area of concrete to be considered when the strength of the joint in a wall or column
is being calculated, should be the greater of
a) the area of the in-situ concrete, ignoring the area of any intruding floor or beam units (but not more
than 90 % of the wall or column area), and
b) 75 % of the area of contact between wall or column and joint.
Consider only those parts of the floor units that are solid over the bearing, and bed the units properly
on concrete or mortar of adequate quality.
147
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A joint may be assumed to transmit a shear force between panels when, for example, a wall acts as
a wind-bracing wall or a floor acts as a wind girder, provided that one of the provisions given below
is complied with.
6.2.5.3.2 When the sides or ends of the panels or units forming the joints have a finish "as-extruded"
(see table 42), and when the shear stress due to ultimate loads does not exceed 0,45 MPa, no
reinforcement need be provided in joints that are under compression in all loading conditions.
6.2.5.3.3 The shear stress due to design ultimate loads, calculated on the minimum root area of a
castellated joint, should be less than 1,3 MPa. Separation of the units normal to the joint should be
prevented either by the provision of steel ties across the ends of the joint or by the provision of a
compressive force normal to the joint under all loading conditions. A taper should usually be provided
to the projecting keys of a castellated joint to ease the removal of formwork; to limit movements in the
joint, ensure that this taper is not excessive.
6.2.5.3.4 When reinforcement is provided to resist the entire shear force due to design ultimate loads,
the shear force V should comply with the following equation:
V = 0,6 Fb tan
f
where
Fb is the lesser of 0,87fyAs or the anchorage value of the reinforcement;
As is the minimum area of reinforcement;
fy is the characteristic strength of reinforcement; and
f
is the angle of internal friction between faces of joint.
Tan f can vary between 0,7 and 1,7 and is best determined by tests. However, for
concrete-to-concrete connections, the following values may be assumed:
a) tan
f
= 0,7 for a smooth interface, as in untreated concrete;
b) tan f = 1,4 for a roughened or castellated joint without continuous in-situ strips across the ends of
joints; and
c) tan f = 1,7 for a roughened or castellated joint with continuous in-situ strips across the ends of
joints.
148
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SABS 0100-1
Ed. 2.2
6.2.5.4.6 If the main reinforcement is hooked or bent vertically, anchor the inclined links by bending
them parallel to the main reinforcement; in this case, or if inclined links are replaced by bent-up bars,
ensure that the bearing stress within the bends does not exceed the value given in 4.11.6.9. Bent-up
bars may only be used to replace inclined links when effective end anchorage is possible (by means
of welded cross-bars or other positive anchorage device).
F
v bd
b
d
6.2.5.4.7 Ensure that horizontal links are capable of carrying horizontal loads that may be applied to
the joint in addition to the forces arising from the vertical reaction.
v
F
6.2.5.4.8 Place vertical links at the end of the full-depth section as near to the end face as possible.
6.3 Structural connections between units
F
6.3.1 General
6.3.1.1 Structural requirements for connections
When designing and detailing the connections across joints between precast units, consider the overall
stability of the structure, including its stability during construction or after accidental local damage.
Take the provisions given in 6.1.2.4 into account and, in addition, consider the severe forces and
stresses that may be applied to units during the various stages of handling, transportation and erection.
Tie all units together adequately as soon as they have been placed in their final positions. When
prestressed elements are built into supports, restrained creep effects should be considered.
F
A
f
F
A
f
6.3.1.2 Design method
Design connections in accordance with the generally accepted methods applicable to reinforced
concrete (see clause 4), prestressed concrete (see clause 5) or structural steel. Where, by the nature
of the construction or material used, such methods are not applicable, prove the efficiency of the
connection by appropriate tests in accordance with 3.4.5.
A
f
6.3.1.3 Considerations affecting design details
In addition to ultimate strength requirements and the provisions given in 6.1.2.4 regarding minimum
tying together of the structure, consider the provisions given below.
F
6.3.1.3.1 Protection
F
So design connections that the standard of protection against weather, fire and corrosion that is
required for the remainder of the structure is maintained.
F
6.3.1.3.2 Appearance
u l
Where connections are to be exposed, so design them that the quality of appearance required for the
remainder of the structure can be readily achieved. This may often be better done by emphasizing the
connections rather than by attempting to conceal them.
u
l
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
6.3.1.3.3 Manufacture, assembly and erection
6.3.2 Continuity of reinforcement
During design, consider methods of manufacture, assembly and erection, and give particular attention
to the following points:
6.3.2.1 General requirements
a) where projecting bars or sections are required, keep them to a minimum and make them as simple
as possible; make such projections no longer than is necessary for security;
Where continuity of reinforcement is required through the connection, use a jointing method such that
the assumptions made in analysing the structure and critical sections are realized. The following
methods may be used to achieve continuity of reinforcement:
b) avoid fragile fins and nibs;
a) lapping of bars;
c) locate fixing devices of adequate strength in concrete sections;
b) sleeving;
d) consider the practicability of both casting and assembly;
c) threading of bars;
e) most connections require the introduction of suitable jointing material; in the design, allow sufficient
space for such material to ensure that the proper filling of the joint is practicable;
d) welding; and
f) it may be desirable to slacken, release or remove levelling devices such as nuts, wedges, etc., that
have no load-bearing function in the completed structure; where this is necessary, ensure that the
details are such that inspection (to make certain that this has been done) can be carried out without
undue difficulty.
6.3.1.4 Site instructions
6.3.1.4.1 The strength and stiffness of any connection can be significantly affected by workmanship
on site. The diversity of types of joints and their critical role in the strength and stability of the structure
place a particular responsibility on the designer to make clear to those responsible for manufacture
and erection, those details that are essential to the correct operation of the joint.
6.3.1.4.2 Consider the following points and, where necessary, pass specific instructions to the site:
a) the sequence of forming the joint;
b) critical dimensions, allowing for permitted deviations, e.g. minimum permissible bearing;
e) any other method proven by tests in accordance with 3.4.5.
6.3.2.2 Lapping of bars
Where straight bars passing through the joint are lapped, the provisions given in 4.11.6.6 apply. When
reinforcement is grouted into a pocket or recess, provide an adequate shear key on the inside of the
pocket.
Where continuity over a support is achieved by having dowel bars pass through overlapping loops of
reinforcement (which project from each supported element), make the bearing stresses inside the
loops in accordance with 4.11.6.9.
6.3.2.3 Sleeving
6.3.2.3.1 Three principal types of sleeve jointing may be used, provided that the strength and
deformation characteristics have been determined by tests in accordance with 3.4.5. The three types
are
a) grout-filled or resin-filled sleeves capable of transmitting both tensile and compressive forces;
c) critical details, e.g. accurate location of a particular reinforcing bar;
b) sleeves that mechanically align the square-sawn ends of two bars to allow the transmission of
compressive forces only; and
d) the method of correcting possible lack of fit in the joint;
e) details of temporary propping, and the stage at which it may be removed (see the relevant clause
of SABS 0100-2);
f) the description of the general stability of the structure, with details of any temporary bracing
necessary;
g) the extent to which the uncompleted structure may proceed above the completed and matured
section;
h) full details of special materials; and
i) the weld sizes, fully specified (where weld symbols are used, ascertain that these are understood
on site).
151
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c) swaged connectors.
6.3.2.3.2 Ensure that the detailed design of the sleeve and the method of manufacture and assembly
are such that the ends of the two bars will be accurately aligned into the sleeve. Ensure that the
concrete cover provided for the sleeve is at least that specified for normal reinforcement.
6.3.2.4 Threading
6.3.2.4.1 The following methods may be used for jointing threaded bars:
a) the threaded ends of bars may be joined by a coupler having left-hand and right-hand threads; this
type of threaded connection requires a high degree of accuracy in manufacture in view of the
difficulty of ensuring alignment;
152
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SABS 0100-1
Ed. 2.2
b) one set of bars may be welded to a steel plate, which is drilled to receive the threaded ends of the
second set of bars; the second set of bars is fixed to the plate by means of nuts; and
c) threaded anchors may be cast into a precast unit to receive the threaded ends of reinforcement.
