Nghiên cứu khả năng chống chọc thủng của sàn phẳng bê tông ứng lực trước ttta

MINISTRY OF EDUCATION AND TRAINING
NATIONAL UNIVERSITY OF CIVIL ENGINEERING

Tran Viet Tam

STUDY ON PUNCHING SHEAR CAPACITY OF
PRESTRESS FLAT SLABS

Major: Construction Engineering
Code: 9580201

SUMMARY OF DOCTORAL DISSERTATION

HA NOI –2019


The Dissertation was completed at the National University of Civil
Engineering

Academic advisors:
1. Prof. Dr. Phan Quang Minh.
2. Assoc. Prof. Dr. Nguyen Ngoc Phuong.

Examiner 1 : Prof. Dr. Nguyen Tien Chương.
Examiner 2 : Assoc. Prof. Dr. Truong Hoai Chinh.
Examiner 3 : Dr. Nguyen Dai Minh.

The doctoral dissertation will be defensed at the level of the State
Council of Dissertation Assessment’s meeting at the National
University of Civil Engineering at...... hour..... day...... month... year
2019.

This Dissertation is available for reference at the Libraries as follows
- National Library of Vietnam;
- Library of National University of Civil Engineering.


1
PREFACE
1. REASON FOR SELECTING THE TOPIC

Nowadays, reinforced concrete and pre-stressed concrete flat
slabs are used commonly in buildings in Vietnam and worldwide,
since they have many advantages in architecture, structures and
construction.
In design of flat slab structures, the design against punching
shear has always been of special interest because this is a
dangerous type of brittle damage. Some buildings in the world
were damaged by punching shear and they caused serious
consequences such as: Sampoong Department Building in Korea
(1995), causing 502 people killed and 1000 injured [86]; the
Virgina State Skyline Plaza - USA (1971) caused casualties for
more than 14 workers [56].
The current design standard in Vietnam is "Concrete and
reinforced concrete structures - TCVN 5574-2018 design code"
[7] based on Russian standard SP 63.13330 [80]. It introduces
mainly the calculation principles of punching shear strength for
normal reinforced concrete members. In the formulae to predict
the punching shear capacity of reinforced concrete and prestressed
concrete flat slabs, influences of the factors such as reinforcement
ratio in the tention zone, compressive stress in concrete due to

prestress and the column dimensions have not been considered.
To increase economic efficiency in using the flat slabs, the
study of punching shear capacity of reinforced concrete and
prestress concrete flat slabs, then proposing new formulae
validated with experimental results are needed.
2. RESEARCH PURPOSES

a) Review extensively previous studies on punching shear
capacity of reinforced concrete and prestressed concrete flat slabs
b) Study punching shear capacity of flat slabs by the numerical
method, to investigate the parameters affecting the punching shear
capacity of flat slabs including tension reinforcement ratio, precompressive stress in concrete, slab thickness, column


2
dimensions.
c) Propose a new formulae to predict the punching shear
capacity of reinforced concrete and prestressed concrete flat slabs.
d) Setup an experimental model to verify the proposed
formulae for the punching shear capacity of reinforced concrete
and prestressed concrete flat slabs.
3. SCOPE OF WORK, SCIENTIFIC BASIS AND RESEARCH
METHOLOGY

Scope of work: Study on the punching shear capacity of
reinforced concrete and prestressed concrete flat slabs with the
concrete grade is not greater than B60, no shear stirrup, no slab
openings, no consideration of influence of moment at column-slab
connections, columns with circle or rectangular section only.
Scientific basis: Through the theoretical study, numerical

simulation and experiment to predict the punching shear capacity
of reinforced concrete and prestressed concrete flat slabs,
clarification of stress state and deformation at column-slab
connections.
Reinforced concrete and prestressed concrete flat slabs have
been widely used in buildings. Therefore, to study and to propose
a suitable formulae with TCVN 5574-2018 are the practical
meanings of this thesis. The proposed formulae takes into account
the influence of tensile reinforcement ratio and pre-compressive
stress in concrete, the ratio between the column height and the slab
effective depth. It helps to predict the punching shear capacity of
flat slabs more exactly and to give more reasonable results in
design.
Research methodology: Theoretical, numerical simulation and
experimental study.
4. NEW CONTRIBUTIONS OF THESIS

a) Create numerical simulated models in ANSYS software
written in ADPL language, from which the important parameters
affecting the punching shear capacity of flat slabs are easily
investigated: tension reinforcement ratio, compressive stress in


