THE ASSESSMENT OF REINFORCED CONCRETE SOLID FLOOR SLABS
SUBJECTED TO COMBINED ACTIONS OF
VERTICAL AND LATERAL LOAD
NIN KA YIK
A project report submitted in partial fulfilment of the
requirements for the award of the degree of
Master of Engineering (Civil – Structure)
Faculty of Civil Engineering
Universiti Teknologi Malaysia
JANUARY, 2012
iii
ACKNOWLEDGEMENTS
Appreciation is expressed to those who have made contribution to this Master
Project. To acknowledge everyone who contributed to this project in some manner is
clearly impossible, but I owe a major debt to my supervisor, Dr Roslli Noor
Mohamed, who is also one of my lecturers of civil-structure master course in UTM.
Thanks for his friendly and considerate way of supervision throughout this project.
Without his continual guidance and valuable suggestions, this master project will not
be done well.
I would like to extend my sincere thanks to the management of company
TYLin International Sdn. Bhd., Malaysia, for granting the permission to me to enroll
in the part time master course. In addition, I am also indebted to my company direct
superior, Ir. Gan Shiao Hui, To her, I express my heartfelt thanks for her constant
encouragement and useful ideas in proposing the title of my master project.
Thanks and apologies to others whose contributions I may have forgotten to
acknowledge. Last, but certainly not least, the continual encouragement and support
of my family and friends throughout this project, is deeply and sincerely appreciated.
To all these wonderful people, I am pleased to express my gratitude.
iv
ABSTRACT
Reinforced concrete floor slabs carry gravity load and behave as rigid floor
diaphragms to provide stability and lateral resistance to wind actions, earthquakes
and lateral soil loads. Floor slabs are often analyzed and designed as uniform plate
elements which only possess out-of plane stiffness to carry forces acting normal to
the plane. However, an important issue which is often overlooked by the design
engineers is that in order for a slab to provide ideal diaphragm actions, the slabs must
possess adequate thickness. When slabs are subjected to out-of-plane bending
moment due to gravity load and significant compressive forces, they would behave
like a slender columns or walls. As consequences of additional deflection and
secondary stresses on slabs, particularly at basement floor where lateral forces due to
earth and water pressure are significant, the concrete slabs might crack. The project
studied the assessment of strength and behaviour of conventional basement floor
solid slabs that are subjected to combined actions of vertical and lateral forces. A
typical conventional basement floor was proposed and analysed. The solid slabs
panels were analysed and designed according to equation and coefficient in code of
practice BS8110. Besides, first order and second order analysis using finite element
method were carried on the proposed model subjected to gravity force and combined
gravity and lateral forces. The results indicate that non-linear analysis could
significantly increase the vertical deflection slabs upto 12.29%, bending moment
upto 8.45% and shear forces upto 5.86% in minor or major axis of the slabs
spanning. Possible visible cracking would occur near to the column support area and
soffit of corner slab panels.
v
ABSTRAK
Papak lantai konkrit bertetulang menampung beban graviti dan berkelakuan
sebagai medan lantai yang tegar untuk menyediakan kestabilan dan rintangan sisi
kepada tindakan angin, gempa bumi dan beban tanah sisi. Papak lantai sering
dianalisis dan direka bentuk sebagai unsur-unsur plat seragam yang hanya
mempunyai sifat kekukuhan “luar-satah” untuk menampung daya yang bertindak
secara normal kepada satah. Walau bagaimanapun, isu penting yang sering diabaikan
oleh jurutera reka bentuk adalah bahawa dalam syarat bagi papak untuk menyediakan
tindakan diafragma yang ideal, papak mestilah mempunyai ketebalan yang
sepatutnya. Apabila papak adalah tertakluk kepada daya lentur luar-satah akibat
beban graviti dan daya mampatan yang ketara, kelakuannya berubah menjadi seperti
tiang-tiang atau dinding langsing. Pesongan tambahan dan tegasan sampingan pada
papak, terutamanya di tingkat bawah tanah di mana daya sisi disebabkan oleh bumi
dan tekanan air yang ketara menyebabkan papak konkrit mungkin mengalami
keretakan. Projek ini mengkaji dan menilai kekuatan dan kelakuan papak lantai
konvensional bawah tanah yang tertakluk kepada tindakan gabungan daya-daya
menegak dan sisi. Satu tingkat besmen tipikal yang konvensional telah dicadangkan
dan dianalisis. Panel papak lantai telah dianalisis dan direka mengikut persamaan dan
pekali dalam kod amalan BS8110. Selain itu, analisis peringkat pertama dan
peringkat kedua menggunakan kaedah elemen terhingga telah dilaksanakan ke atas
model tersebut semasa ditindakan dengan daya graviti serta gabungan daya graviti
dan daya sisi. Keputusan menunjukkan bahawa analisis tidak-linear akan
meningkatkan pesongan tegak sebanyak 12.29%, lentur momen sebanyak 8.45% dan
daya ricih sebanyak 5.86% dalam paksi minor atau major rentangan papak lantai.
Analysis juga mendapati bahawa keretakan mungkin berlaku di kawasan
berhampiran dengan sokongan dan permukaan bawah panel papak sudut.
vi
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
ACKNOWLEDGEMENTS
iii
ABSTRACT
iv
ABSTRAK
v
TABLE OF CONTENTS
vi
LIST OF TABLES
viii
LIST OF FIGURES
ix
LIST OF ABBREVIATIONS
xi
LIST OF SYMBOLS
xii
LIST OF APPENDICES
xvi
INTRODUCTION
1.1
General
1
1.2
Background
1
1.3
Objectives
3
1.4
Scope of Study
4
LITERATURE REVIEW
2.1
Introduction
5
2.2
Analysis and Design of Concrete Floors
5
2.2.1
Design Criteria
5
2.2.2
Structural Modeling and Analysis
6
2.2.3
Finite Element Analysis
7
2.3
Elastic Buckling Analysis
9
vii
2.4
3
First and Second Order Elastic or Inelastic Analysis
12
METHODOLOGY
3.1
Introduction
14
3.2
Proposed Basement Floor Layout
14
3.3
Select Analysis software and Design Parameter
15
3.4
Analysis Using Equation and Coefficient by Code
16
3.5
Check Slenderness and Additional Moment Using
19
“Moment Magnifier Method”
3.6
Modeling and Analysis Using Finite Element
19
Method
4
5
3.7
Ultimate Limit State design
20
3.8
Serviceability Checking
20
3.9
Conclusion and Recommendation
21
RESULTS AND DISCUSSION
4.1
Introduction
22
4.2
Deflection
23
4.3
Ultimate Bending Moment
26
4.4
Ultimate Shear Force
29
4.5
Design Flexural Reinforcement
32
4.6
Flexural Cracking
37
CONCLUSIONS AND RECOMMENDATIONS
5.1
Conclusions
40
5.2
Recommendations
43
REFERENCES
44
APPENDICES
46 - 101
viii
LIST OF TABLES
TABLE NO.
TITLE
PAGE
4.1
Summary of Maximum Deflection (Unit: mm)
23
4.2
Summary of Maximum Moment for Overall Floor
(Unit: kNm/m)
26
4.3
Summary of Maximum Shear for Overall Floor (Unit:
kN/m)
30
4.4
Summary of Maximum Moment for Slab Panels at
Gridline C-D/1-4 only (Unit: kNm/m)
33
4.5
Summary
of
Maximum
Required
Flexural
2
Reinforcement for Overall Floor (Unit: mm /m)
33
4.6
Summary
of
Maximum
Required
Flexural
Reinforcement for Slab Panels at Gridline C-D/1-4 only
(Unit: mm2/m)
34
4.7
Summary of Maximum Flexural Crack Width for
Overall Floor (Unit: mm)
34
ix
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
A Typical Basement Floor Structure
2
2.1
Flow Chart for Concrete Floor Design
8
2.2
Design Process Using FE Analysis
10
2.3
Categorization of Stability Analysis Method
11
2.4
Column with (a) Pinned Ends, (b) Fixed Ends,
(c) Fixed–free Ends
11
2.5
Behavior of Frame in Compression and Tension
12
3.1
Flow Chart of Methodology
17
3.2
Proposed Basement Floor for Analysis and Design
18
3.3
3D Model of the Proposed Basement Floor
18
4.1
General Vertical Deflection Contour of Basement
Slabs Not Subjected to Lateral Earth Loading
24
4.2
General Vertical Deflection Contour and Laterally
Deformed Shape of Basement Slabs Subjected to
Lateral Earth Loading
24
4.3
Moment Mx(B) Contour
27
4.4
Moment Mx(T) Contour
28
4.5
Moment My(B) Contour
28
x
4.6
Moment My(T) Contour
29
4.7
Shear Sx Contour
30
4.8
Shear Sy Contour
31
4.9
Flexural Reinforcement Mx(B) Contour
35
4.10
Flexural Reinforcement Mx(T) Contour
35
4.11
Flexural Reinforcement My(B) Contour
36
4.12
Flexural Reinforcement My(T) Contour
36
4.13
Cracking Mx(B) Contour
38
4.14
Cracking Mx(T) Contour
38
4.15
Cracking My(B) Contour
39
4.16
Cracking My(T) Contour
39
5.1
Predicted Floor Top Surface Cracking Pattern
41
5.2
Predicted Floor Bottom 5.2Surface Cracking Pattern
41
xi
LIST OF ABBREVIATIONS
3D
–
Three dimensional
DL
–
Dead /permanent load
FE
–
Finite element
FH
–
Basement floor to floor height
r.c.
