PBL Group Ltd.
8/11 Soi Viphavadi 44, Viphavadi-Rangsit Road,
Lardyao, Jatujak,
Bangkok 10900,Thailand.
Design of Post-Tensioned Floor Systems
with the Case of Long Spans
and Applications
in High-Rise Buildings
Presentation by
Mr. Prapat Boonlualoah
Products & R&D
CEO, PBLFactory
Group Ltd.,
Bangkok
Certification
Export
Outreach
PBL Export Vision
Conclusion
Introduction
What is Pre-stressing?
“Pre-stressing is a method of reinforcing concrete. Externally
applied loads induce internal stresses (forces) in concrete
during the construction and service phases of a member. The
concrete is pre-stressed to counteract those anticipated
stresses during the service life of the member”
Products & R&D
Certification
Factory
Export Outreach
Export Vision
Conclusion
Source: PBL
Post-tensioning
Institute
(2006)
Introduction
Methods of Pre-stressing
Pre-tensioning
Post-tensioning
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Pre-tensioning
• Steel tendons are stressed before the concrete is placed
at a precast plant remote from the construction site.
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Post-tensioning
•
Steel tendon are stressed after the concrete has
been placed and gained sufficient strength at
the construction site.
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Benefits of Post-tensioning
Effective use of high strength materials
Better cost effectiveness
Thinner slab, lower mass, more attractive structures
Better deflection control
Better crack control
Better water-tightness
Improved seismic performance (due to lower mass of
structure)
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Post-tensioning vs. Typical RC Construction
Faster floor construction cycle (typically 4-7 days cycle per floor)
Lower floor weight (typically 1/5-1/3 less)
Lower floor-to-floor height (no beams)
Larger spans between columns (optimum 8-10 m for flat plate
system)
Reduced foundations
Products & R&D
Certification
Factory
Export Outreach
Export Vision
Conclusion
Source: PBL
Post-tensioning
Institute
(2006)
Introduction
Post-tensioning Applications
Office buildings
Car parks
Shopping centers
Hotels, apartments
Hospitals
Industrial buildings
Ground/rock anchors
Silos/water tanks/nuclear containments
Bridges/girders
Products & R&D
Certification
Factory
Export Outreach
Export Vision
Conclusion
Source: PBL
Post-tensioning
Institute
(2006)
Introduction
Cost comparison – flat plate
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Cost comparison – one way slab with slab band
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Post-tensioning Systems
Un-bonded Post-tensioning System
Bonded Post-tensioning Systems
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Bonded vs. Unbonded Tendons
Bonded
Products & R&D
Certification
Factory
Export Outreach Source:
PBLThe
Export
VisionSociety
Conclusion
Concrete
(1994)
Introduction
Arrangement of Bonded Post-tensioning System
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Introduction
Bonded vs. Un-bonded Tendons
Unbonded
Products & R&D
Certification
Factory
Export Outreach Source:
PBLThe
Export
VisionSociety
Conclusion
Concrete
(1994)
Introduction
Arrangement of Unbonded Post-tensioning System
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Design Considerations and Selection of Suitable Floor Systems
Flat plate system
Flat plate with drop panels/caps
Slab with banded beams (one/two ways)
Slab with long span beam/other supporting structures
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Flat Plate Systems
Common geometries*
• Two-way system
• Suitable span: 8 m
• Limiting criterion: Punching
shear
• Rebar**:
1.08 kg/m2
• PT:
2.84 kg/m2
* for typical office/residential buildings using
ACI/UBC requirements
** quantity assume no bottom reinforcement
Products & R&D
Certification
Factory
Export Outreach
PBL Export
Conclusion
Source:
AalamiVision
& Bommer
(1999)
Design of PT Slabs
Flat Plate with Drop Panels
Common geometries*
•
•
•
•
•
Two-way system
Suitable span: 12.2 m
Limiting criterion: Deflection
Rebar**:
2.94 kg/m2
PT:
3.87 kg/m2
* for typical office/residential buildings using
ACI/UBC requirements
** quantity assume no bottom reinforcement
Products & R&D
Certification
Factory
Export Outreach
PBL Export
Conclusion
Source:
AalamiVision
& Bommer
(1999)
Design of PT Slabs
Slab with Banded Beams/slab bands
Common geometries*
• Two-way system
• Suitable span: 13.4 m
• Limiting criterion: Rebar
congestion
• Rebar**:
• PT:
2.01 kg/m2
4.16 kg/m2
* For typical office/residential buildings using
ACI/UBC requirements
** case of slab band type
Products & R&D
Certification
Factory
Export Outreach
PBL Export
Conclusion
Source:
AalamiVision
& Bommer
(1999)
Design of PT Slabs
SLAB with Long Span Beam/other Supporting Structures
Common geometries*
•
•
•
•
•
•
One-way system
Beam spans:
Slab spans:
Slab thickness:
Beam depth:
Beam width:
18-20 m
5.5-6.0 m
125-150 mm
750-900 mm
400-460 mm
* For typical office/residential buildings using
ACI/UBC requirements
Products & R&D
Certification
Factory
Export Outreach
PBL Export
Conclusion
Source:
AalamiVision
& Bommer
(1999)
Design of PT Slabs
Suitable Span Arrangements vs. Floor Thickness
Criteria of span combinations (internal/external/cantilever span)
Span-to-depth ratio of slab
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Criteria of Span Combinations (Internal/External/Cantilever Span)
1.
2.
3.
4.
5.
Internal spans should be approximately equal.
External span should be approximately 0.8 times the
length of the internal span.
Cantilevers should not exceed 0.3 times the length of the
adjacent span.
Expansion joints – unless formed with double columns
(completely separated slabs) should be approximately in
the quarter span locations.
Size of slabs between expansion joints should be limited