3
concrete due to prestress, the ratio between height and width of the
rectangular column section.
b) Propose a new formulae to predict the punching shear
capacity of reinforced concrete flat slabs suitable for TCVN 55742018.
c) Propose a new formulae to evaluate the punching shear
capacity of prestress concrete flat slabs suitable for TCVN 55742018.

d) Set up an experimental model capable to verify the punching
shear capacity of reinforced concrete and prestressed concrete flat
slabs. The collected experimental data are not only to verify the
two proposed formulae of the thesis, but also for further studies on
the punching shear capacity of flat slabs.
5. CONTENT OF THESIS

The thesis includes preface, 3 chapters, conclusions and
recommendations, published works by the author and references.
CHAPTER 1 RESEARCH OVERVIEW ON PUNCHING SHEAR
CAPACITY OF FLAT SLABS
1.1 DEFINITION OF PUNCHING SHEAR CAPACITY OF
REINFORCED CONCRETE FLAT SLABS

Punching shear failure is a local
failure caused by shear force in two
directions at the positions of columnflat slab connection. The failure area
has a truncated cone around the
column (Fig 1.1).
Punching shear capacity of
Fig 1. 1 Typical punching shear
reinforced flat slabs depends on
failure
in reinforced flat slabs
many factors such as: concrete
quality, tensile reinforcement (ratio, distribution of
reinforcement), column size, column position, size factor,
prestressing force in concrete, and boundary conditions ...

4
1.2 MODELS TO DETERMINE PUNCHING SHEAR CAPACITY OF
REINFORCED CONCRETE FLAT SLABS

Many theoretical and experimental models are summarized as
follows:
1.2.1 Mechanical models based on equilibrium conditions
 Shehata (1985) and Regan (1989) [79]
 Brom’s model [28]
1.2.2 Truss model
 Truss and tie model of Marzouk and Tiller [66]
1.2.3 Tension failure models
 Truss and tie model of Alexander -Simmonds [25]
 Truss and tie model of Georgopolous [74]
 Truss and tie model of Menétrey [67]
1.2.4 Flexural approach
1.2.5 Critical shear crack theory (2008)

Fig 1.2 Procedure to specify punching shear strength of slabs
according to Critical Shear Crack Theory (Muttoni 2008)
1.3 MODELS TO DETERMINE THE PUNCHING SHEAR CAPACITY
OF PRESTRESS CONCRETE FLAT SLABS

1.3.1 Principal tensile stress approach
1.3.2 Equivalent reinforcement ratio approach
1.3.3 Decompression stress approach


5
1.4 PREVIOUS EXPERIMENTAL STUDIES ON PUNCHING SHEAR

CAPACITY OF REIFORCED CONCRETE FLAT SLAB

The thesis has collected 270 published experimental specimens
of punching shear studies, in order to verify the numerical models
and the proposed formulae. Details of these experiments can be
found in Appendix A.
1.5 SIMULATION ON PUNCHING SHEAR CAPACITY OF
REINFORCED CONCRETE FLAT SLABS

A new research method to determine the punching shear capacity
of reinforced concrete flat slabs is the application of finite element
method (FEM) and RC simulation software. The numerical
method takes into account of
nonlinear
behaviour
of
concrete,
allowing
the
observation and evaluation
before
conducting
the
experimental research. It is a
low-cost and easy-to-build
tool, and allows to change the
Fig 1.13 Simulation model of
parameters
during
the