6.3.2.4.2 When there is a risk of the threaded connection working loose, e.g. during vibration while
in-situ concrete is being cast, use a locking device.
6.3.2.4.3 Restrict the threading of reinforcement to plain round mild steel bars. Where there is
difficulty in producing a clean thread at the end of a bar, use steel that is normally specified for black
bolts and that has a characteristic strength of 430 MPa.
6.3.2.4.4 Base the structural design of special threaded connections on tests in accordance with 3.4.5.
Where tests have shown the threaded connection to be at least as strong as the parent bar, the
strength of the joint may be based on 80 % of the specified characteristic strength of the joined bars
in tension and on 100 % of that of bars in compression, divided in each case by the appropriate m
factor.
6.3.2.5 Welding of bars
The design of welded connections may be in accordance with 4.11.6.7, provided that the welding is
carried out as recommended in the relevant clause of SABS 0100-2.
6.3.3 Connections with structural steel inserts
6.3.3.1 Joints with structural steel inserts generally consist of a steel plate or rolled steel section
projecting from the face of a column to support the end of a beam. Design the reinforcement in the
ends of the supported beam in accordance with clause 4.
6.3.3.2 Design the steel sections and any bolted or welded connections in accordance with
SABS 0162. Bearing stresses of up to 0,8fcu may be used, unless higher values can be justified by
means of tests.
f
6.3.3.3 Except where the design ensures that the reaction does not act at the end of the steel section,
base the design of the supported unit on a span equal to its overall length, including any projecting
steel sections. For the design of the supporting unit and its projecting steel section, assume that the
reaction is applied at the end of the projecting steel section.
6.3.3.4 In the design, consider the possibility of vertical splitting under the steel section due to
shrinkage effects and localized bearing stresses, e.g. under a narrow steel plate.
6.3.4 Other types of connection
Any other type of connection that can be shown to be capable of carrying the ultimate loads acting on
it may be used. Amongst those suitable for resisting shear and flexure are those made by prestressing
across the joint.
Resin adhesives may be used to form joints subjected to compression but may not be used to resist
tension or shear. Use them only where they are adequately protected from the effects of fire.
153
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SABS 0100-1
Ed. 2.2
analysis may be as given in 5.3.3. However, the compressive stresses in the precast unit at the
interface may be increased by not more than 50 % above the value given in table 29, provided that
the ultimate failure of the composite element is due to excessive elongation of the steel.
a
6.4.3.3 Tension in the concrete in the case of prestressed precast units
When there is a danger of corrosion (e.g. if there is non-prestressed reinforcement in the in-situ
concrete), the flexural tensile stress in the in-situ concrete should be limited by crack control
Amdt 1, Apr. 1994
measures, in accordance with 4.3.7.
|
|
|
Table 41 Deleted by amendment No. 1.
|
Where continuity is obtained with reinforced concrete cast in-situ over the supports, the flexural tensile
stresses and the hypothetical tensile stresses in the precast prestressed units at the supports should
Amdt 1, Apr. 1994
be limited in accordance with 5.3.2.3.
|
M
6.4.3.4 Differential shrinkage
6.4.3.4.1 The effects of differential shrinkage are not generally of great importance in simply
supported elements. However, where there is an appreciable difference between the age and quality
of the concrete in the components, differential shrinkage may lead to increased stresses in the
composite section and these must be investigated. The effects of differential shrinkage are likely to
be more severe when the precast component is of reinforced concrete or of prestressed concrete with
an approximately triangular distribution of stress due to prestress. In particular, the tensile stresses
due to differential shrinkage may require consideration in design, and the engineer should refer to
specialist literature in deciding when these stresses may be significant.
e
e
e
6.4.3.4.2 In the calculation of the tensile stresses, a value will be required for the differential shrinkage
coefficient (the difference in total free strain between the two components of the composite element),
the magnitude of which will depend on many variables. For a structure in a normal environment, and
in the absence of more exact data, assume a value of 100 x 10-6 for the differential shrinkage when
calculating stresses in composite T-beams with an in-situ concrete flange.
6.4.3.5 Continuity in composite construction
6.4.3.5.1 When continuity is obtained in composite construction by providing reinforcement over the
supports, give consideration to the secondary effects of differential shrinkage and creep on the
moments in continuous beams and on the reactions at the supports. Take the hogging restraint
moment Mcs at an internal support of a continuous composite beam and slab section due to differential
shrinkage as
Mcs
=
diff
EcfAcfacent
(19)
where
diff
is the differential shrinkage strain;
Ecf
is the modulus of elasticity of the flange concrete;
Acf
is the area of effective concrete flange;
v
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bv
A
f
b
v
f
l
l
l
l
l
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The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
where lo is the clear height of the wall between lateral supports; for gable walls, lo may be measured
midway between eaves and ridge.
6.5.3.3 Effective height of braced plain concrete walls
The effective height of braced plain concrete walls should be taken as follows:
a) where the lateral supports provide resistance both to lateral movement and to rotation, le equals
three-quarters of the clear distance between lateral supports or twice the distance between a
support and a free edge, as appropriate;
NOTE This distance is measured vertically if the lateral supports are horizontal (e.g. floors) or horizontally if the
lateral supports are vertical (e.g. other walls).
b) where the lateral supports provide resistance to lateral movement only, le equals the distance
between centres of supports, or two and a half times the distance between a support and a free
edge, as appropriate.
6.5.3.4 Limits of slenderness
SABS 0100-1
Ed. 2.2
6.5.3.7.2 Loads may be applied to walls at eccentricities exceeding half the thickness of the wall by
means of special fittings (e.g. joist hangers), provided that the adequacy of such fittings against local
failure is proved by testing or other means.
6.5.3.7.3 The resultant eccentricity of the total load on a braced wall at any level may be calculated
on the assumption that, immediately above a lateral support, the resultant eccentricity of all the vertical
loads above that level is zero.
6.5.3.8 In-plane and transverse eccentricity of resultant force on an unbraced wall
At any level, full allowance should be made for the eccentricity of all vertical loads and the overturning
moments produced by any lateral forces above that level.
6.5.3.9 Concentrated loads
When loads are purely local (as at beam bearings), they may be assumed to be immediately
dispersed, provided that the local design stress under the load does not exceed 0,6fcu for concrete of
grade 25 or higher, or 0,5fcu for concrete of a lower grade.
6.5.3.10 Calculation of design load per unit length
The slenderness ratio le/h should not exceed 30, whether the wall be braced or unbraced.
The design load per unit length nw should be assessed on the basis of a linear distribution of load along
the length of the wall, with no allowance for any tensile strength.
6.5.3.5 Minimum transverse eccentricity of forces
Whatever the arrangements of vertical or horizontal forces, the resultant force in every plain concrete
wall should be assumed to have a transverse eccentricity of the greater of at least h/20 or 20 mm. In
the case of a slender wall, additional eccentricity can arise as a result of deflection under load.
Procedures allowing for this are given in 6.5.3.12 and 6.5.3.13.
6.5.3.6 Eccentricity in the plane of the wall
6.5.3.11 Maximum unit axial load for short braced plain walls
The maximum design ultimate axial load per unit length of wall due to ultimate loads, nw, should satisfy
the following equation:
nw < 0,3 (h - 2ex) fcu
6.5.3.6.1 In the case of a single wall in-plane
(20)
where
Eccentricity due to forces may be calculated by statics alone.
nw is the maximum design axial load per unit length of wall due to design ultimate loads;
6.5.3.6.2 In a case where a horizontal force is resisted by two or more parallel walls
h
The force should be assumed to be shared between the walls in proportion to their relative stiffnesses,
provided the resultant eccentricity in any individual wall does not exceed one-third of the length of that
wall.
is the thickness of wall;
ex is the resultant eccentricity of load at right angles to plane of wall (see 6.5.3.5 for minimum
value); and
fcu is the characteristic strength of concrete.
Where the eccentricity in any individual wall is found to exceed this, the wall stiffness should be
regarded as zero and an adjustment made to the forces that are assumed to be carried by the
remaining wall(s).