–
Reinforced concrete
LL
–
Live /imposed load
LEL
–
Lateral earth load
M&E
–
Mechanical and electrical
Mid
–
Middle
SDL
–
Superimposed dead load
Supp
–
Support
xii
LIST OF SYMBOLS
au
–
Calculated additional deflection for member subjected
to axial load
av
–
Distance of a concrete section from support face
Ac
–
Net cross section area of concrete
As
–
Area of tension reinforcement
As’
–
Area of compressive reinforcement
Asc
–
Area of reinforcement
Asv/sv
–
Area of shear link reinforcement to link spacing
b
–
Slab / beam design width
B1
–
Resultant lateral earth force on basement 1 floor
B2
–
Resultant lateral earth force on basement 2 floor
B3
–
Resultant lateral earth force on basement 3 floor
c
–
Concrete cover
d
–
Effective depth of tension reinforcement
d'
–
Depth of compressive reinforcement
Dx
–
Horizontal deflection in the X-axis direction of analysis
model
Dy
–
Horizontal deflection in the Y-axis direction of analysis
model
Dz
–
Vertical deflection in the Z-axis direction of analysis
model
E
–
Modulus of elasticity.
xiii
ELT
–
Long Term Modulus of elasticity
EST
–
Short Term Modulus of elasticity
fcu
–
Concrete grade /compressive strength.
fy
–
Strength of flexural reinforcement
fyv
–
Strength of shear reinforcement
F
–
Ultimate vertical design load
GL
–
Resultant lateral earth force on ground floor
h
–
Slab thickness
h1
–
Ground water level below ground
h2
–
Height of ground water constituting water pressure
H
–
Storey floor height
I
–
Area moment of inertia
K
–
Column effective length factor / Strength reduction
factor for concrete section subjected to axial load
Ko
–
Coefficient of at-rest lateral earth pressure
KL
–
Effective length of column
L
–
Span of member or length of cantilever/ unsupported
length of column
Le
–
Effective member span length
Lo
–
Clear member span length
Lfac
–
Modification factor for span length in deflection
checking
M
–
Design bending moment
M1 , M2
–
Initial moment
Madd
–
Additional moment due to additional deflection
Mft
–
Modification factor for tension reinforcement in
deflection checking
xiv
Mfc
–
Modification factor for compressive reinforcement in
deflection checking
Mmid
–
Moment at mid-span
Msupp
–
Moment at support
Mx(B)
–
Bottom surface local X-axis moment / flexural
reinforcement / crack width
Mx(T)
–
Top surface local X-axis moment/ flexural
reinforcement / crack width
My(B)
–
Bottom surface local Y-axis moment/ flexural
reinforcement / crack width
My(T)
Top surface local Y-axis moment/ flexural
reinforcement / crack width
N
–
Design ultimate axial load
Nuz
–
Design ultimate axial capacity
Nbal
–
Design axial capacity of balanced section
Pcr
–
Maximum or critical force for buckling
P–į
–
Member curvature effects
P–ǻ
–
Member side sway effects
q
–
Surcharge load on ground
Sx
–
Local X-axis shear force
Sy
–
Local Y-axis shear force
T
–
Design torsional force
V
–
Design shear force
vc
–
Concrete section shear capacity
Vc,av
–
Enhanced Shear Strength at distance 'av' from support
face
Vsupp
–
Design shear force at support
vt
–
Torsional shear stress
xv
vt,min
–
Minimum torsional shear stress, which reinforcement is
required
vtu
–
Maximum combined shear stress (shear plus torsion)
W1, W2, W3
–
Calculated lateral earth pressure
Wbeam
–
Supporting beam width
z
–
Lever arm of the design concrete section
Ȝ
–
Slenderness of member
ȕ
–
Coefficient value for effective span length
ȕa
–
Coefficient value for calculated additional deflection for
concrete section subjected to axial load
ǚ
–
30 Years Creep Coefficient
Ȗ
–
Soil bulk density
Ȗsat
–
Saturated soil density
Ȗw
–
Water density
xvi
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Manual Analysis and Design Calculation to
BS8110: 1997
46
B
LUSAS Output Results – Deflection
54
C
LUSAS Output Results – Ultimate Bending
Moment
72
LUSAS Output Results – Ultimate Shear
Force
84
LUSAS Output Results – Flexural
Reinforcement
90
LUSAS Output Results – Flexural Cracking
96
D
E
F
1
CHAPTER 1
INTRODUCTION
1.1
General
Slabs are the flooring systems of most structures including office,
commercial and residential buildings, bridges, sports stadiums and other facilities
building. The main functions of slabs are generally to carry gravity forces, such as
loads from human weight, goods and furniture, vehicles and so on. In modern
structure design particularly for high rise buildings and basement structures, slabs as
floor diaphragms help in resisting external lateral actions such as wind, earthquake
and lateral earth load.
Depending on the structure framing configuration, architectural requirement,
analysis and design methods selected by the engineer, slabs can be uniform thickness
or ribbed spanning in one way or two ways between beams and/or walls. These
flooring systems can be cast-in-situ reinforced concrete, metal deck with in-situ
concrete, precast concrete or prestressed concrete. Concrete slabs which are resting
on support columns only either with or without column heads and drop panels are
defined as flat slabs.
1.2
Background
In general, reinforced concrete floor slabs are often analyzed and designed as
uniform plate elements which only possess out-of plane stiffness to carry loads
2
acting normal to the plane of the slab. In other words, slabs are designed to resist
only the bending moment in two orthogonal directions as well as twisting moments .
Besides that, slabs also contribute to the lateral load resistance and stability
by transmitting the forces to main framing systems, that are, the floor beams,
columns, shear walls or core walls. This is based on the assumption that in-plane
stiffness of slabs is so great that it act as a rigid diaphragm. Three common types of
lateral actions on a structure are the lateral earth pressures, wind forces and seismic
loads.
Gravity Load
Lateral
Soil
Pressure
Lateral
Soil
Pressure
Floor Slab
Diaphragm
/ RC Wall
Column/
Wall
Pileca
Piles
Figure 1.1:
A Typical Basement Floor Structure
However, an important issue which is often overlooked by the design
engineers is that in order for a slab to provide ideal diaphragm actions, the slabs
must possess adequate thickness [1]. The diaphragm stresses in slab due to in-plane
forces, might have exceeded the concrete resistance capacity and often slabs are not
checked regarding this matter. The cast-in-situ reinforced concrete connection
between slabs and beams or between slabs and columns or walls is another important
feature that is often not carefully reviewed and detailed by the end of design stage to
tally with the preceding analysis assumption.
3
In addition, when slabs are subjected to out-of-pane bending moment due to
gravity load and significant compressive forces due to lateral forces simultaneously,
they would behave like uniaxial bending slender columns. There might be significant
secondary moment and shear forces due to axial forces acting on the deflected slab.
This is difficult to identify based on the first order linear elastic analysis that are
usually adopted for slab design.
The additional deflection and stresses due to additional lateral forces,
improper connection detailing and secondary effect of combined actions, may cause
slabs to crack or even fail, should these are not taken into consideration of analysis
and design. Once the slabs start to crack, the stiffness would be reduced affecting the
performance of the floor system as well as the diaphragm effect on structural
stability. For example, cracks are often observed at basement floor slabs where the
structure may be subjected to both lateral load and gravity load simultaneously.
Figure 1.1 illustrate a typical basement floor structure subjected both gravity loads
and lateral soil loads.
1.3
Objectives
The main objectives of this project are as below:
i.
To study the behaviour of reinforced concrete solid slabs at basement
floor subjected to combined actions of gravity loading and lateral
earth loading and investigate the possibility of cracking,
ii.
To investigate the impact of second order analysis on slender solid
floor slabs, considering nature of geometrical non-linear, concrete
short term and long term modulus of elasticity.
iii.
To propose recommendation for design and detailing requirement of
reinforced concrete solid floor slabs, depending local floor stresses,
framing configuration and support systems.
4
1.4
Scope of Study
In this study, only numerical analysis has been carried out and there is no
experimental work or laboratory test. The structural analysis is based on static
analysis of combined gravity loads and lateral forces on slabs. The study focuses on
a proposed conventional type of car park floor model with typical design
superimposed load of 0.5kN/m2 and imposed load of 2.5kN/m2. Besides carrying
gravity load, the basement slabs also act as a strut system to a series of diaphragm
walls or reinforced concrete walls that retains the surrounding earth. As the loads
acting on the structures are stationery or very slowly over time, the dynamic effect is
assumed insignificant and not considered in the analysis.
Prior to the analysis, suitable thickness for the slab models is determined
using the simple calculation span-to-effective-depth ratio method as recommended
by the code of practice The critical force is later compared with some calculated
lateral soil loads, assuming the slabs to be constructed at basement floor with both
functions of flooring and strutting system to earth retaining wall.
Then, first order linear and second order elastic analysis using finite element
method is carried on the proposed slab models which are applied with gravity force
and followed by combined gravity and lateral forces. The results of internal forces,
displacements, bending moments and shear forces for both types of analysis are
observed and discussed. Possible cracks in slabs due to the stresses and strains are
checked and identified by comparing with the typical design provision and detailing.
Based on the analysis results, some designs and detailing requirements of
reinforced concrete basement slabs are proposed to optimize the design and to avoid
slab cracking and failure.
5
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
The characteristics of reinforced concrete structure in many aspects have
been studied by many researchers. This chapter will briefly reviews on some designs
and analysis methodologies, numerical modeling studies related to reinforced
concrete slabs.
2.2
Analysis And Design Of Concrete Floors
2.2.1
Design Criteria
According to O. A. Bijan et al. (2001) [6], concrete floors designed as plates
should have not failed under code stipulated factored loads and possesses deflections
and crack widths with allowable limits under serviceability condition. In other
words, both ultimate limit and serviceability limit states need to be fulfilled by the
structures.
British Code BS8110 [7] sets the ultimate limit state and serviceability limit
state conditions. At ultimate limit state, the structure must able to resist the most
sever combination of loads to permit uncertainties in estimated loads and
6
performance of materials, besides partial safety factors are applied to the
characteristics loads and characteristics material strengths. The detail partial safety
for load combinations and material strengths are given in the Table 2.1 and Table 2.2
respectively in the code. Characteristic loads are outlined in BS6399 [8] while
characteristic material strength in BS8500 [13] for concrete and BS4449 [9] for steel
reinforcements. As further illustrated by Bhatt et al. [3], plastic analysis on the short
term design stress-strain curves of concrete and reinforcement is used to determine
the section strength.
As stipulated BS8110 Part 2, the maximum total deflection should not exceed
L/250, where L is the span of member or length of cantilever. Besides, the
deflections after installation such as finishes and partitions are only allowed up to
minimum of L/500 for brittle materials; L/350 for non-brittle materials or 20mm.
However, initial camber to the member is allowed to overcome the partial
deflections. Guidance is given by the code that the maximum calculated crack width
should not be more than 0.3mm for ordinary reinforced concrete elements. Bhatt et
al. [3] illustrated that the deflection or cracks of the concrete elements should not
significantly affect the efficiency and appearance. The concept of linear elastic
relationship of steel and concrete stresses is adopted to check the deflection and
cracking taking account of temperature, creep, shrinkage and other possible effects
in short and long term.
2.2.2
Structural Modeling And Analysis
O. A. Bijan et al [6] has summarized that design process of concrete floors
into four main procedures that are, (1) structural modeling, (2) analysis, (3) design
and (4) detailing, as illustrated in chart as shown in Figure 2.1. Prior to the modeling,
the structure outline, supports and design requirements including loads and material
properties are selected.