to a maximum of about 100m.
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Span-to-depth Ratio of Slab
Total
imposed
loading
(kN/m2)
Section type
Solid flat slab
2.5
5.0
10.0
2.5
5.0
10.0
Slab with drop panels
Slab with band beams*
2.5
5.0
10.0
Slab with long span beam
2.5
5.0
10.0
Span/depth ratios
6m≤L≤13m
40*/45**
36*/40**
30*/36**
44*/48**
40*/45**
34*/40
slab
beam
45*/48** 25*/35**
40*/45** 22*/30**
35*/40** 18*/25**
slab
beam
45*/48** 20*/25**
40*/45** 16*/20**
35*/40** 13*/15**
* Recommended by The Concrete Society
** Recommended by The Post-Tensioning Institute
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Design Principles
Equivalent frame method
Finite element analysis
Load balancing of effective pre-stressing forces
Pre-stress losses
The concept of banded/distributed tendon system
Moment redistribution
Strength of section (flexure &shear)
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Flowchart for PT Floor Slab
1
CONCRETE OUTLINE AND
SUPPORTS
2
DESIGN
REQUIREMENTS
3
STRUCTURAL
MODELING
OPTIONAL PATH
LOADING
(a)
STRUCTURAL SYSTEM AND
LOAD PATH SELECTION
(b)
ANALYSIS OPTION
5
4
SIMPLE
FRAME
Products & R&D
Certification
6
EQUIVALENT
FRAME
FINITE
ELEMENTS
7
CALCULATION OF REBAR
FOR DESIGN SECTIONS
8
STRUCTURAL
DETAILING
9
(c)
CONSTRUCTION
DETAILING
Factory
(SHOP DRAWINGS)
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Design Steps
Sizing
Cover to reinforcement and tendons
Sizing
•Span
•Thickness
Cover to reinforcement and tendons
•Corrosion
•Wear
•Fire
Loading
Structural system
Analysis
Loading
•Dead
•Live
•Prestressing
Design
Products & R&D
Certification
Factory
Export Outreach
PBL Export
Conclusion
Source
AalamiVision
and Jurgens
(2001)
Design of PT Slabs
Structural System
•Structure
•One-way
•Two-way
• Model Pre-stressing
Design Steps
Sizing
Cover to reinforcement and tendons
Analysis
•Elastic theory
•Gross cross-section
•Redistribution of moments due to limited
plasticity
•Two-way systems
•Simple frame
•Equivalent frame
•Finite Elements
Loading
Structural system
Analysis
Design
Design
•Serviceability
•Crack control
•Deflection control
•Safety
•Add passive reinforcement if necessary
Products & R&D
Certification
Factory
Export Outreach
PBL Export
Conclusion
Source
AalamiVision
and Jurgens
(2001)
Design of PT Slabs
Design Steps
Products & R&D
Certification
Factory
Export Outreach Source:
PBLThe
Export
VisionSociety
Conclusion
Concrete
(1994)
Design of PT Slabs
Design Steps
• For given:
– Structural geometry and boundary conditions
– Material properties
– Loading
There is a unique design for nonprestressed concrete
members
Added information is needed for prestressed members
– Tendon profile
– Average precompression
– Percentage of loading to balance
Based on added information, a multitude of design
alternatives are possible
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Initial Assumptions for Post-Tensioning Design
REBAR AS
(a) NONPRESTRESSED BEAM
(ii) TENDON
FORCE
?
REBAR A
S
?
(i) TENDON SHAPE
(iii) TENDON DRAPE
?
(b) POST-TENSIONED BEAM
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Design Focus
Crack control in service condition
Safety against overload
Durability
Products & R&D
Certification
Factory
Export Outreach
PBL Export
Conclusion
Source:
AalamiVision
and Jurgens
(2001)
Design of PT Slabs
Equivalent Frame Method
• The equivalent frame method is currently the most
common method of analyzing and designing concrete floor
systems, including post-tensioned floors. It is flexible and
efficient, equally suited for both regular and irregular floor
systems
Products & R&D
Certification
Factory
Source: Aalami and Bommer (1999)
Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Column stiffness representation using equivalent frame modeling
Products & R&D
Certification
Factory
Source: Aalami and Bommer (1999)
Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Structural model for gravity
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami and Bommer (1999)
PBL Export Vision Conclusion
Design of PT Slabs
Break down of floor into design strips in two directions
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami and Bommer (1999)
PBL Export Vision Conclusion
Design of PT Slabs
Plan of Floor Slab
COLUMN
SLAB
OPENING
SLAB
EDGE
BEAM
Y
X
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
Support Lines in X-direction
A
B
Support line
C
D
E
F
Y
X
Products & R&D
Certification
Factory
G
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
Support Lines in Y-direction
2
1
3
4
5
Y
X
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
Selection of Design Strips
6
A
8
B
5
3
1
2
9
4
C
7
D
E
F
Y
X
Products & R&D
Certification
Factory
G
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
2
1
3
4
5
Design Strips Tributaries (X-axis)
A
B
C
D
E
F
Y
X
Products & R&D
Certification
Factory
G
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
2
1
3
4
5
Design Strips Tributaries (Y-axis)
A
B
C
D
E
F
Y
X
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
2
1
3
4
5
Design Sections for Design Strips B and E
A
B
C
D
E
F
Y
X
Products & R&D
Certification
Factory
DESIGN
SECTION
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
1
2
9
3
10
4
10
5
9.2 0.8
Construction of Design Strip in Plan
B
(a) DESIGN STRIP IN PROTOTYPE
9
10
10.6 10.5 0.8
B
(b) STRAIGHTENED DESIGN STRIP
IDEALIZED
B
ACTUAL
(c) IDEALIZED TRIBUTARY FOR DESIGN
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
Design Strips in Elevation
1
Products & R&D
2
Certification
3
Factory
4
Export Outreach
5
PBL Export Vision
Conclusion
Source: Aalami
(b)
Design of PT Slabs
Finite Element Analysis
In the FEM analysis, the plate is subdivided into a number of
small parts, referred to as elements.
The elements are connected at reference points called nodes