6.5.3.12 Maximum unit axial load for slender braced plain walls
6.5.3.6.3 In the case of a shear connection being assumed between vertical edges of adjacent
walls
At every section of a slender braced wall, the maximum design axial load nw should satisfy
equation (20) and, additionally, the following:
An appropriate elastic analysis may be made, provided the shear connection is designed to resist the
design ultimate forces.
nw < 0,3 (h - 1,2ex - 2ea) fcu
(21)
where
6.5.3.7 Eccentricity at right angles to the wall
6.5.3.7.1 The load transmitted to a wall by a concrete floor or roof may be assumed to act at one-third
of the depth of the bearing area from the loaded face. Where there is an in-situ concrete floor on either
side of the wall, the common bearing area may be assumed to be shared equally by each floor.
159
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nw, h, ex and fcu are as in 6.5.3.11; and
ea is the additional eccentricity due to deflections, which may be taken as le2/2 500 where le is the
effective height of the wall.
160
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The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
6.5.3.13 Maximum unit axial load for unbraced plain walls
The maximum unit axial load at every section of an unbraced plain wall should satisfy the following
two conditions:
a) nw < 0,3 (h - 2ex1) fcu
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The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
horizontal and vertical directions; it should consist of bars of small diameter, relatively closely
spaced, with adequate cover near the exposed surface (see also 6.5.3.15);
b) in an internal wall it may only be necessary to provide reinforcement in that part of the wall where
junctions with floors and beams occur, in which case it should be equally dispersed between each
face (see also 6.5.3.15).
6.5.3.17.2 In general, it will not be necessary to provide reinforcement to counteract shrinkage and
temperature effects in walls made of no-fines concrete.
b) nw < 0,3 [h - 2(ex2 + ea)] fcu
where
6.5.3.18 Reinforcement around openings in plain walls
nw, h, ea, and fcu are as in 6.5.3.11 and 6.5.3.12;
Nominal reinforcement should be considered.
ex1 is the resultant eccentricity calculated at top of wall (see 6.5.3.7); and
6.5.3.19 Deflection of plain concrete walls
ex2 is the resultant eccentricity calculated at bottom of wall (see 6.5.3.7).
6.5.3.14 Shear strength
The design shear resistance of plain walls need not be checked if one of the following conditions is
satisfied:
a) the horizontal design shear force is less than one-quarter of the design vertical load; or
b) the horizontal design shear force is less than that required to produce an average design shear
stress of 0,45 MPa over the whole wall cross-section.
NOTE For concrete of grades lower than grade 25 and for lightweight aggregate concrete, the figure of 0,30 MPa
should be used instead of 0,45 MPa.
The deflection in a plain concrete wall will be within acceptable limits if the preceding provisions have
been conformed to and if, in the case of a cantilever shear wall, the total height of the wall does not
exceed ten times its length.
7 Fire resistance
7.1 General
7.1.1 When a structural concrete element is subjected to fire, it undergoes a gradual reduction in
strength and rigidity. For limit state design, therefore (as stated in 3.2.4.3), there are three conditions
to be considered:
6.5.3.15 Cracking of concrete
a) retention of structural strength;
Reinforcement may be needed in walls to control cracking due to flexure or thermal and hydration
shrinkage (see 6.5.3.16 to 6.5.3.18). Wherever reinforcement is provided, the quantity should be:
b) resistance to penetration of flames; and
a) for reinforcement of grade 450: at least 0,25 % of the concrete cross-sectional area; and
c) resistance to heat transmission.
b) for reinforcement of grade 250: at least 0,30 % of the concrete cross-sectional area.
The first criterion is applicable to all structural elements while the other two criteria are applicable to
walls and floors, which perform a separating function.
6.5.3.16 Reinforcement in plain walls for flexure
7.1.2 The requirements for fire resistance for various elements in a structure are either checked by
If, at any level, a length of wall exceeding one-tenth of the total length is subjected to tensile stress
resulting from in-plane eccentricity of the resultant force, vertical reinforcement may be necessary to
distribute potential cracking. Reinforcement need only be provided in the area of wall found to be in
tension under design service loads. It should be arranged in two layers and should comply with the
spacing rules given in 4.11.8.2.
6.5.3.17 Reinforcement in plain walls to counteract cracks resulting from shrinkage and
temperature
6.5.3.17.1 Plain concrete walls that exceed 2 m in length and are cast in-situ, may have to be
reinforced to control cracking arising from shrinkage and temperature effects, including temperature
rises caused by the heat of hydration released by the cement. Reinforcement for this purpose should
be considered as follows:
a standard test on a specimen or satisfied by suitable choices based on the data given in this clause.
NOTE Standard fire tests are not intended to give information on the use of an element after it has been subjected to
fire.
7.1.3 The following factors influence the fire resistance of concrete structures (some of these factors
cannot be taken into account quantitatively):
a) the size and shape of the element;
b) the type of concrete;
c) the type of reinforcement or tendon;
d) the protective concrete cover provided to reinforcement or tendons (see 7.1.9);
a) in an external plain wall directly exposed to the weather, reinforcement should be provided in both
161
162
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© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
© SABS. This non-printable standard is exclusively for approved users of the SABS’ Complete Collection of Standards and Related Documents.
The standard must reside on an internal network or intranet and may only be used for reference purposes in compliance with SABS
copyright rules. The standard or parts thereof may not be distributed in any form without permission from the SABS.
SABS 0100-1
Ed. 2.2
e) the load supported; and
SABS 0100-1
Ed. 2.2
Vermiculite slabs
f) the conditions of restraint.
7.1.4 Concretes made with siliceous aggregates have a tendency to spall when exposed to high
temperatures but this tendency can be reduced by the incorporation of supplementary reinforcement
in the concrete cover. Spalling does not generally occur with either calcareous or lightweight
aggregates. The insulation properties of concrete made from lightweight aggregates are superior to
those of concrete made from siliceous and calcareous aggregates. Other measures that may be taken
to prevent spalling from occurring are
a) a finish of plaster, vermiculite, etc., applied by hand or sprayed;
b) the provision of a false ceiling as a fire barrier; and
1,0 x concrete thickness; < 2 h
1,5 x concrete thickness; > 2 h
(See also table 47 for the effect of soffit treatment on the fire resistance of slabs.)
7.2 Beams
7.2.1 The fire resistance of a reinforced or prestressed concrete beam depends on the amount of
protective cover, consisting of concrete with or without an insulating encasement, provided to the
reinforcement or tendons. It is also necessary that the beam have a minimum width to avoid failure
of the concrete before the reinforcement or tendons reach the critical temperature. For -beams, the
web thickness bw of a fully exposed beam should be at least 0,5 of the minimum width stated in tables
43 and 44 for the fire resistance of various beams.
7.2.2 Typical performances are given in table 43 for reinforced concrete beams and in table 44 for
c) the use of sacrificial tensile steel.
7.1.5 Concrete, prestressing tendons, and reinforcement show a reduction in strength at high
temperatures. At about 400 C, tendons are likely to lose about 50 % of their strength at ambient
temperature and in the case of reinforcement, a similar reduction in strength occurs at about 550 C.
7.1.6 The fire resistance of structural elements is generally determined when the element is
supporting its service load, which is taken as the sum of all the nominal self-weight and imposed loads.
Tables 43 to 46 show the minimum dimensions for various elements when these loads are to be
supported; any reduction in load will be reflected by an increase in fire resistance, but there are not
sufficient data available to define the relationship.
7.1.7 Recent investigations have shown that the provision of end restraint against thermal expansion
can substantially increase the fire resistance of a structural element. Until this aspect is more fully
investigated, it is proposed that in beams and slabs so built into a structure that restraint against
thermal expansion caused by fire would be provided at two opposite ends, the amount of protective
cover to reinforcement and tendons be reduced to the value shown for the next lower period in tables
43 to 46. Thermal restraint can be assumed to be provided by the surrounding structure if no gaps or
combustible materials exist between the structure and the ends of the floor or beam and if the
surrounding structure is capable of withstanding the thermal stresses induced by the heated floor or
beam.