Aikaterini Genikomsou (2015)
simulation.
1.6 PRACTICE CODES AND STANDARDS

1.6.1 US Codes ACI-318-2014 [19]
1.6.2 European Codes EC2 (2004) [36]
1.6.3 Australian Codes AS3600 (2018) [18]
1.6.4 Canadian Codes CSA A23.3-14 [30]
1.6.5 Chinese Codes GBJ 50010-2010 [47]
1.6.6 British Codes BS 8110-1997 [29]
1.6.7 German Code DIN 1045-2008 [34]
1.6.8 FIB - Modal Code 2010 [37]
1.6.9 Vietnamese Code TCVN 5574-2018 [7]


6
1.7 PREVIOUS STUDIES ON PUNCHING SHEAR CAPACITY OF
REINFORCED CONCRETE FLAT SLABS IN VIETNAM

Associate Professor, Dr. L. T. Huan, in the study "Effect of
prestress in column-slab connections of flat slabs" [1], conducted
4 specimens with an average compressive stress of 2 MPa to verify
the formulae: Fb = (1+n). Rbt . um . ho
P. N. Vuong (2018) [3] in the study "Analysis of punching
shear capacity of reinforced concrete flat slabs taking into account
influences of boundary conditions by ANSYS software" simulated
the column-slab connections and use this model to investigate the
stiffness of edge beams that affects the punching shear capacity of
flat slabs.
1.8 SALIENT REMARKS FROM LITERATURE REVIEW

1. The punching shear capacity of reinforced flat slabs depends
on the concrete strength, ratio of tension reinforcement, stirrup,
slab-column size parameters, pre-compressive stress in concrete...
2. The formulae predicting the punching shear capacity of
reinforced concrete and pre-stressed concrete flat slabs according
to the design standards were based on theoretical and experimental
models, but there is still discrepancy. For example, using the two
most commonly used Codes, ACI-318-14 and EC2-2004, to verify
with 270 published specimens, the average discrepancy between
EC2-2004 and ACI-318-2014 is 15.66% (ACI-318 gives greater
results in prediction). However, in many cases the discrepancy can
be over 30%.
Using TCVN 5574-2018 to predict the punching shear capacity
of reinforced concrete and pre-stressed concrete flat slabs with
270 published specimens as shown in Figure 1.22, the ratio of Putest
/ PuTCVN code is 1.45. It should be noted that the predictions do not
consider the influence of tensile reinforcement and compressive
stress due to prestress in concrete. In some cases, when the slab
thickness or the ratio between the height and width of the
rectangular columns is large, the prediction PuTCVN code is not in the


7
safe side (Appendix A, No. 236 slab samples, 240, 250, 251, 252,
255).
3. Nowadays, with development of the numerical methods and RC
simulation software especially Ansys, it is possible to setup a
simulation model to analyse the punching shear capacity of
reinforced concrete and pre-stressed concrete flat slabs. The

advantages of the numerical models are easy to change the
parameters to be investigated such as floor and column sizes,
materials, reinforcement layout, pre-compressive stress in
concrete... This is a new trend to solve the problem when the
boundary conditions, the shape of the column-slab connections are
complicated, and cost-effective.
4. The above remarks are the continuous research orientation of
the thesis. The thesis uses the numerical method to investigate the
parameters affecting the punching shear capacity of reinforced
concrete and pre-stressed concrete flat slabs. From the numerical
results, it proposes the formulae which can predict the punching
shear capacity of reinforced concrete and pre-stressed concrete
flat slabs, taking into account the effect of reinforcement ratio,
compressive stress in concrete, parameters of slab and column
sizes. The proposed formulae are suitable with TCVN 5574-2018
and are validated by the experimental results of the thesis.
CHAPTER 2 RESEARCH OF PUNCHING SHEAR CAPACITY
OF RC FLAT SLABS BY NUMERICAL SIMULATION
METHOD
2.1 INTRODUCTION

Nowadays, numerical simulation has become one of the
reliable and effective methods to study the punching shear
capacity of reinforced concrete and prestressed concrete flat slabs.
Using this method, it is possible not only to determine the value of
punching shear force, but also to consider other influential
parameters such as tensile reinforcement ratio, effect of column
size, slab thickness, boundary conditions, pre-compressive stress