The force assume at the nodes are generally Mx, My, and Fz
when dealing with the flexural respond of the plate
The force assume at the nodes are generally Mx, My, Fz, Fx and
Fy when the plate respond is due to both flexure and stretching
(membrane action)
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Finite element for plate bending
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami and Bommer (1999)
PBL Export Vision Conclusion
Design of PT Slabs
Flexural and membrane actions for elements in PT slabs
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami and Bommer (1999)
PBL Export Vision Conclusion
Design of PT Slabs
Discretization of floor slab
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (b)
PBL Export Vision Conclusion
Design of PT Slabs
Diagram of load flow under service condition
Y
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (b)
PBL Export Vision Conclusion
Design of PT Slabs
Zero line of shear transfer in Y-direction
A
B
C
D
E
F
G
Products & R&D
Y
Certification
Factory
Export Outreach
Source: Aalami (b)
PBL Export Vision Conclusion
Design of PT Slabs
Assumed design strips superimposed on natural tributaries in X-direction
A
0
0
0
0
0
0
0
0
0
0
0
B
0
0
0
0
0
-250
0
0
0
0
0
0
0
C
-250
0
0
0
-250
250
0
250
0
0
0
0
0
-250
0
D
0
0
250
0
0
0
0
0
-250
-250
0
0
0
0
-250
E
0
0
0
0
-250
-250
0
250
-250
250
250
250
0
0
F
0
Y
G
Products & R&D
0
X
Certification
0
0
Factory
0
Export Outreach
0
0
250
Source: Aalami (b)
PBL Export Vision Conclusion
Design of PT Slabs
Partial view of in-service moments My for design strip B
2
1
-281 kN-m
-12.1 kN
128 kN-m
B 4.88 kN
-74.8 kN-m
19.9 kN
-15.2 kN
21.4 kN
-83.2 kN
+
-8.61 kN
3.99 kN
6.86 kN
DESIGN STRIP
A
-2.52 kN
1.37 kN
Y
X
Products & R&D
CONTOURS AT 20kN INTERVALS
Certification
Factory
Export Outreach
Source: Aalami (b)
PBL Export Vision Conclusion
Design of PT Slabs
Function of Post-tensioning tendon
Uplift
- Counteract selfweight
Precompression
- Mitigate cracking
- Reduce deflection
- Add strength
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Load balancing of effective prestressing forces
hc
Neutral axis
Pe
h1
h2
L1
Pe
h3
L2
L3
Lc
Load balancing for uniform distributed load
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Load balancing of effective prestressing forces
EQ
P1
Pe
EQ
P2
h1
L1
EQ
P2
P3
h2
h3
L2
L3
h4
P4
Pe
Lc
Load balancing for concentrated load.
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Idealised tendon profile
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Idealised tendon profile for two spans with single cantilever
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Idealised tendon profile for two spans with point load
Note:
The center of gravity of the concrete and the center of gravity of the tendon coincide
at the end of the member so that no equivalent load moments are applied at the end
of the member
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Load dumping at peaks
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Equivalent loads with constant prestress force
Products & R&D
Certification
Factory
Source: Post Tensioning Institute (2006))
Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Practical representation of idealised tendon profile
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Resultant balancing forces
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Percentage of Dead Load to Balance
Start with…
Determine PT Force
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Percentage of Dead Load to Balance
Other considerations for percentage of dead load to balance
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Percentage of Dead Load to Balance
INFLECTION
POINT
INFLECTION
POINT
TENDON
Y1
Y2
X1
EQUAL
W2
EQUAL
W3
W1
X1
X3
W4
EQUAL
W2
EQUAL
W3
W1
(a) REVERSED PARABOLA WITH TWO
INFLECTION POINTS
P1
(b) REVERSED PARABOLA WITH ONE
INFLECTION POINT
% of DL balanced = 100[(W2+W3)/DL]
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Average Pre-compression
Defined as the effective post-tensioning force divided by the
gross cross-sectional area of tributary
CENTROID
TOTAL STRESS
PRECOMPRESSION
BENDING
In ribbed structures, such as beam and slab construction,
use the entire cross-section
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Illustration of Tributaries for Axial and Flexural Actions
A
AXIAL FORCE
CENTER
(a) TRIBUTARY FOR AXIAL LOADING
B
CENTROIDAL
AXIS
MOMENT
(b) TRIBUTARY FOR MOMENT
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Pre-compression
• MINIMUM
– Use of 0.85 MPa (125 psi)
•
OPTIMUM
– Use 1.0 (150 psi)
– For roofs use 1.4 MPa (200 psi) if water tightness relies partly on
the structural slab.
• UPPER OPTIMUM
– limit the maximum precompression to 2.0 MPa (275 psi) for slabs
and 2.50 MPa (350 psi) for beams.
– Higher values, while permissible by Code do not generally yield
economical designs.
– Other effects on slab and attached structural member should be
consider
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Tendon Layout
Tendon shape (profile)
Tendon drape
Banded/distributed layout
Tendon stressing
Special layout arrangement
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Profile for Beams and Distributed Tendons
CONTROL POINTS AS
SHOWN ON PLAN
TERMINATED TENDONS
STAGGER AT 300MM
(ANCHOR AT CENTROIDAL AXIS)
STRESSING
END
TYP. UNO
LOW
POINT
SPAN/5
0.6L1
0.4L1
0.5L2
L1
0.5L2
a
TYP.
0.4L3
CGS
TYP. UNO
0.6L3
L3
L2
EXTERIOR SPAN INTERIOR SPAN EXTERIOR SPAN
WITH STRESSING
NO STRESSING
NOTES: a = 0.1 L
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Profile for Banded Slab Tendons
CONTROL POINTS AS
SHOWN ON PLAN
TERMINATED TENDONS
STAGGER AT 300mm
(ANCHOR AT CENTROIDAL AXIS)
STRESSING
END
TYP. UNO
SPAN/5
L1/2
L1/2
LOW
POINT
L2/2
L1
L2/2
L2
b
CGS
TYP. UNO 400