7.1.8 In tables 43 to 50 (inclusive), the "minimum dimension" and the "minimum thickness" quoted
are all recommended dimensions that are subject to the dimensional deviations given in SABS 0100-2.
prestressed concrete beams, both for siliceous aggregate concrete and for low-density aggregate
concrete.
7.2.3 The average concrete cover is determined by summing the product of the cross-sectional area
of each bar or tendon and the distance from the surface of the bar to the nearest relevant exposed
face, and dividing the sum by the total area of these bars or tendons. Only those bars or tendons
provided for the purpose of resisting tension due to ultimate loads should be considered in this
calculation. When reinforcement is used in combination with tendons, its total area should be used.
7.2.4 Tables 43 and 44 give the average concrete cover required to provide the stated fire resistance,
but in no case may the nominal concrete cover to any bar or tendon be less than half this value, or less
than the value given for the half-hour period appropriate to that form of construction.
7.2.5 In addition, in certain cases where siliceous aggregate concrete is used, it will be necessary to
consider the provision of supplementary reinforcement to hold the concrete cover in position.
7.2.6 Supplementary reinforcement will be required in those cases indicated in tables 43 and 44
where the cover to all the bars and tendons under consideration exceeds 40 mm. When used,
supplementary reinforcement shall consist of expanded metal lath or a wire fabric not lighter than
0,5 kg/m2 (2 mm diameter wires at centres not exceeding 100 mm) or a continuous arrangement of
links at centres not exceeding 200 mm, incorporated in the concrete cover at a distance not exceeding
20 mm from the face.
7.1.9 Where plaster or sprayed fibre is used as an applied finish to elements other than the ones in
tables 43 to 50, it may be assumed that the thermal insulation provided is at least equivalent to the
same thickness of concrete. Such finishes can therefore be used to remedy deficiencies in cover
thickness. For selected materials, the following guidance can be given with respect to allowing the use
of additional protection not exceeding 25 mm in thickness as a means of providing effective cover to
steel reinforcing or prestressing elements. In each case, the equivalent thickness of concrete may be
replaced by the protection named.
Mortar
Gypsum plaster
0,6 x concrete thickness
Lightweight plaster
1,0 x concrete thickness; < 2 h
Sprayed lightweight
insulation
2,0 x concrete thickness; > 2 h
163
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164
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Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . .
Thickness under cores . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . .
Thickness of bottom flange . . . . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . .
Width of rib, or beam, at soffit . . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to reinforcement . . . . . . . . . . . . . . .
Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . .
Least width of downstanding leg . . . . . . . . . . . . . . . . . . . .
Thickness of flange*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to reinforcement . . . . . . . . . . . . . . .
Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . .
Least width of each downstanding leg . . . . . . . . . . . . . . . .
Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to reinforcement . . . . . . . . . . . . . . .
Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . .
Least width of each downstanding leg . . . . . . . . . . . . . . . .
Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
b) Cored slabs in which the cores are circular or are higher than
they are wide. Not less than 50 % of the gross cross-section of
the floor should be solid material
c) Hollow box sections having one or more longitudinal cavities,
which are wider than they are high
d) Ribbed floors having hollow infill blocks of clay, or inverted Tsection beams with hollow infill blocks of concrete or clay. A
floor in which less than 50 % of the gross cross-section is solid
material shall be provided with a 15 mm plaster coating on
soffit
e) Upright T-sections
Inverted channel sections with radius at intersection of soffits
with top of leg not exceeding depth of section
f)
g) Inverted channel sections or U-sections with radius at
intersection of soffits with top of leg exceeding depth of section
5
167
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Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . .
Width of rib, or beam, at soffit . . . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to tendons . . . . . . . . . . . . . . . . . . . .
Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . .
Least width of downstanding leg . . . . . . . . . . . . . . . . . . . . .
Thickness of flange*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to tendons . . . . . . . . . . . . . . . . . . . .
Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . .
Least width of each downstanding leg . . . . . . . . . . . . . . . . .
Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Average bottom cover to tendons . . . . . . . . . . . . . . . . . . . .
Side cover to reinforcement . . . . . . . . . . . . . . . . . . . . . . . . .
Least width of each downstanding leg . . . . . . . . . . . . . . . . .
Thickness at crown*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
d) Ribbed floors having hollow infill blocks of clay, or inverted Tsection beams with hollow infill blocks of concrete or clay. A
floor in which less than 50 % of the gross cross-section is
solid material shall be provided with a 15 mm plaster coating
on soffit
e) Upright T-sections
f) Inverted channel sections with radius at intersection of soffits
with top of leg not exceeding depth of section
g) Inverted channel sections or U-sections with radius at
intersection of soffits with top of leg exceeding depth of section
**)65
**)35
70
125
50
25
55
125
40
20
45
100
25
15
30
90
25
15
30
90
5
**)85
**)45
90
150
40
20
45
100
25
25
60
90
h
50
25
60
125
40
40
90
100
mm
**)65
**)35
75
125
50
50
120
125
4
**)100
**)50
110
150
**)85
**)45
100
150
**)100
**)50
125
150
**)65
**)65
150
125
15
50
100
15
20
105
15
20
100
Description
**)85
**)85
200
150
25
70
110
25
25
130
3
**)100
**)100
250
150
30
80
140
30
30
155
0,5
40
90
160
40
40
180
Minimum dimension of concrete
50
100
175
50
50
205
2
65
125
190
65
50
190
15
90
1
6
4
3
2
1,5
1
0,5
a) Siliceous aggregate concrete:
1) average concrete cover to tendons . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
*)100
280
*)85
240
*)65
180
*)50
140
40
110
25
80
b) As in (a) with vermiculite concrete slabs,
15 mm thick, used as permanent
shuttering:
1) average concrete cover to tendons . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 75
210
*)60
170
*)45
125
35
100
25
70
15
70
c) As in (b) but with slabs 25 mm thick:
1) average concrete cover to tendons . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
65
180
50
140
35
100
25
70
15
60
15
60
d) As in (a) with gypsum plaster, 15 mm
thick, with light mesh reinforcement
1) average concrete cover to tendons . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 90
250
*)75
210
*)50
150
40
110
30
85
15
70
e) As in (a) with vermiculite/gypsum
plaster**) or sprayed asbestos, 15 mm
thick:
1) average concrete cover to tendons . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 75
170
*)60
145
*)45
115
30
85
25
60
15
60
f) As in (e) but with coating 25 mm thick:
1) average concrete cover to tendons . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
*) 50
140
*)45
125
30
100
25
70
15
60
15
60
g) Low-density aggregate concrete:
1) average concrete cover to tendons . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
80
250
65
200
50
160
40
130
30
100
20
80
*)Non-combustible screeds and floor finishes may be included in these dimensions.
**)Supplementary reinforcement may be necessary to hold the concrete cover in position (see 7.3).
Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . .
Thickness of bottom flange . . . . . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
c) Hollow box sections having one or more longitudinal cavities,
which are wider than they are high
25
25
110
SABS 0100-1
Ed. 2.2
30
30
140
165
40
40
160
by 0,6 to allow for the additional heat transfer through the upper flange face.
50
40
175
7.2.7 For -beams, the average concrete cover determined as in 7.2.3 is adjusted by multiplying it
65
50
190
**)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . .
Thickness under cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
80
b) Cored slabs in which the cores are circular or are higher than
they are wide. Not less than 50 % of the gross cross-section of
the floor should be solid material
20
100
0,5
*)Supplementary reinforcement may be necessary to hold the concrete cover in position (see
7.2.6).