Modeling involves selecting the structural system and the load paths. Load
path designation is important as the layout of reinforcements governs the orientation
7
and magnitude if the resistance of slab, besides, the skeleton of the structural system
is related. During the structural analysis, internal forces such as axial, shear and
moment forces, displacement, stresses, and strains are computed. Designer can
choose using simple frame, equivalent frame or finite element method for analysis.
Alternatively, when fulfilling some rules, the slabs may also be analyzed using the
design equations and coefficients for moment and shear given in the code of practice
which has been obtained from yield line analysis. Next, structural design involves
determination of the adequacy of the concrete section and amount of required
reinforcement to resist the forces. Last but not least, structural detailing determines
the layout of reinforcement. BS 8110 has recommended some simple detailing rules
for slabs. Additional steel is required for crack control or load distribution. Structural
detailing is very much dependent on experience and engineering judgment.
2.2.3
Finite Element Analysis
According to Brooker [5], finite element analysis is a power computer
analysis method to solve one-, two and three-dimensional structural problems
involving the use of ordinary or partial differential equation. It involves breaking
down the structure member into numerous of discrete elements where each has a
finite size. Solving a series of algebraic equations, the displacements of each element
nodes are obtained. As the solution give approximate results, the smaller the element
the closer the approximation is to the true solution. Finite analysis is useful for slab
design when the geometry is complex, possesses large openings and unusual loading
situation. The design process using finite element (FE) analysis is summarized by
Brooker in the following Figure 2.2.
A. Bijan et. al. [6] explain that FE method is similar to frame method that
require determination of load paths resulting in design strips and design sections for
serviceability and strength check, FE analysis have the advantage of analyzing the
floor at one time and selecting design strips that are more in-line with the natural
response of slabs, resulting in more accurate data on the floor system subjected to
forces.
8
Figure 2.1:
Flow Chart for Concrete Floor Design [6]
As mentioned in Brooker’s technical paper [5], linear analysis is adequate for
ultimate design besides satisfying serviceability check using span-to-effective depth
ratio or conservative value of elastic modulus and slab stiffness. The estimated
deflection may varies from +15% to -30% even though a more sophisticated analysis
is used. Non-linear analysis is carried out to model and check the cracked behaviour
of concrete as slabs crack and reduce stiffness when loaded. There are available
program that can carry out the non-linear analysis with uncracked section properties
9
at initial step and then reanalyze the model using calculated cracked section
properties.
2.3
Elastic Buckling Analysis
In structural stability analysis [1], bucking is a sudden failure of an idealized
structural member when it is subjected to pure compressive axial force and without
direct bending. Buckling or bifurcation (or eigenvalue) analysis is used to compute
the Elastic buckling load. As illustrated in Figure 2.3, when the buckling occurs, the
displacements increase without bound and cause the member to be in as state of
unstable equilibrium. As this stage, the maximum applied axial load is called the
buckling or bifurcation load. Mathematician Leonhard Euler had derived the
following formula to compute critical axial load that can be resisted by a slender and
ideal column.
Pcr =
Where, Pcr
π 2 EI
(KL) 2
Eqn. 2.1
= maximum or critical force
E
= Modulus of elasticity
I
= Area moment of inertia
L
= unsupported length of column
K
= column effective length factor, whose depends on the
columns end support condition as follow:
= 1.0 for both ends pinned (free to rotate)
= 0.50 for both ends fixed
= 0.699 for one end fixed and the other end pinned
= 2.0 for one end fixed and the other end free to move laterally
KL
= effective length of column
10
Although the buckling analysis does not predict actual behaviour of structure
as it is impossible to have idealized structures, the above concept is useful to check
the stability of structure and for computation of column effective lengths.
From the equation, it is observed that the load bearing resistance of a ideal
and slender member depends on the elasticity (E), the second moment of inertia (I)
and support conditions (K) but not the material compressive strength.
Figure 2.2: Design Process Using FE Analysis [5]
11
Figure 2.3: Categorization of Stability Analysis Method [1]
Figure 2.4: Column with (a) Pinned Ends, (b) Fixed Ends,
(c) Fixed–free Ends [1]
12
Figure 2.5: Behavior of Frame in Compression and Tension [1]
2.4
First And Second Order Elastic Or Inelastic Analysis
W.F. Chen and Eric M. Lui [1] report that the type of analysis either first or
second order to be selected for a structural system would depend on magnitude of
applied force, purpose of analysis and the accuracy desired. The main purpose is to
find the force–displacement or stress–strain behaviour of the structural system.
First order analysis is adopted when the deformations of the structure are
small enough to be negligible and hence, there is no change of structure stiffness
throughout the analysis process. Though the results of first order analysis are less
precise than the second-order analysis, it is less complex but sufficient for design
purpose for little deformed structures,
In the second order analysis, both the member curvature (P–į) and the side
sway (P–ǻ) stability effects are considered. The P–į effect is influenced by the axial
force acting through the member displacement due to the rotation of chord. When an
axial force acts through the relative side sway displacements of the member ends, the
consequence effect is called the P–ǻ effect. As shown in Figure 2.5, a tension
member will become stiffer, whereas a member will become softer in compression.
13
Therefore, second-order deformations caused by compression forces are significant
in designing structure elements which are subjected gravity loads. Unlike first order
analysis, numerous iterative procedures are usually required to obtain the final
results.
Elastic analysis assume that there is no effect of yielding as all strains are
recoverable, whereas inelastic analysis consider the loading history or loading path
dependent effect. A second order inelastic analysis will consider both geometry and
material non-linearity structure. Spread-of-plasticity (elasto-plastic) and elastic–
plastic hinged approaches are usually adopted for second order inelastic analysis
.
14
CHAPTER 3
METHODOLOGY
3.1
Introduction
The study of this project relies entirely on numerical experiments, which is
the detailed full-scale simulations using structural software analysis modeling
strategy. This chapter will describe all the project activities that are to be carried out,
involving the work of design and modeling. Figure 3.1 presents the flow chart of
methodology, which are the schematic arrangement of activities until the completion
of project. The details of each of these sequel activities are further explained in the
following sections.
3.2
Proposed Basement Floor Layout
A simple three levels basement car park building is proposed to be analyzed
and designed according to the subsequent proposed methods. Figure 3.2 indicate the
proposed simplified typical basement structural layout plan. Compared to ordinary
floor structure, the main difference to be emphasized here is that the floor slabs have
duo functions of carrying gravity load and strutting the basement wall system that
retains the surrounding earth. To assess the underground multiple car parks floors,
split levels or staggered floors system with ramps is usually adopted in the
conventional basement floor. This type of structural configuration is also included in
this study. The second basement floor (6m below ground) is analysed as maximum
15
horizontal loading would occur at this floor based on the wall analysis (refer
Appendix A for detail calculation).
For the past decade, it has become common to construct basement structure
using reinforced concrete beam and slabs with diaphragm wall system particularly in
city center such as Kuala Lumpur of Malaysia where land area is limited. The same
structure concept is adopted for this project. The typical floor height is 3000mm. The
structure elements to be modeled are 600mm width by 600mm deep floor beams,
600mm width by 600mm deep slopping ramp beams, 250mm thick typical slabs,
600mm thick diaphragm walls and 900x900mm columns.
3.3
Select Analysis Software And Design Parameters
LUSAS structural analysis software is adopted to model, analyze and design the
proposed basement floor structure. The software system uses finite element analysis
method to solve all types of linear, non-linear stress, dynamic and thermal and field
problems such as in bridge engineering, civil and structural works, composite and
general engineering. Hence, LUSAS is suitable for the linear and non-linear analysis
in this study.
Two main design parameters to be determined prior to start of modeling and
analysis are the design strength and design forces. The parameters for the design
strength are determined as following.
i.
Concrete grade, fcu = 35 N/mm2 (cube strength)
ii.
Steel reinforcement strength, fy = 460 N/mm2
iii.
Concrete cover, c = 25mm
iv.
Short Term Modulus of elasticity, EST = 20+0.2(35) = 27 kN/mm2
v.
30 Years Creep Coefficient, ǚ = 2
vi.
Long Term Modulus of elasticity, ELT= EST /(1+ ǚ) = 9 kN/mm2
vii.
Design code to BS8110: 1997
The parameter for design loads are:
16
(a) Dead load, DL
= self-weight of r.c. structure
(Concrete Density = 25kN/m3)
(b) Superimposed dead load, SDL
= 0.5 kN/m2 (M&E services)
(c) Live load (car park), LL
= 2.5 kN/m2 (to code BS6399)
(d) Soil bulk density
= 18 kN/m3
(e) Soil saturated density
= 22 kN/m3
for lateral earth
(f) Soil surcharge load
= 20 kN/m2
load, LEL calculation
(g) Coefficient of at-rest lateral earth pressure = 0.6
= 10 kN/m3
(h) Water density
(i) Serviceability cases: (i)
1.0 (DL+SDL) + 1.0LL (short term)
(ii) 1.0 (DL+SDL) + 0.25LL (long term)
(iii) 1.0 (DL+SDL) + 1.0LL + 1.0LEL (short term)
(iv) 1.0 (DL+SDL) + 0.25LL +1.0LEL (long term)
(j) Ultimate load cases:
(i)
1.4 (DL+SDL) + 1.6LL
(ii)
1.4 (DL+SDL) + 1.6LL + 1.4LEL
Pattern loading is also considered where dead load is applied over the full
length of all spans or bays alternating with the live loading across the full length of
the adjacent bay. Figure 3.3 indicates the 3D model of the proposed basement floor
with pattern loadings created by LUSAS analysis software.
3.4
Analysis Using Equation And Coefficient By Code
To simplify the design, the slabs are analyzed as one way spanning
continuous slab. The slab larger span is two times larger than the smaller span as
shown in Figure 3.2. The shear and moment coefficient from Table 3.12 of BS8110
are adopted to derive the shear and moment forces of the slabs due to gravity load.
The calculation is illistrated in the Appendix A.