L3/2
L3/2
L3
EXTERIOR SPAN INTERIOR SPAN EXTERIOR SPAN
WITH STRESSING
NO STRESSING
NOTE: b = 600mm
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Tendon Layout Over and Adjacent to a Wall
SLAB/BEAM
CONTROL POINT
(a) ELEVATION AT COLUMN
SLAB/BEAM
CONTROL POINT
WALL
TENDON
L
(b) ELEVATION AT WALL
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Tendon Layout Over and Adjacent to a Wall
(a)
COLUMN
TRIBUTARY
1.5m (5') < L/4
(b)
(a)
WALL
REGION OF
STRAIGHT
TENDONS
(c) PARTIAL PLAN OF SLAB
DISTRIBUTED DIRECTION
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Tendon Profile and Anchorage at Exterior Support
STRAIGHT (OPTIONAL)
SLAB/BEAM
PARABOLA
TENDON
WALL
CENTROID
(a) SLAB/BEAM AND EXTERIOR WALL
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Tendon Profile and Anchorage at Exterior Support
AXIS
TENDON
h/2
(b) ANCHORAGE AT EXTERIOR SUPPORT
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Tendon Layout
Fully banded tendon
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Tendon Layout
Uniformly distributed tendon
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Tendon Layout
50% banded plus 50% evenly distributed tendons over full width
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Tendon Layout
Tendon fully banded in one direction and uniformly distributed in the other direction
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Tendon Arrangement
Use banded tendons in one-direction,
distributed in the orthogonal direction.
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Tendon Layout Options
Aligned Columns
Non-Aligned Columns
SLAB
COLUMN
COLUMN
SLAB
(a) PLAN
REQUIRES ADDED
REBAR
(a) PARTIAL PLAN
(b) BANDS IN THE SHORT DIRECTION
BANDED
TENDONS
DISTRIBUTED TENDONS
(b) TENDON LAYOUT
(c) BANDS IN THE LONG DIRECTION
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Example of Temperature and Shrinkage Reinforcement at Slab Edge
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Banded tendon swerves over non-aligned supports
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Source: Aalami
(a)
Design of PT Slabs
Tendon spacing in slabs
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami and Bommer (1999)
PBL Export Vision Conclusion
Design of PT Slabs
Tendon placement at horizontal curves
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami and Bommer (1999)
PBL Export Vision Conclusion
Design of PT Slabs
Load balancing with banded tendons
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Secondary effects- hyperstatic
•
Prestressed element as part of a statically determinate structure
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Secondary effects- hyperstatic
•
Reactions on a prestressed element due to secondary effects
Products & R&D
Certification
Factory
Export Outreach
Source: The Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Loss of Pre-stressing Forces
 Immediate loss of stress
 Friction loss
 Seating loss (draw-in)
 Elastic shortening
 Long-term losses
 Relaxation in prestressing
 Shrinkage in concrete
 Creep in concrete
 Others, such as
 Change in stress due to flexing of member under applied
loading
 Aging of concrete
 Temperature
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Loss due to Friction and Seating
STRESSING END
TENDON
DEAD END
(a) TENDON GEOMETRY
F
AVERAGE FORCE
Fo
TENDON FORCE
Fx
x
(b) TENDON FORCE PROFILE
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (c)
PBL Export Vision Conclusion
Design of PT Slabs
Loss due to Friction and Seating – ACI 318-02 clause 18.6.2
Effect of friction loss in post-tensioning tendons shall
be computed by
Ps  PxeKl x  
When (Klx+μα) is not greater than 0.3, effect of friction
loss shall be permitted to be computed by
Ps  Px (1  Kl x   )
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Loss due to Friction and Seating – ACI 318-02 clause 18.6.2
Friction coefficients for post-tensioned tendon
Products & R&D
Certification
Factory
Export Outreach
Source: ACI 318-02
PBL Export Vision Conclusion
Design of PT Slabs
Loss due to Friction and Seating
Friction loss diagrams
Products & R&D
Certification
Factory
Export Outreach
Source: ADAPT (2006)
PBL Export Vision Conclusion
Design of PT Slabs
Loss due to Friction and Seating
Friction and long term stress loss diagrams
Products & R&D
Certification
Factory
Export Outreach
Source: ADAPT (2006)
PBL Export Vision Conclusion
Design of PT Slabs
One-end and Two-end Stressing
10m (33 ft)
SLAB
10m (33 ft)
36m (120 ft)
36m (120 ft)
DEAD END
STRESSING END
JACKING STRESS 80% OF ULTIMATE STRENGTH
EFFECTIVE FORCE = 120kN (27k) FOR 12mm (0.5") STRAND
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (a)
PBL Export Vision Conclusion
Design of PT Slabs
Loss due to anchor set
Products & R&D
Certification
Factory
Source: Post Tensioning Institute (2006))
Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Effect of restraint to floor shortening
Post-tensioned floors must be allowed to shorten to enable
the prestress to be applied to the floor. Shortening occurs
because of:
•
•
•
Elastic shortening due to the prestress force
Creep shortening due to the prestress force
Shrinkage of concrete
The elastic shortening occurs during stressing of the
tendons, but the creep and shrinkage are long-term effects
Products & R&D
Certification
Factory
Export Outreach
Source: Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Contribution of Different Factors to Typical Slab Shortening*
PERCENTAGE
%
DESCRIPTION
SHRINKAGE
(SH)
66
CREEP
(CR)
11
ELASTIC SHORTENING (ES)
7
TEMPERATURE
16
(ES)
100
TOTAL
* For a parking structure in southern California
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (d)
PBL Export Vision
Conclusion
Design of PT Slabs
Restraint to floor shortening
 i   LT li
12Ec I i i
Hi 
3
hcol
 