25
100
15
60
1
15
60
30
125
15
70
1,5
15
85
40
125
20
110
50
150
30
150
65
150
40
210
Average cover to tendons . . . . . . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
*)50
250
a) Solid slab
b) As in (a) with cement or gypsum, 15 mm
thick, with light mesh reinforcement:
1) average concrete cover to main
reinforcement . . . . . . . . . . . . . . . . . . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
h
7
2
15
80
3
25
110
4
35
140
mm
Fire resistance
Fire resistance
7
30
130
|
Floor construction
6
*)45
180
5
*)55
240
4
*)65
280
Minimum dimension of concrete
a) Siliceous aggregate concrete:
1) average concrete cover to main
reinforcement . . . . . . . . . . . . . . . . . . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
3
6
2
Table 43 Fire resistance of reinforced concrete beams
Table 46 Fire resistance of prestressed concrete floors (siliceous or calcareous aggregate)
15
85
15
10
25
65
1
25
15
35
75
1,5
35
20
40
100
5
**)45
**)25
50
100
15
10
30
90
35
160
25
15
40
100
15
115
35
20
50
125
2
**)45
**)25
60
125
15
15
60
90
4
**)55
**)30
60
150
**)55
**)30
70
150
**)65
**)40
75
150
25
25
75
100
45
200
35
35
90
125
15
145
**)45
**)45
115
125
15
50
100
15
20
105
15
20
100
15
100
3
**)55
**)55
140
150
15
70
110
15
25
130
15
25
110
0,5
Description
**)65
**)65
150
150
20
80
140
20
30
155
20
30
140
1
15
100
50
250
20
90
160
20
40
180
20
40
160
20
125
1,5
*)25
170
25
100
175
h
20
125
2
d) Low density aggregate concrete:
1) average concrete cover to main
reinforcement . . . . . . . . . . . . . . . . . . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
25
40
205
25
40
175
25
150
3
mm
Fire resistance
7
SABS 0100-1
Ed. 2.2
1
6
4
3
**)65
**)40
70
150
4
2
25
125
190
3
Minimum dimension of concrete
c) As in (a) with vermiculite/gypsum plaster**)
or sprayed asbestos, 15 mm thick, on
light mesh reinforcement securely fixed
to the beam:
1) average concrete cover to main
reinforcement . . . . . . . . . . . . . . . . . . . . .
2) beam width . . . . . . . . . . . . . . . . . . . . . .
25
50
230
25
50
190
25
150
4
2
1
*)Non-combustible screeds and floor finishes may be included in these dimensions.
**)Supplementary reinforcement may be necessary to hold the concrete cover in position (see 7.3).
Average cover to reinforcement . . . . . . . . . . . . . . . . . . . . .
Depth, overall*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
a) Solid slab
Floor construction
1
Table 45 Fire resistance of reinforced concrete floors (silliceous or calcareous aggregate)
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SABS 0100-1
Ed. 2.2
Table 44 Fire resistance of prestressed concrete beams
Amdt 1, Apr. 1994
Minimum dimension of concrete
7
Fire resistance
mm
h
*)Supplementary reinforcement may be necessary to hold the concrete cover in position (see
7.2.6).
**)Vermiculite/gypsum plaster must have a mix ratio in the range 1,5:1 to 2:1 by volume.
166
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SABS 0100-1
Ed. 2.2
168
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SABS 0100-1
Ed. 2.2
Table 47 Effect of soffit treatment
1
2
3
4
Minimum thickness of
finish
mm
Ceiling finish
Increase in fire resistance
h
a)
Vermiculite/gypsum plaster*) or sprayed
asbestos with light mesh reinforcement
fixed securely to the underside of the slab
(as in table 45) . . . . . . . . . . . . . . . . . . . . . .
b)
Vermiculite/gypsum plaster*) or sprayed
asbestos**) on expanded metal as a
suspended ceiling to floor construction 5-7
(as in table 45) . . . . . . . . . . . . . . . . . . . . . .
c)
Gypsum/sand or cement/sand on expanded
metal as a suspended ceiling to any floor
type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1,5
1
0,5
15
10
10
10
10
10
15
10
10
)
* Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by
volume.
**)When suspended ceilings are used, the increased fire resistance only holds if
ducts, light fittings, etc., do not penetrate the ceiling and if services and
combustible materials are kept out of the space between the ceiling and the floor
construction above.
7.5 Columns
7.5.1 The minimum dimension of a column is a determining factor in the fire resistance it can provide.
The dimensions given in table 48 relate to columns that, when subjected to service loads, may be
exposed to fire on all faces. The use of limestone or other calcareous aggregates will, as indicated,
reduce spalling and allow a reduction in the size of the section. When siliceous aggregates are used,
the concrete cover to the main bars should not exceed 40 mm unless supplementary reinforcement
is provided. Ensure that the cover to reinforced concrete columns is the same as that given in table
43 for beams.
d
t
t
h
t
7.5.2 Supplementary reinforcement shall consist of either a wire fabric not lighter than 0,5 kg/m2
(2 mm diameter wires at centres not exceeding 100 mm) or a continuous arrangement of links at
centres not exceeding 200 mm, incorporated in the concrete cover at a distance not exceeding 20 mm
from the face.
h
7.5.3 When supplementary reinforcement as in item (b) of table 48 is used to obtain a reduced size
t
of column, it should be placed at mid-cover but not more than 20 mm from the face, and should be
in the shape of a rectangular or circular cage.
7.5.4 Columns that are built into fire-resistant walls to their full height are likely to be exposed to fire
on one face only. Where fire-resistant walls are required to have the same fire-resistance rating as the
columns, the data given in table 49 apply to the situation where the face of the column is flush with the
170
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SABS 0100-1
Ed. 2.2
wall or where that part embedded in the wall is structurally adequate to support the load, provided that
any opening in the wall is not nearer to the column than the minimum dimension specified in table 49
for that column.
Table 48 Fire resistance of concrete columns (all faces exposed)
1
2
3
4
5
6
Concrete cover to the reinforcement should be at least 15 mm for a fire resistance of up to 1 h, and
at least 25 mm for a fire resistance for longer periods. Unless shown otherwise by a test, walls
containing vertical reinforcement of less than 1,0 % are regarded as plain concrete walls (see 7.6.2)
for fire-resistance purposes.
mm
Fire resistance
h
a) Siliceous aggregate concrete:
1) without additional protection . . . . . . . . . . . .
2) with cement or gypsum plaster, 15 mm
thick, on light mesh reinforcement . . . . . . . .
3) with vermiculite/gypsum plaster*) or
sprayed asbestos, 15 mm thick, on light
mesh reinforcement securely fixed to the
column . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Walls
7.6.1 Concrete walls containing at least 1,0 % of vertical reinforcement
The fire resistance of concrete walls containing at least 1,0 % of vertical reinforcement is given in
table 50. The minimum thicknesses shown are for siliceous aggregate concrete. When low-density
aggregate concrete is used, a reduction in thickness is permissible if the fire resistance of such a wall
is confirmed by a test.
7
Minimum dimension of concrete
Type of construction
SABS 0100-1
Ed. 2.2
4
3
2
1,5
1
0,5
450
400
300
250
200
150
300
275
225
150
150
150
275
225
200
150
120
120
300
275
225
200
190
150
300
275
225
200
150
150
Walls exposed to fire on more than one face are to be regarded as columns (see 7.5).
Table 50 Fire resistance of siliceous aggregate concrete walls
containing at least 1,0 % of vertical reinforcement and exposed to
fire on one face only
1
b) Limestone aggregate concrete or
siliceous aggregate concrete, with
supplementary reinforcement in concrete
cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
c) Low-density aggregate concrete . . . . . . . . . .
4
5
6
None . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cement or gypsum plaster on exposed face
Vermiculite/gypsum plaster*) or sprayed
asbestos, 15 mm thick, on exposed face . .
7
Fire resistance
4
3
2
1,5
1
0,5
180
180
150
150
100
100
100
100
75
75
75
75
125
100
75
75
65
65
7.6.2 Plain concrete walls
mm
From the limited data available, the fire resistance of plain siliceous aggregate concrete walls can be
taken as follows:
Fire resistance
h
a) Siliceous aggregate concrete:
1) without additional protection . . . . . . .
2) with vermiculite/gypsum plaster*)
or sprayed asbestos, 15 mm thick, on
exposed faces on light mesh
reinforcement securely fixed to the
column . . . . . . . . . . . . . . . . . . . . . . . .