Ultimate Limit
State Design
Conclusion &
Recommendation
Long
Term
Figure 3.1: Flow Chart of Methodology
Serviceability Check–
Deflections & Cracks
Short
Term
Short
Term
Long
Term
Second Order Static
Analysis (Non-Linear)
Check Slenderness &
Additional Moment Using
“Moment Magnifier Method”
– Consider Combined
Gravity & Lateral Load
First Order Static
Analysis (Linear)
Modeling & Analysis Using Finite Element Method
- Consider All Load Cases
Select Analysis Software
(LUSAS) & Design
Parameters (By Code)
Analysis Using Equation & Coefficient By Code
- Consider Gravity Load Only
Propose Basement Slab
Layout Model &
Preliminary Member Size
17
18
Figure 3.2: Proposed Basement Floor for Analysis and Design
Figure 3.3: 3D Model of the Proposed Basement Floor
19
3.5
Check Slenderness And Additional Moment Using “Moment Magnifier
Method”
As the slab would be subjected to axial load, slenderness of slab is check base on
the effective length divided by the slab thickness. The checking is according to BS
8110 Clause 3.8.1.3 to 3.8.1.8 and assuming it is braced by beams and columns or
walls. Slabs are usually slender as its effective length dimension more than 10 times
larger than slab thickness. Thus, it is checked as compressive member with bending
moment like a column by using “Moment Magnifier Method” as recommended by
BS8110 Clause 3.8.2 to 3.8.4. The following assumption is adopted to calculate the
additional moment induced by deflection:
(1) Connection between slab and diaphragm wall is pinned as minimum post
installed anchorage is provided due to construction sequence. These support
condition will provide nominal restraint to slab which stimulate the end
condition ‘3’ as per Clause 3.8.1.6.2.
(2) It behave as braced element as supported by beams, walls and columns are
design to resist gravity load. Assumption is made with no significant vertical
deflection at supports.
(3) As in conventional design procedure, the beams and columns are not design
to provide rotation resistance to slabs, the end condition is also defined as ‘1’
as per Clause 3.8.1.6.2.
The calculation is presented in Appendix A.
3.6
Modeling & Analysis Using Finite Element Method
The basement floor structures are modeled using LUSAS Modeller
component. The input sequences are geometry, attributes, load cases, meshing,
utilities and controls. Slabs modeled as “Shell” element whereas Beams modeled as
“Beam” element. Columns are modeled as vertical transition restraint supports,
while walls are defined as supports providing vertical transition restraint and inplane transition restraint. All beams, columns and walls are not providing rotation
restraint to the slabs.
20
Then, the model is analyzed using LUSAS Solver. Lastly, the results
available are averaged contours, deformed mesh, moment and shear forces, woodarmer reinforcement calculation, displacement and combined or enveloped results.
The types of analysis carried out are:
(1) First order static analysis (linear) – short term behaviour
(2) First order static analysis (linear) – long term behaviour
(3) Second order static analysis (geometric non-linear) – short term
behaviour
(4) Second order static analysis (geometric non-linear) – long term behaviour
Second order analysis considers non-linearity in geometry, including P–į and
P–ǻ effect.. The program will analyze the geometrical changes with increment of
combined axial and lateral loading until the displacement and element forces
converged.
3.7
Ultimate Limit State Design
Ultimate limit state design on slabs is carried out to check section adequacy
and determine the required reinforcement to resist the design forces - moment, shear,
torsion and axial forces. Forces resulted from each of the analysis method except
Euler Buckling, are designed to code BS8110. Manual calculation is carried out for
the analysis using equation and coefficient and moment magnifier method by code.
Ultimate limit state design will be done by LUSAS program for the relevant analysis
methods.
3.8
Serviceability Checking
Deflection and cracking of the floor slabs are checked to requirement of code
BS8110. Manual calculation is carried out for the analysis using equation and
21
coefficient and moment magnifier method by code. LUSAS program was used to
calculate slab deflection for the relevant analysis methods.
3.9
Conclusion and Recommendation
The results from serviceability limit and ultimate limit state from each
analysis method are summarized in figures, tables and write-up. Objective of the
project is reviewed and results are concluded. Some recommendation for future work
would be proposed as well.
22
CHAPTER 4
RESULTS AND DISCUSSIONS
4.1
Introduction
All the analysis and design results obtained in this study rely on the manual
calculation to British code of practice and output data of the computer software
analysis - LUSAS. There are four (4) types of analysis models created as listed
below:
1.
Model (M) – Manual calculation to BS8110:1997
2.
Model (A) – Linear model subjected to gravity load only
3.
Model (B) – Linear model subjected to gravity and lateral forces
4.
Model (C) – Non-linear model subjected to gravity and lateral forces
Results from software analysis model are compared with the manual
calculation output. The detail calculation and results of respective models are
compiled in Appendices. The following analysis and design outputs are summarized
and discussed.
(i)
Deflection
(ii)
Ultimate Bending Moment
(iii)
Ultimate Shear Forces
(iv)
Design Flexural Reinforcement
(v)
Flexural Cracking
23
4.2
Deflection
Figure 4.1 and Figure 4.2 illustrates general vertical deflection contour and
laterally deflected shape of the basement slabs with and without lateral earth loading.
More details of deflection contour and values for respective load cases of each
analysis model are presented in Appendix B.
Table 4.1: Summary of Maximum Deflection (Unit: mm)
Deflection
Diretion
Type
Short
Term
Dx
Long
Term
%
Difference
Short
Term
Dy
Long
Term
%
Difference
Short
Term
Dz
Long
Term
%
Difference
%
%
%
Model
Model
Model
Differ.
Differ.
Differ.
(A)
(B)
(C)
(A) &
(B) &
(A) &
(B)
(C)
(C)
0.13
4.40
3.93
+3284.62
-10.68
+2923.08
0.29
11.82
11.82
+3975.86
+0.00
+3975.86
+123.07
+168.64
+200.76
-
-
-
0.43
2.69
1.84
+525.58
-31.60
+327.91
0.91
5.83
5.59
+540.66
-4.12
+514.29
+111.63
+116.73
+203.80
-
-
-
10.51
10.75
11.33
+2.28
+5.40
+7.80
23.44
26.23
26.32
+11.90
+0.34
+12.29
+123.03
+144.00
+132.30
-
-
-
Notes: 1. Concrete Short Term Modulus of elasticity, EST = 27 kN/mm2
2. Concrete Long Term Modulus of elasticity, ELT = 9 kN/mm2
24
Figure 4.1:
General Vertical Deflection Contour of Basement Slabs Not
Subjected to Lateral Earth Loading
Figure 4.2:
General Vertical Deflection Contour and Laterally Deformed Shape
of Basement Slabs Subjected to Lateral Earth Loading
25
The analysis is based on assumption that resistance to horizontal movement
of perimeter basement walls and columns are fully dependant on the in-plane
stiffness of floor slabs. Nevertheless, in actual condition, the basement walls and
columns would provide some out-of-plane stiffness. Prior to modeling the basement
floor using LUSAS software, the slab thickness and beam sizes are selected were
analyzed and designed by manual calculation to satisfy the minimum requirement of
the Code of Practice BS8110:1997. The vertical deflection of slab and beam is
controlled by the span-to-depth ratio and enhancement of flexural reinforcement.
The detail calculation is attached in Appendix A.
Horizontal movement of slabs and wall are mainly caused by lateral earth
loading. As shown in Table 4.1, with the long term creep effect on concrete, the
value of deflections for both horizontal and vertical have increased to more than two
times (approximate within 100% to 200% increment).
As consequences of the nature configuration of conventional basement floor
with split levels or staggered floors with car ramps, the stiffness of floor slabs would
be varies throughout the entire floor, depending on the width and length of the floor
area against the lateral earth loading. Therefore, it could be observed that maximum
long term horizontal movements, Dx = 11.82mm and Dx = 5.59 occur at the location
of ramp which is just next to the basement wall at Gridline A-B/3-5. The 4.3m width
of the ramp resisting the lateral earth loading from basement wall is relatively small
compared to other slabs (•17.2m width adjacent to wall). The wider the slab width
perpendicular to wall, the larger the slab in-plane stiffness, resulting in lesser
horizontal movement caused by earth pressure.
In addition, the horizontal forces have increased the vertical deflection of
slabs by 11.90% and 12.29% for the long term linear Model (B) and non-linear
Model (C) analysis. All maximum vertical deflection happens near the mid-span of
floor slabs. Hence, analysis combining lateral and gravity loading would have
significant impact on the movement of basement wall and slabs.
Despite the horizontal forces on basement slabs, the vertical and horizontal
displacements of this propose basement floor 2 (6m below ground) are still within
26
the permissible limit. Allowable deflection limit as per BS8110: Part 2: Clause 3.2
calculated as below:
(i)
Limit Dx = Dy = Floor height, H / 500
= 3000/500
= 6 mm
(ii)
Limit Dz
= Span Length, L / 250
= 8600/250
= 34.4mm
However, it is predicted that the deeper the basement floor, the larger the
horizontal forces that would causes more significant movement to the wall and slabs.
4.3
Ultimate Bending Moment
The summary of maximum ultimate moment for overall basement floor slab
is tabulated in Table 4.2.
Table 4.2: Summary of Maximum Moment for Overall Floor (Unit: kNm/m)
%
%
%
Differences
Differences
Differences
(A) & (B)
(B) & (C)
(A) & (C)
65.57
+0.10
-4.32
-4.22
61.29
66.19
+0.43
+7.99
+8.45
100.09
100.31
99.92
+0.22
-0.39
-0.17
113.57
114.30
117.22
+0.64
+2.55
+3.21
Type of
Model
Model
Model
Moment
(A)
(B)
(C)
Mx(B)
68.46
68.53
Mx(T)
61.03
My(B)
My(T)
Notes: 1. Mx(B) = Bottom surface local x moment (minor axis sagging)
2. Mx(T) = Top surface local x moment (minor axis hogging)
3. My(B) = Bottom surface local y moment (major axis sagging)
2. My(T) = Top surface local y moment (major axis hogging)
From Table 4.2, it is observed that relatively, there is an increase to the
ultimate moment in slabs when it is subjected to lateral earth loading (Model (B) and
27
(C)). The second order analysis (geometric non-linear) has increased the hogging
moment Mx(T) and My(T) by 8.45% and 3.21% respectively. In this analysis,
My(T) denotes the top surface moment of the main spanning direction of the slabs
while Mx(T) is the top surface moment in the distribution direction.
From Figure 4.3, it is found that sagging moments Mx(B) are significant
higher at the corner slab panels of basement floors mainly due to the gravity load
and there are hogging moments My(T) for slab panel adjacent to the down side of
ramps is higher. From Figure 4.3 to Figure 4.6, it appears that large hogging and
sagging moment will occur at the corner edges between walls, between beams or
between beam and wall.
Figure 4.3:
Moment Mx(B) Contour
To compare with the manual calculation, ultimate moments of slab panels at
Gridline C-D/1-4 are extracted from analysis models and tabulated in Table 4.4. For
linear analysis Model (M) and Model (A), the calculated moment My(B) is very
close to the computer analysis as there is only different of 1.28%. However, despite
one way slab is assumed in manual calculation, there are moments in the minor
spanning of slab (distribution direction) from the finite element analysis. Calculated
28
hogging moment My(T) is less than the values from the software analysis (> 18%
difference).