8
in concrete... Many prediction formulae have not taken into
account these factors.
ANSYS [12] [26] is a powerful structural software based on
FEM method that can simulate and analyze reinforced concrete
structures. The advantages of this software are that it uses
nonlinear material models and template modules available in the
software. The users also can integrate the material models suitable
with the problems to be studied, or it is possible to write a model
with APDL parametric design language for each problem.
ADPL parametric design language (ANSYS Parametric
Design Language) [19] is FORTRAN programming language,
providing full functions to create variables, constants, functions,
vectors, matrices, iterations to model the problems with complex
boundary conditions, when you need to solve iterations and create
common modules. The model is built in ADPL language as a file
that contains written source code, allowing to change parameters
of input data such as model size, reinforcement grid, tendon grid,
model and material strength, load ...
This chapter presents the study on punching shear capacity of
reinforced concrete and prestressed concrete flat slabs using the
numerical simulated models in ANSYS Mechanical V.15.0
software written in APDL language. Using these models, the
parameters are varied to investigate the factors affecting punching
shear capacity of flat slabs, then a formulae is proposed to predict
the punching shear capacity of flat slabseVietnamese design Code
for reinforced concrete structures TCVN 5574-2018.
2.2 MODELLING OF REINFORCEMENT IN CONCRETE

According to the FEM method, there are three different models

to model reinforcing rebars in concrete: smeared model,
embedded model, discrete model [35] [38].
In this study, stresses of concrete and reinforcement are
required at every stage, so that the "discrete" model is chosen to
simulate reinforcement element in concrete for the tested
specimens.


9
2.3 MODELLING OF CRACK IN CONCRETE

There are three models oftenly used to model cracks in
concrete: discrete, smeared and fracture modelS [22]. This thesis
adopts the "smeared" model to model cracks in concrete.
2.4 FINITE ELEMENT MODEL

2.4.1 Types of elements
• Element SOLID65: used to model concrete elements.
• Element LINK180: used to model reinforcement elements.
• SOLID45 element: used to model padding steel plate.
2.4.2 Mesh and boundary conditions
2.4.3 Materials
2.4.3.1 Concrete
 Compressive behaviour: In this thesis, the constitutive law
for compressive branch is taken according to EC2 model and does
not consider the downward segments of the compression branch.
 Tensile behaviour: Stress strain relationship model of
concrete in tension is defined based on ANSYS template.
2.4.3.2 Steel: The material model for reinforcement is followed
the elasto-plastic model (bilinear curve).

2.4.3.3 Reinforcement, tendon, steel plate: Properties for
LINK180 element are taken from steel tensile tested results Es =
210000 MPa, fy = yeild strength, poission coefficient νs = 0.3.
2.5 FAILURE CRITERIA

2.5.1 Failure criterion of concrete
The concrete failure criterion proposed by William and
Warnke [50] in ANSYS is used for the simulation. Concrete will
be cracked or crushed if it reaches the condition in the equation:
F
S 0
f c'

2.5.2 Failure criteria of specimens due to punching shear
- The plate is completely failed: Observing the graph (P-d) in
Figure 2.20, the load increases incrementally but the displacement


10
increases greatly to infinity.
- If the plate has the bending resistance greater than the shear
resistance, the graph (P) of Figure 2.20a, the compressive strain
in concrete exceeds the ultimate strain c = 0.35%. At that time,
reinforcement has not yielded yet according to graph (P-) in
Figure 2.20b, thus the plate is failed by shear.
- If the plate has the bending resistance smaller than the
shear resistance, reinforcement reaches the yield strength, strain in
concrete reaches the ultimate strain , Pyfailed by bending.
- Crack pattern was observed carefully to capture the crack

development.