6
*)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
7
Minimum dimension of concrete
Type of construction
5
h
Table 49 Fire resistance of concrete columns (one face exposed)
3
4
mm
Description of applied finish
* Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
2
3
Minimum dimension of concrete
)
1
2
Concrete, 150 mm thick: 1 h;
4
3
2
1,5
1
0,5
300
250
200
150
100
100
200
150
120
100
90
90
Concrete, 175 mm thick: 1,5 h.
*)Vermiculite/gypsum plaster should have a mix ratio in the range 1,5:1 to 2:1 by volume.
171
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172
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SABS 0100-1
Ed. 2.2
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SABS 0100-1
Ed. 2.2
governs the long-term effects; lack of knowledge of the precise imposed load is not likely to be
a major cause of error in deflection calculations; for the proportion of imposed loading that may
be considered to be permanent and that will influence the long-term behaviour, see 3.3.4.1;
Annex A
(informative)
Methods of checking for compliance with serviceability
criteria by direct calculation
A.1 Analysis of structure for serviceability limit states
c)
lightly reinforced elements may well have a working load that is close to the cracking load for the
element; considerable differences will occur in the deflections, depending on whether the element
has or has not cracked;
d)
the effects of finishes and partitions on deflection are difficult to assess and are often ignored;
if a partition is built on top of a beam where there is no wall built up to the underside of the beam,
the long-term deflection will cause the beam to creep away from the partition; the partition may
be left spanning as a deep beam that will apply significant loads at its ends only to the supporting
beam; thus, if a partition wall is built over the whole span of a beam with no major openings near
its centre, its mass may be ignored in the calculation of long-term deflections of the supporting
beam; the suitable approach for assessing the magnitude of this effect is to calculate a likely
maximum and minimum deflection and to take the average.
A.1.1 Loads
See 3.3.4.1.
A.1.2 Moments and forces
In general, it will be sufficiently accurate to use an elastic analysis to assess the moments and forces
in elements subjected to their appropriate loadings for the serviceability limit states.
Where a single value of stiffness is used to characterize an element, the stiffness of the element may
be based on the concrete section. In this case, it is likely to provide a more accurate picture of the
moment and force fields than will the use of a cracked transformed section, even though calculation
shows the elements to be cracked. Where more sophisticated methods of analysis are used, in which
variations in properties over the length of elements can be taken into account, it will frequently be more
appropriate to calculate the stiffness of highly stressed parts of elements on the basis of a cracked
transformed section.
A.1.3 Material properties
For checking serviceability limit states, the modulus of elasticity of the concrete should be taken as
the mean value given in table C.1, appropriate to the characteristic strength of the concrete. The
modulus of elasticity may be corrected for the age of loading if this is known. Owing to the large range
of values for the modulus of elasticity that can be obtained for the same cube strength, it might be
appropriate to consider either calculating the behaviour of the element (by using moduli at the end of
the ranges given in table C.1 to obtain an idea of reliability of the calculation) or having tests done on
the actual concrete to be used. For appropriate values of creep and shrinkage, refer to annex C.
A.2 Calculation of deflection
A.2.1 General
A.2.1.1 When the deflections of reinforced concrete elements are calculated, note that there are a
number of factors that may be difficult to allow for in the calculation but that can have a considerable
effect on the reliability of the result.
The following points should be taken into consideration:
a)
estimates of the restraints provided by supports are based on simplified and often inaccurate
assumptions;
b)
the precise loading, or the part of it that is of long duration, is unknown; the self-weight, which is
known to within quite close limits, is the major factor determining the deflections, since this largely
173
A.2.1.2 Any method of calculation that can be demonstrated to yield results of acceptable accuracy
can be used, provided that points such as those listed in A.2.1.1 have been correctly accounted for,
and may be logically applied over a wide range of problems. The approach used in the method of
calculation given in A.2.3 is to assess the curvatures of sections under the appropriate moments (as
in A.2.2) and then calculate the deflections from the curvatures. The method of calculation given in
A.2.4 is an alternative to the method given in A.2.3 and deals additionally with the deflection of fully
and partially prestressed concrete elements. Shrinkage deflection may be calculated as in A.2.5.
A.2.2 Calculation of curvatures
A.2.2.1 Sets of assumptions
The curvature of any section may be calculated by employing whichever of the following sets of
assumptions, A or B, gives the larger value. Set of assumptions A applies to a section that is cracked
under the loading under consideration, while set of assumptions B applies to an uncracked section.
A.2.2.2 Set of assumptions A (section cracked)
A.2.2.2.1 Strains are calculated on the assumption that plane sections remain plane.
A.2.2.2.2 The reinforcement, whether in tension or in compression, is assumed to be elastic. Its
modulus of elasticity may be taken as 200 GPa.
A.2.2.2.3 The concrete in compression is assumed to be elastic. Under short-term loading, the
modulus of elasticity may be taken as that given in 3.4.2.1. Under long-term loading, an effective
modulus may be taken as having a value of 1/(1 + ) times the short-term modulus, where is the
appropriate creep factor (see C.2).
A.2.2.2.4 Stresses in the concrete in tension may be calculated on the assumption that the stress
distribution is triangular, having a value of zero at the neutral axis and a value of 1 MPa at the centroid
of the tension steel in the short term, reducing to 0,55 MPa in the long term.
174
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SABS 0100-1
Ed. 2.2
r
f
f
xE
d x E
r
f
E
f
d
x
E
r
M
E I
NOTE –
M
I
h
d
x
fc
fs
As
Ec
Es
is the overall depth of section;
is the effective depth of section;
is the depth from compression face to neutral axis;
is the maximum compressive strength in concrete;
is the tensile strength in reinforcement;
is the area of reinforcement;
is the modulus of elasticity of concrete; and
is the modulus of elasticity of reinforcement.
Figure A.1 — Assumptions made in calculating curvatures
A.2.2.5 Total long-term curvature
In the assessment of the total long-term curvature of a section, the following procedure may be
adopted:
a)
calculate the instantaneous curvatures under the total load and under the permanent load;
b)
calculate the long-term curvature under the permanent load;
c)
to the long-term curvature under the permanent load, add the difference between the
instantaneous curvatures under the total and permanent loads; and
176
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S
r
l
I
r
K
r
E
K
E
K
E
E
E
E
l
I
S
d
dx
r
x
r
x
Kl
r
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SABS 0100-1
Ed. 2.2
KM
l2
Ec e
M
l
E
I
K
I
I
M
M
I
M
M
I
I
Figure A.2 — Values of K for various bending moment diagrams
179
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M
fr
M
g
yt
p
f
f
f
f
f
p
M
I
I
I
I
y
I
x
I
x
M
M
x
M
M
x
x
x
x
x
x
M
M
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l
kk
h
k
f E f
E
k
a
k
a
c
h x
l
A
bd
w
a
A
bd
c
h
x
A
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SABS 0100-1
Ed. 2.2
b h
x a
E A
d
Annex B
x
(informative)
x
Movement joints
B.1 General
b
Many factors influence the tendency of concrete to crack, and the limitation of such cracking is also
influenced by many factors, probably the most important of which is the proper provision of adequate
reinforcement. However, there are cases where the most appropriate or indeed the only control
measure is a movement joint.
h
B.2 Need for movement joints
x
B.2.1 In common with all other structural materials, concrete expands when heated and contracts
when cooled; it also expands when wetted and shrinks when dried. It also undergoes other strains
owing to the hydration of the cement and other properties of the material itself and of its constituent
parts. If these expansions and contractions are restrained, stresses will occur that can be of sufficient
magnitude to cause immediate cracking of the concrete, or cracking will occur later owing to fatigue
failure resulting from long-term repetition of the stresses. Creep of the concrete over a long period can
in some cases reduce stresses due to restraint, but generally this should not be relied upon.
Differential settlements of foundations due, for example, to mining subsidence might also need to be
provided for. As these factors may cause unsightly cracking, damage to finishes, and even structural
failure, the possibilities and effects of such cracking should be properly investigated in relation to the
design, reinforcement and form of the element or structure concerned and in the light of published
information. If it is then found necessary to prevent or limit the effects of such potential cracking,
movement joints should be provided at predetermined locations.