Figure 4.4:
Figure 4.5:
Moment Mx(T) Contour
Moment My(B) Contour
29
Figure 4.6:
Moment My(T) Contour
The nature of beams sagging may have induced additional moment to be
redistributed to the supports at the stiffer location near to column where full vertical
restraint is assigned in analysis. In contrary, manual design calculation for slab
supported by beams assumes that there is no significant deflection at supporting
beams. Without geometric non-linear analysis, despite subjected to lateral earth
loading, there is no significant secondary moment added to the initial moment.
Comparing the value of M+Madd and Model (C) in Table 4.4, the additional
moment calculated using magnifier method to code BS8110 is relatively close to the
result generated from second order analysis using software, that are, 100.27 kNm
and 106.42 kN respectively. The percentage of increment in moment generated by
non-linear analysis is more than 5.52% for minor moment Mx and 7.92% for major
moment My (refer Table 4.4).
4.4
Ultimate Shear Force
From Table 4.3, it shows that the manually calculated shear forces are
relatively much lower than the result from finite element using software analysis. As
30
one way spanning slab is assumed in manual calculation, there is no shear force in
Sx minor axis direction. As presented in Figure 4.7 and Figure 4.8, all these high
shear forces are located at the interfacing area between walls and slabs, columns and
slabs or beam-wall-slab intersection area.
Table 4.3: Summary of Maximum Shear for Overall Floor (Unit: kN/m)
Type
Manual
of
Calcula-
Shear
tion (M)
SxMax
SxMin
SyMax
SxMin
Model
Model
Model
% Differ.
% Differ.
% Differ.
(A)
(B)
(C)
(A) & (B)
(B) & (C)
(A) & (C)
0
427.47
426.48
421.85
-0.23
-1.09
-1.31
0
-345.13
-348.34
-365.36
+0.93
+4.89
+5.86
67.60
761.88
763.59
760.78
+0.22
-0.37
-0.14
-67.60
-718.62
-717.55
-736.63
-0.15
2.66
+2.51
Figure 4.7:
Shear Sx Contour
31
Figure 4.8:
Shear Sy Contour
The vertical displacement of supporting beam considered in software
analysis may have caused the shear forces to be redistributed and concentrated at the
stiffer supports – columns and walls. A check on maximum shear capacity for slab
design is done based on enhanced shear strength calculation as allowed in BS8110
Clause 3.8.5.8 (refer Appendix A). The maximum shear forces occurred within the
distance of two times of slab effective depth (av ” 2d) from supporting face, are still
within the allowable shear capacity. No shear reinforcement is required for all load
cases.
From Table 4.3, the geometric non-linear analysis (Model (C)) has shown
increment in the ultimate shear forces in slabs. Without performing this second order
analysis, the additional shear forces in slab would not be generated when it is
subjected to lateral earth loading.
32
4.5
Design Flexural Reinforcement
Maximum required slab flexural reinforcements for overall floor are
summarized in Table 4.5.
From Table 4.5, it is observed that there is a significant short fall in flexural
reinforcement provided for minor-axis Mx(T) and Mx(B) as only nominal
reinforcement (§0.13% of concrete area) is provided as distribution bar for the one
way spanning slabs as per manual design calculation. The required flexural
reinforcement is proportional to the design moment forces. Hence, additional
reinforcement is required for the added secondary moment in non-linear analysis,
particularly for reinforcement Mx(T) and My(T) by comparing Model (A) to Model
(C). In addition, more reinforcement is required at the corner edges of slabs where
moments are higher. The pattern of flexural reinforcement contour is similar to the
moment contour as shown in Figure 4.9 to Figure 4.12.
Without considering second order analysis, the area of reinforcement
calculated manually will be a short fall of more than 21% for My(T) and My(B).
However, as more reinforcement is provided for My(B) to control deflection as per
manual calculation, the reinforcement provided is sufficient. In contrary,
reinforcement provided for My(T) is not enough.
From Table 4.6, summary of reinforcement for slab panel at Gridline C-D/14 indicates insufficient reinforcement provided at Mx(T) and My(T) near to the
columns supporting area. Minimum reinforcement as per manual calculation is
sufficient for bottom distribution reinforcement in this panel although minor axis
moments are observed in the finite element analysis. Generally, there is no top
reinforcement Mx(T) and My(T) required at the mid-span of slabs for all load cases,
except for the slab panel adjacent to the down side of ramps where there is a present
of top surface moment (hogging) throughout the span.
0
83.32
83.32
Mx(T)
My(B)
My(T)
100.27
100.27
0
0
Madd
M+
98.61
82.25
42.37
21.83
(A)
Model
98.56
82.22
42.48
21.79
(B)
Model
106.42
91.80
44.71
24.82
(C)
Model
+18.35
-1.28
-
-
(M) & (A)
Differences
%
+6.13
-8.45
-
-
(C)
(M + Madd) &
Differences
%
-0.05
-0.04
+0.26
-0.18
(A) & (B)
Differences
%
+7.97
+11.65
+5.25
+13.91
(B) & (C)
Differences
%
+7.92
+11.61
+5.52
+13.70
(A) & (C)
Differences
%
0
934
934
Mx(T)
My(B)
My(T)
*1141
1141
0
0
Madd
M+
*1307
1138
*724
*817
(A)
Model
*1316
1141
*727
*818
(B)
Model
*1353
1136
*789
*781
(C)
Model
+39.94
+21.84
-
-
(M) & (A)
Differences
%
+1.05
-0.44
-
-
(C)
(M + Madd) &
% Differences
+0.69
+0.26
+0.41
+0.12
(A) & (B)
Differences
%
%
+2.81
-0.44
+8.53
-4.52
(B) & (C)
Differences
Notes: 1. ‘*’ Denote area of reinforcement required has exceeded the area of reinforcement provided (refer Table 4.7)
0
(M)
Calculation
Manual
Mx(B)
Reinf.
Type of
Table 4.5: Summary of Maximum Required Flexural Reinforcement for Overall Floor (Unit: mm2/m)
+3.52
-0.18
+8.98
-4.41
(A) & (C)
Differences
%
Notes: 1. ‘-’ denotes values that are not able to be compared as there is no design forces calculated in distribution direction Mx of the slabs in
the manual calculation for one way spanning slabs.
0
(M)
Calculation
Mx(B)
Moment
Type of
Manual
Table 4.4: Summary of Maximum Moment for Slab Panels at Gridline C-D/1-4 only (Unit: kNm/m)
33
0
934
934
Mx(T)
My(B)
My(T)
*1141
1141
0
0
Madd
Mi +
*1119
922
*503
325
(A)
Model
*1119
921
*504
325
(B)
Model
*1217
1037
*531
325
(C)
Model
+19.81
-1.28
-
-
(Mi) & (A)
Differences
%
+6.66
-9.11
-
-
(C)
(Mi + Madd) &
% Differences
0.00
-0.11
0.20
0.00
(A) & (B)
Differences
%
T12-300
T12-300
T16-100
T16-200
Mx (T)
My (B)
My (T)
Provided
Provided
Reinf.
1005
2010
377
377
(mm /m)
2
Steel Area
Type of
Mx (B)
Crack
Type of
0.2899
0.0956
0.4300
0.5006
(A)
Model
0.2922
0.0958
0.4328
0.5013
(B)
Model
0.2996
0.0100
0.4698
0.4666
(C)
Model
+0.79
+0.21
+0.65
+0.14
(A) & (B)
Differences
%
+2.53
+4.38
+8.55
-6.92
(B) & (C)
Differences
%
Table 4.7: Summary of Maximum Flexural Crack Width for Overall Floor (Unit: mm)
%
+3.35
+4.60
+9.26
-6.79
(A) & (C)
Differences
%
+8.76
+12.60
+5.36
0.00
(B) & (C)
Differences
Notes: 1. ‘*’ Denote area of reinforcement required has exceeded the area of reinforcement provided (refer Table 4.7)
0
(Mi)
Calculation
Manual
Mx(B)
Reinf.
Type of
%
+8.76
+12.47
+5.57
0.00
(A) & (C)
Differences
Table 4.6: Summary of Maximum Required Flexural Reinforcement for Slab Panels at Gridline C-D/1-4 only (Unit: mm2/m)
34
35
Figure 4.9:
Flexural Reinforcement Mx(B) Contour
Figure 4.10:
Flexural Reinforcement Mx(T) Contour
36
Figure 4.11:
Flexural Reinforcement My(B) Contour
Figure 4.12:
Flexural Reinforcement My(T) Contour
37
4.6
Flexural Cracking
The flexural cracking is checked in the finite element analysis model by using
the flexural reinforcement calculated by manual calculation to BS8110:1997. Table
4.7 summarizes the maximum flexural crack width of slab. As top and bottom
flexural reinforcement provided (T12-300) was not sufficient for the minor axis
direction, the crack width for Mx(T) and Mx(B) larger than the limitation of 0.3mm
as per the code of practice. As shown in Figure 4.13 and Figure 4.14, larger Mx(T)
cracking appears at top surface of the column support area, while Mx(B) cracking
appears at the slab soffit of corner and edge panels. Both type large cracking also
occur at the sharp corner edges.
Despite the reinforcement provided for My(T) for some area is insufficient in
the ultimate design, the My(T) cracking is still within permissible 0.3mm. The closer
spaced reinforcement (T16-200) may have controlled the cracking at serviceability
state. Additional reinforcement with closer spacing is recommended to be provided at
the expected stress concentrated area to control cracking.
In general, the reinforcement spacing rules given in BS8110 Clause 3.12.11
controls the flexural cracking in slab panels. No crack width calculation checking is
necessary for the manual calculation as the requirement specified in Clause
3.12.11.2.7 is complied.
38
Figure 4.13:
Cracking Mx(B) Contour
Figure 4.14:
Cracking Mx(T) Contour
39
Figure 4.15:
Cracking My(B) Contour
Figure 4.16:
Cracking My(T) Contour
40
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
5.1
Conclusions
Based on the results of all load cases and analysis methods, the following conclusions
can be drawn:
(1)
The total vertical and horizontal deflection of slabs and wall caused by
gravity and lateral earth loading in long term, would increase to more than
two times. Nevertheless, the span-to-depth ratios method with enhancement
by flexural reinforcement may be used to satisfy the deflection controlling in
general.