Fig 2.20 Failure criteria in Ansys model
2.6

INPUT DATA

2.6.1 Concrete
2.6.2 Concrete for boundary
2.6.3 Reinforcement, tendon, steel plate
2.6.4 Vertical plate
Vertical load is applied as uniform pressure at the column top.
2.6.5. Prestressing load
ANSYS has no tool to model prestressed load directly to solve
the prestressed concrete problems, thus an equivalent simulation
using the thermal effect instead of prestressed effect is adopted.
2.7
2.8

PROPOSED DIAGRAM TO DETERMINE PUNCHING SHEAR
CAPACITY OF FLAT SLABS IN ANSYS ADPL
VERIFICATION OF ANSYS MODEL WITH PUBLISHED TEST
DATA


11
2.8.1 Yaser Mirzae’s specimens
2.8.2 Alam’s specimens
2.8.3 Franklin and Long’s specimens
2.8.4 Rahman’s specimens

2.8.5 Comments
The validation results for punching shear force from Ansys
simulation for 4 published specimens with reinforced concrete
slab and prestressed concrete flat slabs are close to each other.
On the other hand, because in the simulation models, bonding
behavior between concrete and reinforcement is assumed to be
perfect; the boundary conditions, crushing and cracking behavior
in concrete are not exactly the same as in the experiment; and due
to shear locking phenomenon in solid element, the deflection at
the midpoint of the plate in simulation is usually smaller than one
in the experiments.
2.9

INVESTIGATION ON THE INFLUENCE OF REINFORCEMENT
RATIO TO PUNCHING SHEAR CAPACITY OF FLAT SLABS

Fig 2.32 Relationship between reinforcement ratio and punching
shear capacity of flat slabs in group N1R
2.10 INVESTIGATION

ON

THE

INFLUENCE

OF

PRE-

COMPRESSIVE STRESS TO PUNCHING SHEAR CAPACITY OF
PRE-STRESS CONCRETE FLAT SLABS


12

Hình 2.38 Relationship between effective stress and punching shear
capacity of pre-stress flat slabs
2.11 INVESTIGATION ON THE INFLUENCE OF CONCRETE
STRENGTH, SIZE EFFECT TO PUNCHING SHEAR CAPACITY
OF FLAT SLABS

2.11.1 Influence of concrete strength
2.11.2 Influence of slab effective depth
2.11.3 Influence of the ratio between the depth and the width
of rectanglar columns

Fig 2.45 Relationship between c and punching shear capacity of
reinforced concrete flat slabs
2.12 PROPOSED FORMULAE TO DETERMINE THE PUNCHING
SHEAR CAPACITY OF

REINFORCED CONCRETE FLAT

SLABS

2.12.1 Principles for proposed formulae


13

2.12.2 Proposed formulae to determine the punching shear
capacity of normal reinforced concrete flat slabs
(2.33)
F   k s k c u m h 0 R bt
where:
-

-

-

-

-

: Coefficient of concrete type, 1 for heavy-weight concrete
and 0.8 for light-weight concrete;
Rbt: Concrete tensile strength;
ho: Slab effective depth;
ks : Coefficient taking into account of influence of tensile
reinforcement ratio;
0.9s uc
ks  (1 
) ; 1.0 ≤ ks ≤ 1.30.
0.021  s ud
s : Average reinforcement ratio distributed in the floor in x
direction (sx) and y direction (sy), but not greater than 2%
[36] : s = (sx + sy)/2
kc: Coefficient considering the influence of the ratio between
the depth and the width of rectangular columns (c): if c >2

0.15
then kc   hc / h0  ; if c ≤ 2 then kc=1;
um: Control perimeter of the design section taking as h0/2 from
the column edge, in case of rectangular sections then um =
2(bc+hc +2h0).
ud: Bottom perimeter of the punching shear cone taking as h0
from the column edge, in case of rectangular sections then um
= 2(bc+hc +4h0).

2.12.3 Proposed formulae to determine the punching shear
capacity of pre-stresss concrete flat slabs
(2.34)
F   k s k c u m h 0 ( Rbt  0.12 p )
Where: p: Effective compressive stress in pre-stress concrete,
taking not greater than 3.5 MPa [19].
2.12.4 Evaluation of the proposed formulae with numerical


14
simulation results
2.12.5 Evaluation of the proposed formulae with the published
test data

Fig 2.49 Comparison between the proposed formulae 2.33, 2.34
with the published test data

Figure 2.49 shows the comparison results of the proposed
formulae 2.33 and 2.34 with 270 published specimens in the world
for punching capacity of reinforced and pre-stress concrete flat
slabs. The details of the specimens can be found in Appendix A.

