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The Punching Strength of High-Strength Flat Slabs: Experimental Study Qi Zhang

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TABLE OF CONTENTS

Abstract 3

Notation 4

Introduction 5

Approaches of Prediction 7

Hussein’s Experimental Program and Rearrangement Consideration 10

Group I, Concrete strength with reinforcement ratio and slab depth 13

Group 2, Load area and slab depth 19

Group III, Reinforcement ratio and slab depth 23

Discussion and Recommendation 27

Conclusion 33

Reference 34


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The Punching Strength of High-Strength Flat Slabs: Experimental Study

Abstract

The paper reviews an experimental program consisting of 17 high-strength concrete slabs that

were conducted by Dr. A. Hussein and Dr. H. Marzouk. The test data from the experiment is

rearranged, analyzed by Design-Expert software, and divided into three groups. The three

groups are primarily concerned with the effects of four variables on the punching strength of

high-strength concrete slabs: the concrete strength, the reinforcement ratio, the slab depth and

the column size. The predictions of three approaches, ACI 318-95, BS8110 and Rankin’s

approach, are compared with the experimental results.

The experimental results indicated that shear strength depends on a power of the concrete

compressive strength, fc’, that is less than 0.5 and more like a cubic root relationship. The

assumption that the critical perimeter is at a distance 0.5d from the load area is reasonable, and

the reinforcement ratio has a considerable effect on the shear strength especially when the slab

depth is at a high level. A modified approach, modeled after the Rankin’s approach, is proposed

and verified by this experiment and another tests. A recommended experiment, a one-half

fraction of a 24 experiment combined with a face centered central composite response surface

design, would reveal the interaction among the variables and the punching strength. Therefore,

the proposed method should improve the understanding of the behavior of high-strength slabs.


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Notation

L slab span (= 2.5 a)

M moment per unit width

Mb bending moment of resistance

Mbal balanced moment of resistance

Pk characteristic punching resistance, calculated by different approaches

Pmod modified predicted punching capacity

Pu ultimate punching load

Pvf predicted flexural punching capacity

Pvs predicted shear punching capacity

a distance between supports of conventional slab specimen (=0.4L)

c length of column side

d average effective depth to tensile reinforcement

f'c cylinder strength of concrete

fcu cube strength of concrete

fy yield stress of reinforcement

h overall thickness of slab

kb ratio of applied load to internal bending moment at column periphery

kl ratio of applied load to ultimate moment of resistance at failure

kyl moment factor for overall tangential yield

rf reduction coefficient to allow for column shape

rs radius of conventional slab specimen

ry radius of yield zone

s side length of conventional slab specimens

p reinforcement ratio

u length of control perimeter used in punching calculations

vck basic characteristic shear stress


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Introduction

High-Strength concrete (HSC), concrete with the strength above 45 MPa, has been widely used

in the construction industry due to increasing requirements and economical consideration for

structures. Since HSC members not only have higher modulus of elasticity but also exhibit

different failure mechanism from the normal concrete, it is unsafe to directly extrapolate the

models and equations based on normal concrete to HSC members.

Punching in the vicinity of a column is a possible failure mode for reinforced concrete flat slabs.

The undesirable suddenness and catastrophic nature of punching failure are of concern to

structural engineers. In this respect, the use of high-strength concrete improves the punching

strength of HSC flat slabs and allows higher forces to be transferred.

However, there is no generally accepted rational treatment for the punching resistance of flat

slabs because of the complicated dependence of shear strength on their flexural behavior as well

as the fact that it is difficult to observe the internal inclined cracks in a slab. The design provisions

of punching strength in the two major building codes, the North American code and the European

code, are significantly different, since they are based on different empirical formulas. This

difference in design provisions leads to different predictions of the punching strength of the same

specimen. Thus, it is important to improve the understanding of the punching failure mechanisms


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and to establish a more reliable method for predicting the punching strength of HSC flat slabs.

This paper, based on the experimental program conducted by H. Marzouk and A. Hussein (1991),

discusses the effects on punching strength of HSC flat slabs by main variables including the

concrete strength, the reinforcement ratio, the slab thickness and the load area. It also presents

and compares three different approaches for predicting the punching strength. In addition, a

modified approach and a recommended experiment for the punching strength of HSC slab are

proposed. Concepts and methods of “Design of Experiment” are utilized in the whole paper.


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Approaches of Prediction

Many codes and researchers have presented different formulae for predicting punching shear

strength of slabs based on their understanding of punching behavior. Two typical approaches in

the building codes, ACI 318-95 and BS8110, are considered and compared to the approach

developed by Rankin and Long (1987).