(2)
The in-plane stiffness of floor slabs would be varies throughout the entire
floor, depending on the configuration of floor framing layout, width and
length of the floor area against the lateral earth loading. Caution should be
made in determining the configuration of structural framing plan, thickness
and size of structural elements to control movements due to effects of
combined gravity and lateral loadings
(3)
Non-linear analysis combining lateral and gravity loading could significantly
increase the vertical deflection slabs, depending on the magnitude of lateral
force and initial vertical deflection due to gravity load or actual site
construction deviation.
41
Figure 5.1:
Figure 5.2:
Predicted Floor Top Surface Cracking Pattern
Predicted Floor Bottom Surface Cracking Pattern
42
(4)
The second order analysis is important for the analysis of basement slabs
subjected to combined gravity and lateral earth loading as there is a
significant increment to the bending moment and shear forces in both minor
and major axis of the slabs spanning.
(5)
Higher flexural moment than expected will occur at the following location:
(i)
Sagging moment Mx(B) at the corner slab panels
(ii)
Hogging moment My(T) at slab areas near to column supports and
adjacent to the down side of ramp.
(iii)
Larger hogging and sagging moments Mx(T), Mx(B), My(T) and
My(B) at the corner edges between walls, beams or beam and wall.
Hence, additional reinforcements or trimmer bars with closer spacing are
recommended to be provided at these potential high flexural stresses areas to
control cracking.
(6)
Despite one way slab is assumed in manual calculation, there is a present of
flexural moment Mx(T) and Mx(B) in the minor axis spanning of slab
(distribution direction) from computer analysis. In actual condition,
depending on the stiffness distribution of overall plan, the classified onespanning slab may have behaved two-way spanning and causing cracking at
areas where nominal reinforcement is provided as distribution bars only.
Finite element analysis with the aid of computer software should be
recognized to predict the behaviour of slab in this complex situation.
(7)
As calculated crack width is more than 0.3mm for Mx(T) and Mx(B), visible
slab cracking would occur at top and bottom surface in same direction of slab
main direction spanning near to the column support area and soffit of corner
slab panels. The predicted visible cracking is shown in Figure 5.1 and Figure
5.2. Besides causing unpleasant external appearance and user comforts, the
excessive cracking may cause reinforcement exposed to potential corrosion
and further degradation of concrete performance.
(8)
The moment magnifier method to code BS8110 could be used as for a
preliminary checking on additional moment to slabs subjected to in-plane
43
forces (axially loaded). However, second order analysis and finite element
method would be recommended to obtain more precise result due to complex
geometry and unusual loadings.
5.2
Recommendations
The followings are some suggestions proposed related to the shortcomings found in
this project and may be adopted to enhance or further the study on basement slabs:
(1)
Thermal and shrinkage effect could be another factor influencing the
performance of basement slabs. Further study to include this factor can be
considered.
(2)
Settlement of foundation, columns and wall support due to ground movement
or concrete elastic or creep shortening may be considered for further study.
(3)
Further analysis based on material non-linear due to the changes of properties
in concrete crack section may be carried out.
(4)
It could be logically predicted that when the basement floor level is deeper,
the larger horizontal forces that would cause more movement and secondary
forces onto the wall, beams and slabs. Hence, analysis of deeper basement
floor should be carried out to study the influences.
(5)
Different configuration of floor layout with more beams can be proposed to
study the differences.
(6)
Case study and monitoring on actual constructed floors or floors to be
constructed should be carried out to verify the behaviour of slabs.
44
REFERENCES
1.
W.F. Chen & E. M. Lui. Handbook of Structural Engineering. 2nd Edition.
Boca Raton, New York: CSR Press. 2005.
2.
S.S. Bryan & C. Alex. Tall Building Structures: Analysis & Design. United
States of America: John Wiley & Sons, Inc. 1991.
3.
P. Phatt, T.J. MarGrinley & B.S. Choo. Reinforced Concrete Design Theory
and Examples. 3rd Edition. London and New Work: Taylor & Francis. 2006.
4.
S.S. Ray. Reinforced Concrete Analysis & Design. New Work: Blackwell
Science. 1999.
5.
Brooker. How to Design Reinforced Concrete Flat Slab Using Finite Element
Analysis. The concrete Centre. 2006.
6.
O.A. Bijan, S.E. & Gail S. Kelly. Design of Concrete Floors with Particular
Reference to Post-Tensioning. PTI Technical Paper. 2001.
7.
British Standard Institution. Structural Use of Concrete. London, BS 8110.
1997.
8.
British Standard Institution. Loading For Buildings - Code of Practice For
Dead Load and Imposed Loads. London, BS 6339. 1996.
9.
British Standard Institution. Steel for The Reinforcement of Concrete Weldable Reinforcing Steel - Bar, Coil and Decoiled Product - Specification.
London, BS 4449. 2005.
45
10.
British Standard Institution. Code of Practice for Earth Retaining Structure.
London, BS 8002. 1992.
11.
British Standard Institution. Code of Practice for Protection Of Structures
Against Water From The Ground. London, BS 8102. 1990.
12.
St George (South London) el at., Case Studies On Applying Best Practice to
in-situ Concrete Frame Buildings. The concrete Centre, 2004.
13.
British Standard Institution. Specification for Constituent Materials and
Concrete. London, BS 8500. 2006.
46
APPENDIX A
MANUAL ANALYSIS AND DESIGN CALCULATION TO BS8110: 1997
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
Slab Analysis to BS8110:1997
Slab Marking:
Typical Basement Floor Slab (250Thk)-One Way Spanning
Dead Load
(Per Meter Strip)
SDL = M&E Services
DL = Slab Selfweight
=
=
kN/m x Span Length, L
0.5 x 8.6
0.25x24x8.6
=
=
kN
4.3
51.6
55.9
Live Load
LL = Car Park
=
2.5x8.6
=
21.5
=
112.66
Loading
Ultimate Design Load
Design Forces
F = 1.4(DL+SDL)+1.6LL
(Cl.3.5.2.4 & Table 3.12)
Max. Bending Moment:
At Mid Span,
At 1st interior Support,
Mmid
Msupp
=
=
0.086FL
-0.086FL
=
=
kNm
83.32
-83.32
Max. Shear
Vsupp
=
0.6F
=
kN
67.60
At 1st interior Support,
Beam Analysis to BS8110:1997
Typical Basement Floor Beam (600x600)
Beam Marking:
2
Loading
Dead Load
SDL = M&E Services
DLslab = Slab Selfweight
DLBeam = Beam Selfweight
=
=
=
kN/m x Span Length, L
0.5 x 8.6x8.6
0.25x24x8.6x8.6
0.6x(0.6-0.25)*24*8.6
Live Load
LL = Car Park
=
2.5x8.6x8.6
Ultimate Design Load
Design Forces
F = 1.4(DL+SDL)+1.6LL
2
=
=
=
kN
36.98
443.76
43.344
524.084
=
184.9
= 1029.5576
(Cl.3.4.3 & Table 3.5)
Max. Bending Moment:
At Mid Span,
At 1st interior Support,
Mmid
Msupp
=
=
0.09FL
-0.11FL
=
=
kNm
796.88
-973.96
Max. Shear
Vsupp
=
0.6F
=
kN
617.73
At 1st interior Support,
1 of 1
Dec 2011
47
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
1 of 1
Dec 2011
Calculation of Lateral Earth Load
3
Soil Properties (Assumption Based on BS8002)
Bulk Density
Saturated Density
Water Density
Lateral Earth Coeeficient
Surchage Load
=
18
=
kN/m
18
sat
=
20
=
20
w
=
10
=
10
=
sat w
=
10
Ko
q
=
=
0.6
20
=
=
0.6 (At-rest Pressures)
20
Other Data (Proposed as per Conventional Typical Basement Floor)
Basement Floor to Floor Height (Typpical)
Ground Water Level Below Ground
Height of Ground Water constituting water pressure
FH =
h1 =
h2 =
3m
1m
8m
Lateral Earth Pressures (Per Meter Strip)
2
At Ground Level
W1
=
Koq
=
kN/m
12.00
At Water Level
W2
=
Koq + Koh1
=
22.80
At Lowest Basement Floor, B3
W3
=
Koq + Koh1
=
150.80
Analysis on Wall Based on Continuous Beam Method
Resultant Lateal Forces:
GL
=
kN/m
24.80
B1
=
152.5
B2
=
367.93
B3
=
166.58
==> Lateral Earth Resultant Force, B2 is Adopted for Floor Analysis
!"#
Diaphragm /
RC Wall
Lateral Soil
Pressure
(BS8102)
48
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
1 of 1
Dec 2011
Moment Magnifier Method Analysis to BS8110:1997
Slab Marking:
Check Slenderness
Slab Thikness
Supporting Beam Width
Actual Span Length
Typical Basement Floor Slab (250Thk)-One Way Spanning
(Cl.3.8.1)
h = 250
W beam = 600
L = 8600
=
=
=
250 mm
600 mm
8600 mm
As maximum delfection and moment at mid-span, analyse half length of actual span length
Lo = L/2 - W beam
Clear Span for Analysis
=
4000 mm < 60h =>ok
Type of Structure
= Unbraced Structures (As no vertical restraint at mid-span)
End Condition Supportrf by Beam
= 1
(Beam & adjacent slab provide full restraint)
End Condition at mid-span
= 1
(Continuity of slab provide full restraint)
Coefficient Value
$ = 1.2
(Table 3.19)
Le = $lo
Effecttive Span Length
=
4800 mm
% = Le / h
Slenderness
=
(Cl.3.8.3)
(Per Meter Strip)
fcu
Slab Concrete Strength
fy
Steel Yeild Strength
Slab Design Width
b
Slab Thickness
h = b'
Slab Effective Depth
d
Asc
Area of Reinforcement
Ac
Net Cross Section Area of Concrete
0.1fcubh
10% Pure Compressive Strength
Nuz
Design Ultimate Axial Capacity
Nbal
Design Axial Capacity of Balanced Section
Design Ultimate Axial Load
N
Recduction Factor
K
19.2 >10 => Slender section
Analysis
=
=
=
=
=
=
=
=
=
=
=
=
35
460
1000
250
250-25-16/2
T16@100c/c
bh - Asc
0.1x35x1000x250x10
0.45fcu Ac+0.95fyAsc
0.25fcubd
From Wall Analysis
Nuz - N
-3
2
=
=
=
=
=
=
=
=
=
=
=
=
35
460
1000
250
217
2010
247990
875.00
4784.21
873.43
367.93
1.13
0.18432
46.08 mm
N/mm
3
N/mm
mm
mm
mm
2
mm
2
mm
kN
kN
kN
kN
< 0.1fcubh
must not > 1.0
NuZ - Nbal
$a
au
Coefficient Value
Calculated Deflection
Moment Additional Due to Deflection
Madd
2
=
=
1(Le/b') / 2000
$aKh
=
=
=
N au
=
16.95 kNm
3,.,'
0
01,0 2
-(.,
Initial Moment (From Slab Vertical Loading)
&''()*+,'
-(., /. 0
0
+
0
Additional Moment
)1,
0
||
0 0
Design Moment Envelope
0 0
kNm
M1 + Madd/2
M2 - Madd/2
= Msupp + Madd /2
= Mmid - Madd /2
=
83.32 +16.94
=
100.27
=
83.32 +16.95
=
100.27
49
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
1 of 1
Dec 2011
Slab Design to BS8110:1997
Slab Marking:
Typical Basement Floor Slab-at Mid Span
Span
Beam breath
Beam depth
Concrete cover
Link dia.