The average value of the ratio of Pcttest / Pctformulae is 1.27, the force
deviation = 0.200, the variation coefficient  = 0.158. It can be
concluded that equations 2.33 and 2.34 have a suitable safety
factor when predicting the punching shear capacity of reinforced
and pre-stress concrete flat slabs.
2.13 REMARKS OF CHAPTER 2

In Chapter 2, numerical models have been built to analyze the
punching shear capacity of reinforced and pre-stress concrete flat
slabs. The models have been simulated in ANSYS software,
written in ADPL language. The parameters can be changed,
including slab and column sizes, reinforcement layout, materials,
pre-compressive stress in concrete. It is very convenient in
numerical study and in design.
Using the simulation models, the parameters affecting the


15
punching shear capacity of reinforced and pre-stress concrete flat
slabs have been investigated. From the investigation results, the
author proposes two formulae to predict the punching shear
capacity of reinforced and pre-stress concrete flat slabs suitable
with TCVN 5574-2018. Applying the formulae to predict over 230
published test data of reinforced concrete flat slabs and 40
specimens of pre-stressed concrete flat slabs, the ratio of Pcttest /
Pctformulae is 1.27 as average. The proposed formulae will be verified
by the author’s experimental study in chapter 3.
CHAPTER 3 EXPERIMENTAL STUDY ON PUNCHING
SHEAR CAPACITY OF REINFORCED CONCRETE AND
PRE-STRESS CONCRETE FLAT SLABS

3.1 EXPERIMENTAL OBJECTIVES AND PROGRAME

3.1.1 Experimental objectives
a) To observe punching shear failure mode and measure the
punching shear force of reinforced and pre-stress concrete flat
slabs;
b) To investigate the relationship between the load and : deflection
at the middle point, slab rotation angle, concrete strain at the
vicinity of column head, reinforcement strain.
c) To investigate the influence of tensile reinforcement ratio on
punching shear capacity of flat slabs.
d) To investigate influence of pre-compressive stress in concrete
on the punching shear capacity of pre-stress concrete flat slabs.
e) To verify the numerical simulated models and the formulae 2.33
and 2.34 proposed in Chapter 2.
3.1.2 Research program
3.2 BASIS TO DESIGN SPECIMENS AND TO SET UP THE
EXPERIMENTAL MODEL

3.2.1 Basis for designing specimens
In this study, the author proposes a modal scale of 1/4 due to


16
the constraints of LAS-XD125 laboratory of the University of
Civil Engineering, and also inherits some experimental results by
Alam [23], Franklin and Long [40] and their partners.
3.2.2 Setting up the experimental models
The experimental specimens of the thesis can be seen in Figure
3.1. All reinforced concrete slabs are 1000mm long x 1000mm

wide with the slab thickness of 60 mm. The column section is
120x120 mm, provided 4 10 as longitudinal rebars and stirrup of
6 a100.

Fig 3.1 Detail of tested specimens
3.3

SPECIMEN MATERIALS

3.3.1 Concrete
Concrete grade of B30, using superplastic admixture for
concrete to achieve the strength within 10-14 days.
3.3.2 Reinforcement
Vietnamese-Italian steel grade CB 240-T with diameter 6.
The material test showed that reinforcement has a minimum yield
strength of 367 MPa and a ultimate strength of 560 MPa.
3.3.3 Tendon
Tendon is the high strength steel type with a diameter of  =
7.1 mm. According to the manufacturer's data (Phan Vu
Investment JSC), the tendon has a yield strength of 1272 MPa and
a ultimate strength of 1420 MPa.
3.4 SPECIMEN DESIGN AND GROUPING


17
- Group 1 (Non pre-stress) S0N1 includes 3 specimens,
namely S0N1-1, S0N1-2, S0N1-3. These are non-prestressed
concrete specimens with a reinforcement ratio of 0.71%
((a100). In this group, the tendon layer 7.1 is still placed in the
middle but will not be stressed.