Generally, punching strength is predicted by considering a nominal shear stress, a control

perimeter and an effective depth. The main differences of approaches depends on the assumed

location of the different the control perimeter, the concrete strength, the size effect and the

reinforcement ratio:

(1) Both the ACI code and the Rankin’s approach assume that the control perimeters is located

at a distance of 0.5 times the effective depth from the edge of load, while the BS8110 code

considers a larger control perimeter, 1.5d.

(2) In the ACI code and the Rankin’s approach, shear stress is expressed in term of square-root

relationship with concrete compressive strength, while the BS8110 code considers a cubic-root

proportion.

(3) Both the British code and the Rankin’s approach take reinforcement ratio and size effect into


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consideration by different modification factor, while the ACI code neglects these effects.

For the purpose of comparing different predictions of the available experimental test results,

safety factors have been removed from the equations of these three approaches, the limit of 40

MPa of the maximum useful cube strength has been ignored while applying BS8110 and the

cube strength in BS8110 has been assumed as fcu = fc’ / 0.8.

The equations of the three approaches are given below. The flexural strength is also considered

and calculated using the yield-line theory. The failure mode is determined by the Rankin’s

approach.

ACI 318-95

'332.0 cck fv =

)(4 dcu += for square loaded area

udvP ckk =

BS8110

433 /40025/10079.0 dfv cuck ⋅⋅⋅= ρ

)3(4 dcu += for square loaded area

udfudvP cuckk 2.1≤=

Rankin’s approach

This is a two-phase approach that classifies the punching failure as flexure and shear. First the


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shear punching strength and the flexural punching strength are calculated. Then, the results are

used to determine the failure mode. For example, the failure mode is the shear punching failure if

the punching shear strength is less than the flexural punching strength.

'4 100415.0 cck fv ⋅⋅= ρ

)(4 dcu += for square loaded area

udvP ckvs =

( )( ) bbalbfbylylvf MMMrKKKP ⋅⋅−−= //

Where,

( )172.0)/(8 −−⋅= casK yl

( ) 5.1/5.2ln/25 caKb ⋅=

( )( )'2 /59.01 cyyb ffdfM ⋅−= ρρ

2'333.0 dfM cbal =

If Pvs < Pvf, then the failure mode is punching shear failure and Pk = Pvs .

Otherwise, when Pvs > Pvf, then the failure mode is flexural punching failure and Pk = Pvf .


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Hussein’s Experimental Program and Rearrangement Consideration

The experimental program conducted by Marzouk and Hussein was based on a series of

practical configurations of a conventional slab-column system. Seventeen specimens were

subjected to concentric vertical loading. The specimens were simply supported along all four

edges to simulate the lines of contra flexure. Such specimen represented the region of negative

bending moment around an interior column. These specimens were divided into four groups in

order to investigate important parameters of flat slabs.

Full details of the test slabs are given in Table 1. Reinforcing bars consisted of Grade 400 steel

conforming to CSA standards with an actual yield strength of 490 MPa. The concrete mix was

designed to produce a 28-day strength of 70 Mpa.

The specimens were loaded monotonically through the center stub column. The load was

applied with a hydraulic actuator that has a maximum capacity of 670 KN. During the test, the

slabs were carefully inspected. Extensive measurements of the strains were used at key

locations on the flexural bar and surface of concrete slabs. Linear variable displacement

transducers (LVDT) were used to measure the deflection of the center of the slabs, and dial

gages were used to measure the vertical displacements at the slab corners.


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Table 1. Details of the tested specimens

Series

No.

Slab

No.

Compressive

strength, fc’

(MPa)

Bar Size

Bar

Spacing

(mm)

Column

size, c

(mm)

Slab

thickness

(mm)

Average

depth, d

(mm)

Steel ratio � %

NS1 42 M10 71.4 150 120 95 1.473

HS1 67 M10 214.3 150 120 95 0.491

HS2 70 M10 125.0 150 120 95 0.842

HS7 74 M10 88.2 150 120 95 1.193

HS3 69 M10 71.4 150 120 95 1.473

1

HS4 66 M15 93.7 150 120 90 2.370

NS2 30 M10 125.0 150 150 120 0.944

HS5 68 M10 125.0 150 150 95 0.640

HS6 70 M10 125.0 150 150 120 0.944

HS8 69 M15 150.0 150 150 120 1.111

HS9 74 M15 100.0 150 150 120 1.611

2

HS10 80 M15 71.4 150 150 120 2.333

HS11 70 M10 150.0 150 90 70 0.952

HS12 75 M10 93.8 150 90 70 1.524 3

HS13 68 M10 71.4 150 90 70 2.000

HS14 72 M10 71.4 220 120 95 1.473 4

HS15 71 M10 71.4 300 120 95 1.473

However, there are some difficulties when trying to utilize the arrangement for the specimens in

the Hussein’s experiment to investigate the punching strength of HSC flat slabs in a statistical

way. Hussein chose four series of specimens in his experiment with four variables, including the

concrete strength, the reinforcement ratio, the slab thickness and the load area. In the first two

series of 12 specimens, the trend of the punching strength of HSC flat slabs based on the main

variable, the reinforcement ratio, was found. The traditional approaches for predicting punching


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strength were compared based on this trend. In the last two series comprising only five

specimens, the variables of the slab depth and the load area were considered, respectively.