For the purposes of calculating Hi, the value
of EcIi for the column may be reduced by
creep in the column and in some cases
cracking. A reduction of at least 50% from the
short-term elastic properties is normally
justifiable
Products & R&D
Certification
Factory
Export Outreach
Source: Concrete Society (1994)
PBL Export Vision Conclusion
Design of PT Slabs
Restraint to floor shortening
PT
SLAB
SHEAR WALL
UPPER LEVELS
DISTRESS
LOCATIONS
DISTRESS AT
PLAZA
LEVEL
LOCATIONS OF POTENTIAL DISTRESS DUE TO SHORTENING OF
POST-TENSIONED SLABS IN MULTISTORY BUILDINGS
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (d)
PBL Export Vision
Conclusion
Design of PT Slabs
Serviceability requirements- flexural members
Allowable stresses (crack/uncrack section criteria)
Prestressed
Class T
Class U
Class C
Nonprestressed
Assumed behavior
Uncracked
Transition between
uncracked and cracked
Cracked
Cracked
Section properties for stress
calculation at service loads
Gross section
18.3.4
Gross section 18.3.4
Cracked section
18.3.4
No requirement
Allowable stress at transfer
18.4.1
18.4.1
18.4.1
No requirement
Allowable compressive stress
based on uncracked section
properties
18.4.2
18.4.2
No requirement
No requirement
Tensile stress at service load 18.3.3
≤ 7.5 c
≤ 7.5 c t ≤ 12c
No requirement
No requirement
Deflection calculation basis
9.5.4.1
Gross section
9.5.4.2 Cracked
section, bilinear
9.5.4.2
Cracked section,
bilinear
9.5.2, 9.5.3
Effective moment
of inertia
Crack control
No requirement
No requirement
10.6.4
Modified by
18.4.4.1
10.6.4
MI (A s x lever
10.6.7
Computation of ps or s for crack
control
-
-
Cracked section
analysis
Side skin reinforcement
No requirement
No requirement
10.6.7
Products & R&D
Certification
Factory
Export Outreach
arm), or 0.6 y
Source:
PBL
ExportACI318-02
Vision Conclusion
Design of PT Slabs
Serviceability requirements- flexural members
Maximum stresses in concrete immediately after prestress
transfer (before time-dependent prestress losses)
(a) Extreme fiber stress in compression…… 0.6 f ’ci
(b) Extreme fiber stress in tension except as permitted in
(c)…..3√f ’ci
(c) Extreme fiber stress in tension at ends of simply support
members ……6√f ’ci
Products & R&D
Certification
Factory
Export Outreach
Source: ACI 318-02
PBL Export Vision
Conclusion
Design of PT Slabs
Serviceability requirements- flexural members
Maximum stresses in concrete at service loads for class U and
class T prestressed flexural members (based on uncracked
section properties, and after allowance for all prestress losses)
(a) Extreme fiber stress in compression due to prestress plus
sustained load ……..0.45 f ’c
(b) Extreme fiber stress in compression due to prestress plus
total load 3√f ’ci
Products & R&D
Certification
Factory
Export Outreach
Source: ACI 318-02
PBL Export Vision
Conclusion
Design of PT Slabs
Serviceability requirements- flexural members
Permissible stresses in prestressing steel
Tensile stress in prestressing steel shall not exceed the following:
(a) Due to prestressing steel jacking force….. 0.94 fpy
But not greater than the lesser of 0.80 fpu and the maximum
value recommended by the manufacturer of prestressing
steel or anchorage devices.
(b) Immediately after prestress transfer ………0.82fpy
But not greater than 0.74fpu
(c) Post-tensioning tendons, at anchorage devices and couplers,
immediately after force transfer………….. 0.70 fpu
Products & R&D
Certification
Factory
Export Outreach
Source: ACI 318-02
PBL Export Vision
Conclusion
Design of PT Slabs
Serviceability limit state after all losses
The bending moments calculated from the critical loading
conditions given, including the tendonn effects, provide the
serviceability stresses at each section using:
P M
ft 