- Group 2 (Non pre-stress) S0N2 includes 3 specimens,
namely S0N2-1, S0N2-2, S0N2-3. These are non-prestressed
concrete specimens with a reinforcement ratio of 1.35% ((a50).
- Group 3 (Non pre-stress) S0N3 includes 3 specimens,
marked as S0N3-1, S0N3-2, S0N3-3. These are non-prestressed
specimens with a reinforcement ratio of 0.39% ((a200).
- Group 4 (Pre-stress) S1 includes 3 specimens, marked as
S1-1, S1-2, S1-3. These are pre-stressed concrete specimens with
an effective stress in concrete of 1.50 MPa, normal reinforcement
ratio of 0.71 % ((a100).
- Group 5 (Pre-stress) S2 includes 3 specimens, namely S21, S2-2, S2-3. These are pre-stressed concrete specimen with an
effective stress in concrete of 2.45 MPa, normal reinforcement
ratio of 0.71 % ((a100).
3.4.1 Detailing of non-prestress group SON1, SON2, SON3
3.4.2 Detailing of prestress group S1, S2
3.5 LOADING SYSTEM

3.5.1 Vertical loading system
The vertical loading system is designed to support the slab and
the applied load from bottom to top.

Fig 3.2 Detail of supporting frame


18
3.5.2 Pre-stress loading system
The pre-stressed loading frame is designed to generate
prestress in 4 tendons with a diameter of 7.1 in each direction.

Fig 3.7 Detail of prestress loading system

3.6 DIAGRAM OF MEASUREMENT EQUIPMENTS

3.6.1 Diagram of LVDT positions
3.6.2 Diagram of position of strain gauges
3.7 SPECIMEN FABRICATION

3.7.1 Casting
3.7.2 Stressing tendon sequence
3.7.3 Release anchoring sequence
3.8 MATERIAL TESTS

3.8.1 Compressive strength, tensile strength, elastic modulus of
concrete
3.8.2 Reinforcement tensile strength
3.8.3 Tendon tensile strength
3.8.4 Stress losses in tendon


19

Fig 3.7 Pre-stress distribution in the specimens
3.9 EXPERIMENT OF PUNCHING SHEAR CAPACITY OF FLAT
SLABS
3.10 EXPERIMENTAL RESULTS

3.10.1 Data and data analysis
3.10.2 Punching shear capacity of flat slabs
Table 3.10 Result of punching shear capacity of reinforced
concrete flat slabs
S0N3

S0N1
S0N2

Group
s

0.71 %

0.39 %

1.35 %

Sample

1

2

3

1

2

3

1

2

3

Putest (i)

78.0

66.8

74.9

86.0

86.6

84.4

118.1

114.7

113.9

Putest aver

73.2

85.7

115.6

Table 3.11 Result of punching shear capacity of pre-stress

concrete flat slabs
Group

S0N1

S1

S2


20
p

0

1.53

2.45

s

0.71 %

0.71 %

0.71 %

Sample

1

2

3

1

2

3

1

2

3

Putest (i)

86.0

86.6

84.4

104.1

102.2

102.3

104.9

115.9

117.3

Putest aver

85.5

102.8

3.10.3 Maximum deflection at the slab midle point
3.10.4 Punching crack patterns
3.10.5 Load-deflection relationship with different
reinforcement ratio

116.6

tensile

Fig 3.38 Load-deflection relationship with different tensile
reinforcement ratio

Fig 3.41 Load-deflection relationship with different effective prestress

3.10.6 Load - concrete strain relationship

21
3.10.7 Load – reinforcement tensile stress relationship
3.10.8 Verification of numerical results with tested results
3.10.9 Verification of the proposed formulae with tested results
Table 3.17 Comparison between the proposed formulae and the