E
A
d
a
h x
h x
h x
h
x
B.2.2 Some indication of the possible magnitude of the movements to be dealt with in a concrete
structure may be gained from the examples given below.
h
B.2.2.1 The average coefficient of thermal expansion of concrete is about 10-5/1 C; thus a 33 C
change in temperature could cause a difference in length of approximately 10 mm in a concrete
element of length 30 m. If this change in length were to be prevented by complete restraint of the
element, it would cause a stress of about 7 MPa in an unreinforced concrete element having a
modulus of elasticity of 20 GPa. If such stress were tensile, and superimposed upon other already
existing tensile stresses, cracking would occur. (If, however, the concrete were to be reinforced, the
distribution of the cracking would be controlled by the amount, form and distribution of the
reinforcement, which might even reduce the crack width and spacing to the extent that no harmful
consequence would be caused.)
B.2.2.2 Drying shrinkage strains may be roughly 500 x 10-6. In thin reinforced sections, this
represents an unrestrained shrinkage of about 1,5 mm per 3 m length of a concrete element. If this
change in length were to be prevented, a tensile stress of about 10 MPa would occur. (See also
annex C.3.)
B.2.2.3 Creep of concrete under stress tends to reduce the maximum stresses arising from the
restraint of movements of the types referred to in B.2.2.1 and B.2.2.2, the degree of reduction
depending on, among other factors, the rate of change of the stresses. Creep is a long-term process
and if the stresses change rapidly, e.g. because the cross-section of the element is small enough to
permit its temperature change or shrinkage to occur in a relatively short time, it has a negligible effect
on reducing the stresses.
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SABS 0100-1
Ed. 2.2
B.2.3 However, creep of the concrete can itself create strains that could lead to harmful and
unsightly effects if no movement joints were to be provided. For example, creep of the concrete can
cause deflections of beams to increase over a long period under sustained loading. Unless suitable
movement joints are provided between floors or roofs and partitions, these deflections can lead to
heavy loads being imposed upon the partitions, which, if of a non-load-bearing type, may then suffer
severe cracking. (See also annex C.2.)
B.3 Types of movement joints
Movement joints may be any one of the types given below.
B.3.1 Contraction joint
A contraction joint is a joint with a deliberate discontinuity but no initial gap between the concrete on
both sides of the joint, the joint being intended to permit contraction of the concrete.
A distinction should be made between a complete contraction joint in which both the concrete and the
reinforcement are interrupted, and a partial contraction joint in which only the concrete is interrupted
but the reinforcement runs through.
B.3.2 Expansion joint
An expansion joint is a joint with complete discontinuity in both reinforcement and concrete and
intended to accommodate either expansion or contraction of the structure.
In general, such a joint requires the provision of a sufficiently wide gap between the adjoining parts
of the structure, to permit the occurrence of the amount of expansion expected. Design of the joint so
as to incorporate sliding surfaces is not, however, precluded and may sometimes be advantageous.
B.3.3 Sliding joint
A sliding joint is a joint with complete discontinuity in both reinforcement and concrete. Special
provision is made at the joint, to facilitate relative movement in the plane of the joint.
B.3.4 Hinged joint
SABS 0100-1
Ed. 2.2
B.4 Provision of joints
B.4.1 The risk of cracking due to thermal movement and shrinkage may be minimized if the changes
in temperature and moisture content to which the concrete of the structure is subjected are limited. The
extent to which this can be done in the completed structure will depend very largely on its type and
environment, ranging from the underground basement, where the temperature and humidity are
relatively constant, to the uninsulated elevated structure, where the temperature and humidity are
close to the atmospheric temperature and humidity.
Furthermore, in modern buildings, the effects of central heating on both the temperature and moisture
content of the structure, combined with the relatively low thermal storage capacity of buildings clad
with low-density curtain walls, may give rise to more onerous thermal and humidity conditions than in
older, heavier, relatively unheated buildings. Thus, the investigation of the necessity of providing
movement joints is becoming more important.
B.4.2 Cracking can be minimized by reducing the restraints on the free movement of the structure,
and the control of cracking normally requires the subdivision of a structure into suitable lengths
separated by the appropriate movement joints.
B.4.3 The effectiveness of movement joints in controlling cracking in a structure will also depend
upon their precise location; this is frequently a matter of experience, and the location of movement
joints may be characterized as the places where cracks would otherwise most probably develop, e.g.
at abrupt changes of cross-section.
B.4.4 The location of all movement joints should be clearly indicated on the drawings, both for
individual elements and for the structure as a whole. In general, movement joints in the structure
should pass through the whole structure in one plane.
B.5 Design of joints
A movement joint should fulfil all necessary functional requirements. It should possess the merits of
simplicity and freedom of movement, yet still retain the other appropriate characteristics necessary,
e.g. weatherproofness, fire resistance, corrosion resistance, durability and sound insulation. The design
should also take into consideration the degree of control and workmanship and the tolerances likely
to occur in the actual structure of the type being considered. Where joints are of a filled type, they
may, in appropriate cases, be filled with a building mastic.
A hinged joint is a joint specially designed and constructed to permit relative rotation of the elements
at the joint. This type of joint is usually required to prevent the occurrence of reverse moments or of
undesirable restraint, for example in a three-hinged portal.
B.3.5 Settlement joint
A settlement joint is a joint intended to permit adjacent elements or structures to settle or deflect
relative to each other in cases, for example, where movements of the foundations of a structure are
likely to take place as a result of mining subsidence. The relative movements may be large.
NOTE It may be necessary to design a joint to fulfil more than one of the requirements given in B.3.1 to B.3.5.
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SABS 0100-1
Ed. 2.2
Annex C
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SABS 0100-1
Ed. 2.2
Values of fcu,t/fcu,28 for use in equation (24) can be obtained from table 2. This table shows that, on
average, there is likely to be a gain of strength beyond 28 d (this will lead to a more realistic
assessment of the modulus of elasticity). It should be noted that there is a difference here from the
main body of this part of SABS 0100 where no increase in strength beyond 28 d is permitted in
satisfying limit state requirements. A smaller increase in strength will occur with small structural
members that are exposed to a dry environment after initial curing.
(informative)
Elastic deformation of concrete
C.1 Modulus of elasticity
C.1.1 The modulus of elasticity of concrete is influenced by the elastic properties of the aggregate
and, to a lesser extent by the aggregate/cement ratio, condition of curing, type of cement and age of
the concrete. In the case of concrete made from natural aggregates and having a density of
2 300 kg/m3 or more, the static or dynamic modulus of elasticity may be taken from table C.1 for
concretes of various compressive strengths.
C.1.2 If a more accurate figure is required for particular materials and a particular mix, tests should
be carried out. Concrete made from a few particular sources of aggregate may have a modulus of
elasticity substantially outside the range given in table C.1. The use of these materials may be
permitted, provided that the appropriate value for elastic modulus obtained from tests is used in design
calculations.
C.1.3 Where, in special circumstances, an as-accurate-as-possible assessment of actual behaviour
is required, it will be necessary to consider possible variations in the value for modulus of elasticity.
Guidance on this follows, but it is emphasized that the value chosen in any particular case will depend
on the importance of the estimate and why it is needed.
Where calculations of deflection or deformation are to be made, the reliability of the estimate of the
static modulus of elasticity will depend on the precision required from the calculation. Where
deflections are of great importance, tests should be carried out on concrete made with the aggregate
to be used in the structure. In other cases, experience with a particular aggregate, backed by general
data, will often provide a reliable value for Ko, and hence for Ec,28, but with unknown aggregates, it
would be advisable at the design stage to consider a range of values for Ec,28, as given in table C.1.
In the case of low-density aggregate concrete, the values of the static modulus in table C.1 should be
multiplied by (w/2400)2 where w is the density of low-density aggregate concrete (in kilograms per
cubic metre). It may be more convenient to use the dynamic modulus method of test to obtain an
estimated value for the static modulus of elasticity, using the formula
Ec = 1,25 Ecq - 19
where Ecq is the dynamic modulus of elasticity obtainable from table C.1.
Such an estimated value will generally be correct to within 5 GPa.