Ac zt
Top fiber stress
Bottom fiber stress
P M
fb 

Ac zb
M  M A  Pe  M S
Where: zt = the top section modulus
e = eccentricity of tendons, taken as positive below
zb = the bottom section modulus
MA = applied moment due to dead and live loads
M = the total out of section moment MS = moment from prestress secondary effects
Products & R&D
Certification
Factory
Source: The Concrete Society (1994)
Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Serviceability requirements- flexural members
Deflection limitation
Maximum permissible computed deflections
Products & R&D
Certification
Factory
Export Outreach
Source:
PBL
ExportACI318-02
Vision Conclusion
Design of PT Slabs
Redistribution of negative moments -Continuous flexural members
•Where bonded reinforcement is provided at supports in accordance with ACI 318-
02 clause 18.9, it shall be permitted to increase or decrease negative moments
calculated by elastic theory for any assumed loading, in accordance with ACI 31802 clause 8.4
• The modified negative moments shall be used for calculating moments at
sections within spans for the same loading arrangement
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Redistribution of negative moments -Continuous flexural members
•For the moment redistribution to be applicable to beams and slabs other than two
way flat slab system with unbonded tendon, sufficient bonded reinforcement must
be contained to ensure they will act as beam and slab after cracking and not as a
series of tied arches. The minimum bonded reinforcement requirement of ACI
318-02 clause 18.9 will serve this purpose
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Redistribution of negative moments -Continuous flexural members
Procedure to determine the permissible moment redistribution
•Determine factored bending moment at supports by analytical methods.
Compute coefficient of resistance Mn/f ’cbd2, or Mu/(Φf ’cbd2) at supports
•Enter the chart (shown in the following slide) with value of Mu/(Φf ’cbd2).
Read up to appropriate curve, and read left to find permissible percent
redistribution
•Adjust support moments, and corresponding positive moments to satisfy
equilibrium
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Redistribution of negative moments -Continuous flexural members
Permissible moment redistribution
Products & R&D
Certification
Factory
Source: Portland Cement Association
Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Redistribution of negative moments -Continuous flexural members
•Support moments and permissible ranges of their redistribution
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami and Bommer (1999)
PBL Export Vision Conclusion
Design of PT Slabs
Flexural strength of section – Strains and stresses
a
As f y
0.85 f c'b
a
a


M n  C , T  d    As f y  d  
2
2


As f y 

M n  As f y  d  0.59 ' 
fcb 

f
   y'
fc
fy 
fy 
Mn

  ' 1  0.59 ' 
2 '
bd f c
fc 
fc 
Note
(Asfy+Apsfps) is used when nonprestressed
reinforcement is used with prestressing steel
for strength computation
Products & R&D
Certification
Factory
 1 0.59 
Source: Portland Cement Association
Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Flexural strength of section – ACI 318-02 clause 18.7 and 18.8
Design moment strength of flexural members shall be
computed by the strength design method.
a) For members with bonded tendon

 p
f ps  f pu 1 

 1


f pu d

  p '     ' 
fc d p

 

b) For members with unbonded tendon (span to depth ration <= 35)
f c'
f ps  f se  10000
100 p
c) For members with unbonded tendon (span to depth ration > 35)
f c'
f ps  f se  10000
300 p
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Flexural strength of section – ACI 318-02 clause 18.7.3
•Nonprestressed reinforcement conforming to ACI 318-02 clause 3.5.3, if used
with prestressing steel, shall be permitted to be considered to contribute to the
tensile force and to be included in moment strength computations at a stress equal
to the specified yield strength fy.
•Other nonprestressed reinforcement shall be permitted to be included in strength
computations only if a strain compatibility analysis is performed to determine
stresses in such reinforcement
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
At column of two way prestressed slabs and footings