tested results with different reinforcement ratio
Group

S0N3

S0N1

S0N2

Reinforcement
ratio

0.39 %

0.71 %

1.35 %

ks

1.08

1.13

1.20

Putest

72.3

85.7

115.6

Pu proposed

65.3

68.3

75.5

Putest / Pu proposed

1.11

1.25

1.53

When the tensile reinforcement ratio in the slabs is less than 1%,
Putest / Pu proposed is 1.11 and 1.25. The safety factor is suitable, since

this is a common reinforcement ratio in flat slabs. With a tensile
reinforcement ratio greater than 1.35%, Putest / Pu proposed is 1.53. With
the flat slabs having a large reinforcement ratio, the flat slabs may
have a larger bending moment or a smaller thickness, thus it could
require a higher safety factor.
Table 3.18 Comparison between the proposed formulae and

the tested results with different concrete effective stress
Group

S0N1

S1

S2

Effective stress

0

1.53

2.45

Reinforcement
ratio

0.71 %

0.71 %

0.71 %

kp

1.12

1.12

1.12


22
Putest

85.7

102.8

116.6

Pu proposed

68.3

76.9

80.6

Putest / Pu proposed

1.25

1.34

1.45

When the effective stress in the concrete is less than 1.53 MPa,
Pu / Pu proposed is 1.25 and 1.34. The safety factor is suitable because
this is an effective stress normally designed in flat slabs. With an
effective stress greater than 2.45 MPa, Putest / Pu proposed is 1.45. When
the effective stress in the concrete is too high, there will be some
risks such as tendon break out, stress losses, thus it could require
a higher safety factor.
test

3.11REMARKS OF CHAPTER 3

Chapter 3 of the thesis has set up an experimental model to
determine the punching shear capacity of reinforced and pre-stress
concrete flat slabs. Through 15 specimens, the effect of tensile
reinforcement ratio, pre-compressive stress in concrete was
investigated, and the accuracy of the proposed formula of 2.33 and
2.34 was verified.
Experimental results on 3 groups of reinforced concrete
specimens show that the tensile reinforcement ratio will be
significantly affected to punching shear capacity of reinforced flat
slabs: when the tensile reinforcement ratio is increased from
0.39% to 0.71%, punching shear force increased by 1.17 times,

when the tensile reinforcement ratio is increased from 0.39% to
1.35%, the punching shear force increased 1.57 times. Formulae
2.33 for coefficients of Putest / Puproposed with the above 3 survey
groups are 1.11, 1.25 and 1.53 respectively.
Experimental results on 2 groups of pre-stressed concrete
specimens shows that the effect of pre-compressive stress in
concrete increases the punching shear capacity of pre-stress
concrete flat slabs: when the pre-compressive stress in concrete is
1.53 MPa, the punching shear force increases by 1.20 times


23
compared to the normal reinforced concrete, when the precompressive stress is 2.45 MPa, the punching shear force increases
by 1.36 times compared to the normal reinforced concrete
speciments. Formulae 2.34 for the coefficients of Putest / Puproposed
with the above two groups are 1.25 and 1.34

CONCLUSION
1. CONCLUSION

Based on the research results on the punching shear capacity of
reinforced concrete and pre-stressed concrete flat slabs, the
following conclusions can be drawn in the thesis:
1. The proposed numerical simulation model in ANSYS
software, written in ADPL language, ensures reliability. With the
numerical model, it is easy to change the slab parameters such as
dimensions, materials, reinforcement layout, compressive stress in
concrete due to pre-stress, position of pre-stressed tendon layout,
boundary conditions ... to investigate the punching shear capacity
of reinforced concrete and pre-stressed concrete flat slabs.

2. The thesis has proposed formulae 2.33 to predict the
punching shear capacity of reinforced concrete flat slabs,
considering influence of the tensile reinforcement ratio, the effect
of the column size. The formulae is quite suitable for Vietnamese
Code TCVN 5574- 2018, and has been verified by 9 specimens
tested by the author and 230 published specimens in the world. It
is found that the formulae can be reliable and can be used in further
research and in design practice.
3. The thesis has proposed formulae 2.34 to predict the
punching shear capacity of pre-stressed concrete flat slabs suitable
for Vietnamese Code TCVN 5574-2018. The formulae has been