Table C.1 Modulus of elasticity of normal-density concrete
The mean values of static modulus of elasticity for normal-density concrete in table C.1 are derived
from the following equation:
1
Ec,28 = Ko + 0,2 fcu,28
Characteristic
strength fcu,
where
Ec,28
MPa
is the characteristic cube strength, in MPa; and
Ko
is a constant closely related to the modulus of elasticity of the aggregate (taken as
20 kN/mm2 for normal-density concrete). The variety of factors affecting the prediction and
determination of the elastic modulus of concrete with specific reference to local aggregates
and cements are discussed in the documents given in (a), (d) and (e) of annex E.
The modulus of elasticity of concrete Ec at an age t may be derived from the following equation:
Ec,t = Ec,28 (0,4 + 0,6 fcu,t/fcu,28)
(25)
Ec,28
is the static modulus of elasticity at 28 d, obtainable from table C.1; and
fcu
is the characteristic strength of concrete.
5
GPa
GPa
Typical range
Mean value
Typical range
20
25
30
25
26
28
21-29
22-30
23-33
35
36
38
31-39
32-40
33-43
40
50
60
31
34
36
26-36
28-40
30-42
40
42
44
35-45
36-48
38-50
C.2 Creep and shrinkage
cc
> 3 d;
4
Dynamic modulus Ecq,
The final (30-year) creep strain in concrete, cc, can be predicted from the formula
where
t
3
Static modulus Ec,
Mean value
is the static modulus of elasticity at 28 d;
fcu,28
2
=
stress
Et
where
Et
is the modulus of elasticity of concrete at age of loading t; and
is the creep factor obtainable from figure C.1.
189
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SABS 0100-1
Ed. 2.2
Figure C.1 — Effects of relative humidity, age of concrete at
loading and section thickness upon creep factor
The effective section thickness is defined in figure C.1 for uniform sections as twice the
cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion in water
or by sealing, the effective section thickness should be taken as 600 mm.
It can be assumed that about 40 %, 60 % and 80 % of the final creep develops during the first month,
first 6 months and first 30 months under load respectively, when concrete is exposed to conditions of
constant relative humidity.
Creep is partly recoverable with a reduction in stress. The final creep recovery after one year is
approximately 0,3 times stress reduction/Eu, where Eu is the modulus of elasticity of the concrete at
the age of unloading.
C.3 Drying shrinkage
An estimate of the drying shrinkage of plain concrete may be obtained from figure C.2.
Recommendations for effective section thickness are given in C.2.
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Ed. 2.2
Annex D
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SABS 0100-1
Ed. 2.2
D.2.2 Equivalent truss analogy (analysis by admissible stress fields)
(informative)
The design of deep beams
D.1 General
Deep beams are defined as prismatic members, generally straight and of constant cross-section
having a ratio of effective span to overall depth of less than 2 and such that the assumption that plane
sections remain plane in bending does not apply.
In the case of continuous beams, the transition to a deep beam for decreasing span to depth ratios is
gradual and depends on the distribution of loading, so that any given ratio is approximate if applied
generally.
The effective span of a simply supported deep beam may be assumed to be the distance between
centre-lines of supports provided that this distance does not exceed 1,15 times the span between the
faces of supports, in which case the effective span is to be taken as 1,15 times the clear span.
If a stress field is chosen which satisfies the equilibrium conditions, a lower bound solution of limit
analysis is considered. For the structure and its loads, an equivalent truss may be investigated,
consisting of concrete struts and arches as compressive members and of steel ties formed by the
reinforcement as tensile elements and their connections (nodes). Any equilibrium model may be
applied for verifying the ULS and also for the SLS, provided that the evaluated stress distribution is
close to the results of the linear analysis (see figures D.1 and D.2). A similar approach is also valid for
continuous beams.
The equilibrium model should preferably be based on the dominating load pattern but where point
loads and distributed loads have similar influences or dominate at various times, a more complex
model being a combination of the extreme patterns is required (see figure D.3).
The above-mentioned nodes are defined as the volumes of concrete contained within the intersections
between compression fields of struts, in combination with anchorage forces or external compressive
forces (imposed loads or support reactions) or both. The nodes should be so dimensioned that all
forces are anchored and balanced safely.
In the case of continuous beams, the above-mentioned definition of the effective span applies if the
effective spans for this purpose are taken as the approximate distances between the points of
contraflexure. Alternatively, if span lengths are calculated as for simply supported beams, the span
to depth ratio would be approximately 2,5 to 3. In the case of cantilevers, the ratio would be
approximately 1.
D.2 Design and analysis
Deep beams may be designed and analysed by means of any of the following:
a) linear analysis based on the theory of elasticity (see D.2.1); or
b) procedures such as the application of statically admissible stress fields in accordance with the lower
bound theorem of limit analysis by analogy with the behaviour of equivalent truss or lattice
structures consisting of struts and ties or tied arches (all preferably following the elastic field)
(see D.2.2); or
c) non-linear analysis (see D.2.3); or
d) methods using the results of experimental tests on models of reinforced concrete or other suitable
materials or on prototypes or based on the extrapolation of published results of experimental or
theoretical work by reputable persons.
D.2.1 Linear analysis
The theory of elasticity may be applied assuming values of Poisson's ratio of 0,0 to 0,2. In most cases,
only numerical solutions are suitable (such as, for example, finite differences, finite-element-methods,
or boundary element-methods). The analysis defines the fields of principal stresses and deformations.
High stress concentrations (for instance, those at the corner of possible openings) may be reduced by
cracking effects. The linear analysis is valid both for serviceability and ultimate limit states.
The analysis in the ULS requires a correct detailing of the reinforcement, to withstand the resultant
forces in tensile zones in the concrete and to satisfy equilibrium conditions.
193
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SABS 0100-1
Ed. 2.2
SABS 0100-1
Ed. 2.2
Figure D.1 — Equivalent truss resisting point loads
Figure D.2 — Equivalent arch resisting UD load and self-weight
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SABS 0100-1
Ed. 2.2
f
f
Figure D.3 — Equivalent truss resisting unequal point loads A > B
b a
a
a
b
b
b a
f
H
F
H
Fa a
f
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SABS 0100-1
Ed. 2.2
Annex E
(informative)
Bibliography
The information contained in this part of SABS 0100 is considered adequate for the design of the
majority of buildings. For buildings, structures or elements that are not adequately covered or where
special conditions apply or where additional information is desired by the designer, the following
publications should be consulted:
a) Alexander, MG. Prediction of elastic modulus for design of concrete structures. The Civil Engineer
in South Africa, June 1985, vol. 27, No. 6, p. 313-324.
b) Alexander, MG and Davis, DE. Properties of aggregates in concrete, Part . Hippo Quarries
Technical Publication, 1989. 44p.
c) Alexander, MG and Davis, DE. Properties of aggregates in concrete, Part 2. Hippo Quarries
Technical Publication, 1992. 48p.
d) Alexander, MG and Davis, DE. The influence of aggregates on the compressive strength and elastic
modulus of concrete. The Civil Engineer in South Africa, May 1992, Vol. 34, No. 5, p. 161-170.
T
b
a
b
e) Chana, PS. Some aspects of modelling the behaviour of reinforced concrete under shear loading.
Cement and Concrete Association Technical Report 543, July 1981.
f) Cross, MG. A proposed parametric design model for shear in reinforced concrete. The Civil
Engineer in South Africa, April 1987, vol. 29, No. 4, p. 127-134.
g) Goldstein, AE. Prestressed concrete flat slabs. (In course of publishing.)
h) Kani, Huggins and Wittkopp (ed.). Kani on shear in reinforced concrete. Department of Civil
Engineering, University of Toronto, 1979.
i) Kemp, AR, Milford, RV and Laurie, JAP. Proposals for a comprehensive limit states formulation for
South African structural codes. The Civil Engineer in South Africa, September 1987, vol. 29, No. 9,
p. 351-360.
j) Scholz, H. Proposed design provisions for reinforced concrete columns. The Civil Engineer in South
Africa, May 1988, vol. 30, No. 5, p. 229-238.
k) BS 8007, Design of concrete structures for retaining aqueous liquids.
sabs pta
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