VC   p

f c'  0.3 f pc bo d  V p
Requirements
a)
No portion of the column cross section shall be closer to a
discontinue edge than 4 times the slab thickness
b)
f’c shall not be taken greater than 5000 psi
c)
fpc in each direction shall not be less than 125 psi, nor be
greater than 500 psi
d)
fpc is the average of fpc in two direction
e)
βp is the smaller of 3.5 or (αsd/bo+1.5); αs = 40 for interior
column, 30 for edge column, 20 for corner column; bo is
perimeter of critical section
f)
Vc <= 2√f’c*(bod)
g)
Vp is the vertical component of all effective prestress forces
crossing the critical section. In prestressed slab, Vp term
contributes only a small amount and is conservatively taken
as zero
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
For an exterior column support where the distance from the outside of
the column to the edge of the slab is less than four times the slab
thickness, the prestress is not fully effective around the perimeter bo of
the critical section. Shear strength in this case is therefore conservatively
taken the same as for a nonprestressed slab
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
For nonprestressed slabs and footings, Vc shall be the smallest of (a), (b) and (c)
(a)

4  '
Vc   2   f c bo d
c 

Where βc is the ratio of long side to short side of the column, concentrated load or reaction area
(b)
  sd
 '
Vc  
 2  f c bo d
 bo

Where αs is 40 for interior columns, 30 for edge columns, 20 for corner columns; and
(c)
Products & R&D
Vc  4 f c' bo d
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
At column of two way prestressed slabs and footings
v n   Vc  Vs  /bo d 
V s
Av f y d
(ACI 318-02, Eq. 11-41)
(ACI 318-02, Eq. 11-15)
s
Note
•
The strength of shear reinforcement Vs shall be calculated in
accordance with ACI 318-02 clause 11.5, equation 11-15
•
The area of shear reinforcement Av used in equation 11-15 is
the cross sectional area of all legs of reinforcements on one
peripheral line that is geometrically similar to perimeter of the
column section
•
Shear reinforcement consisting of multiple legs stirrups shall
be permitted in slab with an effective depth, d, >= 6 inches but
>= 16 times shear reinforcement bar diameter
•
vn <=6√f’c
•
Vu /bod <= Φvn where Vu is the factor shear at the design
section
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections
Assumed position of slab edge in punching shear
calculations of limiting condition
Source: ADAPT (2006)
Products & R&D Certification Factory Export Outreach
PBL Export Vision Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
Transfer of moment in slab connections
•
When gravity load, wind, earthquake, or other lateral forces
cause transfer of unbalanced moment Mu between a slab and
a column, a fraction γfMu of the unbalanced moment shall be
transfer by flexure in accordance with ACI 318-02 clause
13.5.3. The remainder of the unbalanced moment given by
γvMu shall be considered to be transferred by eccentricity of
shear about the centroid of the critical section defined in ACI
318-02 clause 11.12.1.2 where
 v  1   f 
Products & R&D
Certification
Factory
(ACI 318-02, Eq. 11-39)
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
Transfer of moment in slab connections
•
The shear stress resulting from moment transfer by
eccentricity of shear shall be assumed to vary linearly about
the centroid of the critical sections defined in ACI 318-02
clause 11.12.1.2. The maximum shear stress due to the
factored shear force and moment shall not exceed Φvn
•
For members without shear reinforcement
vn  Vc /bo d 
Products & R&D
Certification
Factory
(ACI 318-02, Eq. 11-40)
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
Transfer of moment in slab connections
PUNCHED OUT
COLUMN REGION
Mu
D108 /SLIDES /060591
Vu
SHEAR STRESS
DUE TO kM u
SHEAR STRESS
DUE TO Vu
CRITICAL SURFACE
TWO-WAY SLAB
ILLUSTRATION OF CRITICAL SURFACE
FOR THE EVALUATION OF PUNCHING SHEAR STRESSES
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
Arrangement of stirrup shear reinforcement, interior column
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12
Arrangement of stirrup shear reinforcement, edge column
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Shear strength of sections- ACI 318-02 clause 11.12.4
•
•
Shear reinforcement consisting of structural steel I or channel
shaped sections (shearheads) shall be permitted in slabs. The
provisions of ACI 318-02 clause 11.12.4.1 through 11.12.4.9
shall apply where shear due to gravity load is transferred at
interior column supports.
Where moment is transferred to columns, clause 11.12.6.3
shall apply
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Openings in slabs
•
Note: for slab with shear heads, the ineffective portion of the
perimeter shall be one half of the slab without shear heads
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Minimum bonded reinforcement
In bonded post-tensioning systems, supplemental bonded
reinforcement is not required if:
(a) The post-tensioning meets the stress requirements of the
code under service loading
(b) The post-tensioning by itself is adequate for the strength
requirement
Note
Strength requirements during construction and construction
sequence should be reviewed carefully when employing this
method of construction
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (2001)
PBL Export Vision
Conclusion
Design of PT Slabs
Minimum bonded reinforcement
For two way flat slab unbonded post-tensioning system
(a) Bottom reinforcement not required when tensile stress in
positive moment < 2√f ’c
(b) If > 2√f ’c, AS =Nc/0.5fy shall be provided
(c) Top reinforcement AS = 0.00075Acf must always be provided
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Length of minimum bonded reinforcement
• The bonded reinforcement in positive moment areas should
be at least one third of the clear span length and should be
centered in the positive moment area.
• The bonded reinforcement in negative moment area should
extend one-sixth the clear span on either side of the support.
These length, shown schematically in the following slide,
apply when bonded reinforcement is not required for flexural
strength.
• It is not necessary to add development lengths to the lengths
shown
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Minimum bonded reinforcement
Minimum reinforcement lengths and layout for common conditions
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (2001)
PBL Export Vision
Conclusion
Design of PT Slabs
Minimum bonded reinforcement
Strip for placement of minimum bonded top reinforcement
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (2001)
PBL Export Vision
Conclusion
Design of PT Slabs
Minimum bonded reinforcement
Arrangement of temperature and shrinkage tendons
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (2001)
PBL Export Vision
Conclusion
Design of PT Slabs
Lateral analysis
• In high seismic or wind areas however, buildings are usually
provided with members that are specifically designated to
resist the lateral forces. These members are called the primary
lateral load resisting members
• Post-tensioned buildings that are not subjected to either high
seismic or high wind loadings typically do not have a separate
lateral load resisting system. The slabs and beams are
designed to resist the wind or seismic forces in proportion to
either their tributary area or the area of the façade they
support
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Lateral analysis
• Design strength for wind load (ACI 318-02 clause 9.2)
M u  1.2M d  1.0M L  1.6M w  1.0M sec
M u  0.9M d  0.0M L  1.6M w  1.0M sec
• Design strength for seismic load (ACI 318-02 clause 9.2)
M u  1.2M d  1.0M L  1.0M E  1.0M sec
M u  0.9M d  0.0M L  1.0M E  1.0M sec
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Effective width for gravity and lateral loading
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Combination of lateral and gravity moments
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Lateral analysis- analysis procedures
For slab/beam frames subjected to lateral forces, either
wind or earthquake, the following design procedure is
commonly adopted
1.
2.
3.
Design the frame for gravity loading
Combine the actions due to lateral loading with those from
the gravity loading
Check the adequacy of each member for the combined
actions. If necessary, add mild reinforcement to meet the
requirements of the combined actions
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Lateral analysis- Two way slab systems
In addition to the check for the total combined moment to be resisted by the
frame, there is a second requirement for two-way systems.
•
•
At any joint of a two-way system, ACI requires that a
fraction of column moment be resisted by a narrow strip of
slab (referred to as the “a” strip) immediately over the
column. This is referred to as transfer of unbalanced joint
moment
The “a” strip extends 1.5 times the slab thickness, or the
drop thickness if there is one, on either side of the column
as illustrated in the following slide
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Illustration of “a” strip for transfer of unbalanced joint moment
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Lateral analysis- Two way slab systems
The fraction of unbalanced moment to be transferred by the
“a” strip at each joint is calculated as:

g  1/ 1  2 / 3*c1  d  /c2  d 
1/ 2

where
c1 = size of rectangular or equivalent rectangular column, capital, or bracket measured in the
direction of the span for which moments are being determined
c2 = size of rectangular or equivalent rectangular column, capital, or bracket measured transverse
to the direction of the span
d = distance of compression fiber to center of tension
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Lateral analysis- Two way slab systems
•
Beams and slabs are typically sized and designed on the basis of
the gravity loading analysis. They are subsequently checked for
combinations with lateral loading. Non prestressed reinforcement
is added if the gravity design is not adequate.
•
The combination of gravity and lateral moments may result in
moment reversals at the joints, in which case the post-tensioning
falls in the compression zone. In such conditions, the amount of
rebar in the tension zone must be adequate to compensate for the
tensile force in the prestressing tendon and to develop the
moment imposed on the section
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Tendon in compression zone
Products & R&D
Certification
Factory
Export Outreach
Source: Adapt (2006)
PBL Export Vision
Conclusion
Design of PT Slabs
Optimization aspects
• Slab thickness
• Amount of prestressing forces
• Rebar quantities
Products & R&D
Certification
Factory
Export Outreach
Source: Aalami (2001)
PBL Export Vision
Conclusion
Design of PT Slabs
Slab thickness
•
•
•
•
Deflection
Stresses
Punching shear
Span arrangements
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Amount of pressing forces
• Precompressive stresses (P/A)
• Balance load of prestressing tendons
• Adjustment of profile for span arrangements
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
Rebar quantities
• Minimum top and bottom reinforcement
• Strength requirements
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
References
• Adapt Corporation (2006), ADAPT-PT User Manual
• American Concrete Institute (2002), Building Code Requirements for
Structural Concrete (ACI 318-02) and Commentary (ACI 318-02)
• Bijan O Alami (a), Design Requirements and Criteria For PostTensioned Buildings
• Bijan O Alami (b), Design of Concrete Floors With Particular
Reference to Post-Tensioning
• Bijan O Alami (c), Structural Modeling of Post-Tensioning Tendons
• Bijan O Alami (d), Crack Formation and Its Mitigation
• Bijan O Alami and Allan Bommer (1999), Design Fundamentals of
Post-Tensioned Concrete Floors
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Design of PT Slabs
References
• Bijan O Alami (2001), Nonprestressed Bonded Reinforcement in
Post-Tensioned Building Design, ADAPT Technical Publication P201
• Concrete Society (1994), Post-Tensioned Concrete Floors -Design
Handbook
• Portland Cement Association (2002), Notes on ACI 318-02 Building
Code Requirements for Structural Concrete with Design Applications
• Post-Tensioning Institute (2006), Post-Tensioning Manual Sixth
Edition
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion
Conclusion
Thank You!
Products & R&D
Certification
Factory
Export Outreach
PBL Export Vision
Conclusion