Rebar dia.
Concrete strength
Rebar strength
Link strength
Effective depth
L
b
h
c
=
=
=
=
=
=
fcu =
fy =
fyv =
d =
d' =
8.6
1000
250
25
0
100
35
460
460
217.00
25.0
Bending Reinforcement Design
2
Ratio
M/bd
Coefficient
K
Lever arm
z
As
Tension Reinf. req.
Tension Reinf. prov.
=
=
=
=
T
Add: T
Compr. steel req.
Compr. steel prov.
m
mm
mm
mm
mm
mm
2
N/mm
2
N/mm
2
N/mm
mm
mm
M =
V =
83.32 kNm
67.6 kN
Simply/Continuous/Cantilever? = Continuous
(Cl.3.4.1.6)
Maximum Length = min {60b , 250b^2/d}
60 m
=
• L ==>OK!
% Redistribution =
$4 =
K' =
0 %
1
0.156
(Cl.3.4.4.4)
(Cl.3.4.4 & 3.5.2)
1.769
M/bd 2 f cu
0.0506
=
min{ (0.5+¥(0.25-K/0.9)d , 0.95d }
M / 0.95f y z
16
0
@
@
100
0
As' = Not Required!
T
0
@
Add: T
0
@
T
Distribution Bar prov.
Design moment
Design shear
(250Thk)
12
Shear Reinforcement Design
@
mm
mm
< 0.156 => Compr. Reinf Not Required!
=
204.0 mm
=
934 mm 2
Min. Tension Steel =
325 mm 2 (0.13% bh)
As,prov =
2011 mm 2 •As ==>Ok!
0
0
mm
mm
=
Min. Compress. Steel =
As',prov =
300
mm
As,distr =
0 mm 2
0 mm 2 (0.2% bh)
0 mm 2 • As' ==>Ok!
377 mm 2 • As' ==>Ok!
(Cl.3.4.5 & 3.5.5)
16
@ 200 mm
As =
Add:
0
@ 0.001 mm
1005 mm 2
at Shear Section :
Shear stress
v = V/ bd
=
0.31 N/mm2 ” min {0.8¥fcu, 5} ==>OK!
vc = 0.79{100A s /(bd) ч 3} 1/3 {400/d ш 0.67} 1/4 {(f cu ч 40)/25} 1/3 / 1.25
=
0.64 N/mm 2
Shear capacity
Asv/sv = <vc, Not Required!
Link Req.
0.000 mm 2/mm
/
:A
0.000 mm 2/mm
0 T
0
@
0
Hook/Link Prov.
mm
sv sv, prov =
Shear Reinf. Not Required!
Vc
= 0.8¥fcu x bd
= 56 kN
Max Shear Strength at Centre of Support
Tension Reinf.
Enhanced Shear Strength at distance 'av' from support face
av =
0.2
av =
0.4
av =
0.6
av =
0.8
av =
1.0
av =
1.2
av =
1.4
av =
1.6
av =
1.8
av •
2.0
Deflection Check
d
d
d
d
= 868
= :6
= 6
= 56:
mm
mm
mm
mm
d
d
d
d
d
d
=
=
=
=
=
56
: 68
6
856
; 6:
• 886
mm
mm
mm
mm
mm
mm
9
9
9
9
9
9
9
9
9
9
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
= Min { (bd vc 2d/av) , Vc ) 7 ( bdvc )
= 1027.03 kN
691.62 kN
=
461.08 kN
=
345.81 kN
=
=
=
=
=
=
=
276.65 kN
=
=
=
=
142.53 N/mm 2
230.54 kN
197.61 kN
172.91 kN
153.69 kN
138.32 kN
(Cl.3.4.6 & 3.5.7)
fs
=
2 f y A s,req / {3 A s,prov $b }
2
Mft =
0.55 + (477-f s ) / {120 ( 0.9 + M/bd )}
Mfc =
min { 1 + [ (100As',prov/bd) / (3+100As',prov/bd) ], 1.5}
L fac =
min { 1.0 , 10 / L }
Basic L/d =
Actual L/d
Allowable L/d =
26.00
1.59
1.00
1.00
==>Continuous Slab
L/d
=
39.63
M ft M fc L fac Basic L/d
=
41.45 • L/d ==>Ok!
50
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
1 of 1
Dec 2011
Slab Design to BS8110:1997
Slab Marking:
Typical Basement Floor Slab-at Near Support
Span
Beam breath
Beam depth
Concrete cover
Link dia.
Rebar dia.
Concrete strength
Rebar strength
Link strength
Effective depth
L
b
h
c
=
=
=
=
=
=
fcu =
fy =
fyv =
d =
d' =
8.6
1000
250
25
0
200
35
460
460
217.00
25.0
Bending Reinforcement Design
2
Ratio
M/bd
Coefficient
K
Lever arm
z
As
Tension Reinf. req.
Tension Reinf. prov.
=
=
=
=
T
Add: T
Compr. steel req.
Compr. steel prov.
m
mm
mm
mm
mm
mm
2
N/mm
2
N/mm
2
N/mm
mm
mm
M =
V =
83.32 kNm
67.6 kN
Simply/Continuous/Cantilever? = Continuous
(Cl.3.4.1.6)
Maximum Length = min {60b , 250b^2/d}
60 m
=
• L ==>OK!
% Redistribution =
$4 =
K' =
0 %
1
0.156
(Cl.3.4.4.4)
(Cl.3.4.4 & 3.5.2)
1.769
M/bd 2 f cu
=
0.0506
min{ (0.5+¥(0.25-K/0.9)d , 0.95d }
M / 0.95f y z
16
0
@
@
As' = Not Required!
T
0
@
Add: T
0
@
T
Distribution Bar prov.
Design moment
Design shear
(250Thk)
12
Shear Reinforcement Design
@
200
0
mm
mm
< 0.156 => Compr. Reinf Not Required!
=
204.0 mm
=
934 mm 2
Min. Tension Steel =
325 mm 2 (0.13% bh)
As,prov =
1005 mm 2 •As ==>Ok!
0
0
mm
mm
=
Min. Compress. Steel =
As',prov =
300
mm
As,distr =
0 mm 2
0 mm 2 (0.2% bh)
0 mm 2 • As' ==>Ok!
377 mm 2 • As' ==>Ok!
(Cl.3.4.5 & 3.5.5)
16
@ 200 mm
As =
Add:
0
@ 0.001 mm
1005 mm 2
at Shear Section :
Shear stress
v = V/ bd
=
0.31 N/mm 2 ” min {0.8¥fcu, 5} ==>OK!
vc = 0.79{100A s /(bd) ч 3} 1/3 {400/d ш 0.67} 1/4 {(f cu ч 40)/25} 1/3 / 1.25
=
0.64 N/mm 2
Shear capacity
Asv/sv = <vc, Not Required!
Link Req.
0.000 mm 2/mm
/
:A
0.000 mm 2/mm
Hook/Link Prov.
0 T
0
@
0
mm
sv sv, prov =
Shear Reinf. Not Required!
Vc
= 0.8¥fcu x bd
= 56 kN
Max Shear Strength at Centre of Support
Tension Reinf.
Enhanced Shear Strength at distance 'av' from support face
av =
0.2
av =
0.4
av =
0.6
av =
0.8
av =
1.0
av =
1.2
av =
1.4
av =
1.6
av =
1.8
av •
2.0
d
d
d
d
= 868
= :6
= 6
= 56:
mm
mm
mm
mm
d
d
d
d
d
d
=
=
=
=
=
56
: 68
6
856
; 6:
• 886
mm
mm
mm
mm
mm
mm
9
9
9
9
9
9
9
9
9
9
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
Vc,av
= Min { (bd vc 2d/av) , Vc ) 7 ( bdvc )
= 1027.03 kN
691.62 kN
=
461.08 kN
=
345.81 kN
=
=
=
=
=
=
=
276.65 kN
230.54 kN
197.61 kN
172.91 kN
153.69 kN
138.32 kN
51
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
1 of 1
Dec 2011
Slab Design to BS8110:1997
Slab Marking:
Span
Beam breath
Beam depth
Concrete cover
Rebar dia.
Concrete strength
Rebar strength
Link strength
Effective depth
L
b
h
c
=
=
=
=
=
fcu =
fy =
fyv =
d =
Typical Basement Floor Slab-at Near Support
(250Thk)
** Check Maximum Shear Capacity for Sx Minor Axis Direction
8.6 m
1000 mm
250 mm
25 mm
12 mm
35 N/mm2
460 N/mm2
460 N/mm2
203 mm
Check Enhanced Shear Strength Without Shear Reinforcement
at Shear Section :
Shear stress
12
Add:
0
v = V/ bd
Shear capacity
vc
Tension Reinf.
=
0.79{100A s /(bd) ч 3} 1/3 {400/d ш 0.67} 1/4 {(f cu ч 40)/25} 1/3 / 1.25
Vc
Max Shear Strength at Centre of Support
=
0.8¥fcu x bd
Enhanced Shear Strength at distance 'av' from support face
av =
0.2
av =
0.4
av =
0.6
av =
0.8
av =
1.0
av =
1.2
av =
1.4
av =
1.6
av =
1.8
av •
2.0
d
d
d
d
d
d
d
d
d
d
(Cl.3.4.5, Cl. 3.5.5 & Cl. 3.4.5.8)
@ 300 mm
As =
@ 0.001 mm
=
0.00 N/mm2 ” min {0.8¥fcu, 5} ==>OK!
8 6:
6
6
:68
6
86:
86
86
= :<68
• 8 :6
=
=
=
=
=
=
=
=
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
9
9
9
9
9
9
9
9
9
9
=
=
377 mm 2
0.48 N/mm 2
;: 655 kN
Vc,av = Min { (bd vc 2d/av) , Vc ) 7 ( bdvc )
Vc,av =
960.77 kN
Vc,av =
485.08 kN
Vc,av =
323.39 kN
Vc,av =
242.54 kN
Vc,av =
194.03 kN
Vc,av =
161.69 kN
Vc,av =
138.59 kN
Vc,av =
121.27 kN
Vc,av =
107.80 kN
Vc,av =
97.02 kN
52
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
1 of 1
Dec 2011
Beam Design to BS8110:1997
Beam Marking:
Typical Basement Floor Beam-at Mid Span (600x600)
Span
Beam breath
Beam depth
Concrete cover
Link dia.
Rebar dia.
Concrete strength
Rebar strength
Link strength
Effective depth
L
b
h
c
=
=
=
=
=
=
fcu =
fy =
fyv =
d =
d' =
8.6
600
600
35
10
25
35
460
460
522.50
53.0
Bending Reinforcement Design
2
Ratio
M/bd =
Coefficient
K =
Lever arm
z =
As =
Tension Reinf. req.
Lyr.1:
Tension Reinf. prov.
M =
V =
T =
796.88 kNm
617.73 kN
0 kNm
Simply/Continuous/Cantilever? = Continuous
(Cl.3.4.1.6)
Maximum Length = min {60b , 250b^2/d}
36 m
=
• L ==>OK!
% Redistribution =
$4 =
K' =
0 %
1
0.156
(Cl.3.4.4.4)
(Cl.3.4.4)
M/bd 2 f cu
0.1390
=
< 0.156 => Compr. Reinf Not Required!
=
422.8 mm
=
4313 mm 2
Min. Tension Steel =
468 mm 2 (0.13% bh)
As,prov =
4909 mm 2 •As ==>Ok!
min{ (0.5+¥(0.25-K/0.9)d , 0.95d }
M / 0.95f y z
6 T 25
4 T 25
As' = Not Required!
Lyr.1:
6 T 16
Lyr.2:
0 T 0
Side bar size req.
Side bar prov.
=
=
0 mm
0 T 0
Shear Reinforcement Design
Tension Reinf.
Design moment
Design shear
Design torsion
4.865
Lyr.2:
Compr. steel req.
Compr. steel prov.
m
mm
mm
mm
mm
mm
2
N/mm
2
N/mm
2
N/mm
mm
mm
=
Min. Compress. Steel =
As',prov =
Not Required!
@ Spacing
EF
470
0 mm 2
0 mm 2 (0.2% bh)
1206 mm 2 • As' ==>Ok!
mm
(Cl.3.4.5)
6 T 25
As =
Lyr.2:
6 T 25
v = V/ bd
=
1.97 N/mm2 ” min {¥(0.8fcu), 5} ==>OK!
vc = 0.79{100A s /(bd) ч 3} 1/3 {400/d ш 0.67} 1/4 {(f cu ч 40)/25} 1/3 / 1.25
=
Asv/sv = (v-vc) b / 0.95fyv
Lyr.1:
at Shear Section :
Shear stress
Shear capacity
Link Req.
1 T
Outer Link Prov.
1 T
Internal Link Prov.
Nominal Asv/sv =
10
- 175 mm
10
- 175 mm
0.549 mm 2/mm
Torsional Reinforcement Design
hmin
hmax
vt
vt min
v + vt
vtu
:Asv/sv =
:Asv/sv =
OK!
Total Asv/sv Prov. =
=
min {0.87¥fcu, 5}
=
Torsion Asv,T/sv req.
=
T / {0.8x 1 y 1 (0.95 f yv )}
=
Total Asv/sv req.
=
A sv,T /s v + A sv /s v
=
A sv,T f yv (x 1 + y 1 )/ (s v f y )
=
Deflection Check
0.898 mm 2/mm
0.898 mm 2/mm
1.795 mm 2/mm OK!
x1 =
520 mm
y1 =
520 mm
=
0.000 N/mm 2
=
0.396 N/mm 2
vt < vt,min ==>Torsion Reinf Not Req.!
2T/ { h min 3 (h max -h min /3)}
Total additional reinf. req. =
0.82 N/mm 2
1.585 mm 2/mm
(Cl.3.4.5)
=
=
=
=
=
Torsion stress
5890 mm 2
600
600
min {0.067 я fcu, 0.4}
1.970 N/mm2
4.475 N/mm 2
OK!
0.000 mm 2/mm OK!
1.585 mm 2/mm OK!
0 mm 2
(Cl.3.4.6)
fs
=
2 f y A s,req / {3 A s,prov $b }
2
Mft =
0.55 + (477-f s ) / {120 ( 0.9 + M/bd )}
Mfc =
min { 1 + [ (100As',prov/bd) / (3+100As',prov/bd) ], 1.5}
L fac =
min { 1.0 , 10 / L }
Basic L/d =
Actual L/d
Allowable L/d =
26.00
=
=
=
=
269.47 N/mm 2
0.85
1.11
1.00
==>Continuous Beam
L/d
=
16.46
M ft M fc L fac Basic L/d
=
24.61 • L/d ==>Ok!
53
UNIVERSITY TEKNOLOGI MALAYSIA
Subject:
Faculty of Civil Engineering
Calcs by:
MAE 0024-Master Project
Nin Ka Yik
Sheet:
Date:
1 of 1
Dec 2011
Beam Design to BS8110:1997
Beam Marking:
Typical Basement Floor Beam-at Near Support (600x600)
Span
Beam breath
Beam depth
Concrete cover
Link dia.
Rebar dia.
Concrete strength
Rebar strength
Link strength
Effective depth
L
b
h
c
=
=
=
=
=
=
fcu =
fy =
fyv =
d =
d' =
8.6
600
600
35
10
25
35
460
460
517.50
53.0
Bending Reinforcement Design
2
Ratio
M/bd =
Coefficient
K =
Lever arm
z =
As =
Tension Reinf. req.
Lyr.1:
Tension Reinf. prov.
M =
V =
T =
973.96 kNm
796.88 kN
0 kNm
Simply/Continuous/Cantilever? = Continuous
(Cl.3.4.1.6)
Maximum Length = min {60b , 250b^2/d}
36 m
=
• L ==>OK!
% Redistribution =
$4 =
K' =
0 %
1
0.156
(Cl.3.4.4.4)
(Cl.3.4.4)
M/bd 2 f cu
0.1732
=
> 0.156, Compr. Reinf Required!
=
402.0
=
5470
Min. Tension Steel =
468
As,prov =
5890
min{ (0.5+¥(0.25-K/0.9)d , 0.95d }
M / 0.95f y z
6 T 25
6 T 25
As' = (K – K')fcu bd^2/ {0.95fy(d – d')}
=
Lyr.1:
6 T 16
Min. Compress. Steel =
As',prov =
Lyr.2:
0 T 0
Side bar size req.
Side bar prov.
=
=
0 mm
0 T 0
Shear Reinforcement Design
Tension Reinf.
Design moment
Design shear
Design torsion
6.061
Lyr.2:
Compr. steel req.
Compr. steel prov.
m
mm
mm
mm
mm
mm
2
N/mm
2
N/mm
2
N/mm
mm
mm
Not Required!
@ Spacing
EF
465
mm
2
mm
2
mm (0.13% bh)
2
mm •As ==>Ok!
476 mm 2
720 mm 2 (0.2% bh)
1206 mm 2 • As' ==>Ok!
mm
(Cl.3.4.5)
6 T 25
As =
Lyr.2:
6 T 25
v = V/ bd
=
2.57 N/mm2 ” min {¥(0.8fcu), 5} ==>OK!
vc = 0.79{100A s /(bd) ч 3} 1/3 {400/d ш 0.67} 1/4 {(f cu ч 40)/25} 1/3 / 1.25
=
Asv/sv = (v-vc) b / 0.95fyv
Lyr.1:
at Shear Section :
Shear stress
Shear capacity
Link Req.
1 T
Outer Link Prov.
1 T
Internal Link Prov.
Nominal Asv/sv =
10
- 175 mm
10
- 175 mm
0.549 mm 2/mm
Torsional Reinforcement Design
hmin
hmax
vt
vt min
v + vt
vtu
:Asv/sv =
:Asv/sv =
OK!
Total Asv/sv Prov. =
=
min {0.87¥fcu, 5}
=
Torsion Asv,T/sv req.
=
T / {0.8x 1 y 1 (0.95 f yv )}
=
Total Asv/sv req.
=
A sv,T /s v + A sv /s v
=
A sv,T f yv (x 1 + y 1 )/ (s v f y )
=
Deflection Check
0.898 mm 2/mm
0.898 mm 2/mm
1.795 mm 2/mm NOT OK!
x1 =
520 mm
y1 =
520 mm
=
0.000 N/mm 2
=
0.396 N/mm 2
vt < vt,min ==>Torsion Reinf Not Req.!
2T/ { h min 3 (h max -h min /3)}
Total additional reinf. req. =
0.82 N/mm 2
2.397 mm 2/mm
(Cl.3.4.5)
=
=
=
=
=
Torsion stress
5890 mm 2
600
600
min {0.067 я fcu, 0.4}
2.566 N/mm2
4.475 N/mm 2
OK!
0.000 mm 2/mm OK!
2.397 mm 2/mm NOT OK!
0 mm 2
(Cl.3.4.6)
fs
=
2 f y A s,req / {3 A s,prov $b }
2
Mft =
0.55 + (477-f s ) / {120 ( 0.9 + M/bd )}
Mfc =
min { 1 + [ (100As',prov/bd) / (3+100As',prov/bd) ], 1.5}
L fac =
min { 1.0 , 10 / L }
Basic L/d =
Actual L/d
Allowable L/d =
26.00
=
=
=
=
284.76 N/mm 2
0.78
1.11
1.00
==>Continuous Beam
L/d
=
16.62
M ft M fc L fac Basic L/d
=
22.61 • L/d ==>Ok!
54
APPENDIX B
LUSAS ANALYSIS RESULTS - DEFLECTION
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
APPENDIX C
LUSAS ANALYSIS RESULTS - ULTIMATE BENDING MOMENT
73
74
75
76
77
78
79
80
81
82
83
84
APPENDIX D
LUSAS ANALYSIS RESULTS - ULTIMATE SHEAR FORCE
85
86
87
88
89
90
APPENDIX E
LUSAS ANALYSIS RESULTS - FLEXURAL REINFORCEMENT
91
92
93
94
95
96
APPENDIX F
LUSAS ANALYSIS RESULTS - FLEXURAL CRACKING
97
98
99
100