Depending on these series of specimens and the understanding of shear in HSC slabs, Hussein

analyzed the experimental data and investigated the behavior of HSC flat slabs, including

load-deflection characteristics, ductility and energy absorption characteristics, concrete strains,

steel strains, cracking and failure characteristics, and modes of failure. Unfortunately, the

interaction among the variables, the major concern in HSC flat slabs, was not demonstrated in

Hussein’s study due to the experimental arrangement. Furthermore, the problem that there were

no approaches to consistently predict the punching strength of HSC flat slabs was not solved.

Since a statistical experimental design, such as the 2-level factorial design and the general

factorial design, requires a consistent relationship among the variables, the arrangement in

Hussein’s experiment could not directly apply the statistical program to analyze the variables and

responses. Therefore, the previous experiment series are rearranged in the following sections, in

order to investigate the punching strength of HSC flat slabs and to consider the interaction

effects of variables.


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Group I, Concrete strength with reinforcement ratio and slab depth

Moe’s work (1961) is the basis for ACI 318-95. It advocated that the shear strength was

dependent on the square root of concrete compressive strength because he believed that a

shear failure was controlled primarily by tensile splitting, which is generally assumed proportional

to fc’1/2. However, further research has shown that shear strength depends on a power of fc’ less

than 0.5 and more like the cubic root relationship, especially when fc’ is more than 40 MPa.

Therefore, the relationship between shear strength and HSC flat slabs is considered carefully in

this study by means of investigating normal strength concrete (�40Mpa) and high strength

concrete (70Mpa). In addition, the effects of reinforcement ratio and slab depth are considered.

A series of six HSC flat slabs is investigated for the main effect of concrete strength (fc’) on

punching strength. At the same time, the interaction effect of reinforcement ratio (�) and slabs

depth (d) is investigated. The test factors for this study are laid out in Table 2.

Table 2. Factors and Levels for Flat Slabs in Group 1

Factor Name Unit Low level (-1) High level (+1)

A Concrete strength (fc’) MPa 40 70

B Slabs depth (d) mm 95 120

C Reinforcement ratio (�) % 0.95 1.5

Consider a 23 factorial experiment with eight combinations of the low and high levels of variables.

Unfortunately, six specimens only available in Hussein’s experiment are used in this group. The


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treatment combination in a form of sign table is shown with the experimental data in Table 3.

Table 3. Treatment combinations and Test results in Group 1

Pk / Pu Slab

No.

Combin-

ation

Factor A:

compressive

strength

(MPa)

Factor B:

Average

depth

(mm)

Factor C:

Steel

ratio � %

Ultimate

load Pu

(KN) ACI BS8110 Rankin

Failure

mode*

N/A (1) -1 -1 -1 N/A N/A N/A N/A N/A

HS2 a 1 -1 -1 249 1.04 1.08 1.15 Flexure

NS2 b -1 1 -1 396 0.60 0.74 0.73 Shear

HS6 ab 1 1 -1 489 0.74 080 0.91 Shear

NS1 c -1 -1 1 320 0.63 0.85 0.86 Shear

HS3 ac 1 -1 1 356 0.72 0.90 0.99 Shear

N/A bc -1 1 1 N/A N/A N/A N/A N/A

HS9 abc 1 1 1 543 0.68 0.87 0.96 Shear

*Failure mode is determined by Rankin approach

For a 23 factorial design, 23 – 1 effects, which are

equal to seven effects, can be estimated. The

main effects of A, B and C and two-factor

interactions of AB, AC, and BC, and one

three-factor interaction ABC are included. The

effects are estimated using the Design-Expert

software and are shown in Figure. 1. The analysis

of variance (ANOVA) is presented in Table 4.

DESIGN-EXPERT PlotUltimate load

A: concrete strengthB: slab depthC: reinf orcement ratio

Half Normal plot

Half

Norm

al %

prob

abilit

y

|Effect|

0.00 49.81 99.62 149.44 199.25

0

20

40

60

70

80

85

90

95

97

99

B

Figure.1: Normal probability plot of

estimated effects of Group 1


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Table 4: Analysis of variance table for Group 1

Source Sum of

Squares DF

Mean

Square

F

Value Prob > F Significant at 5%

Model 58452.58 4 14613.15 20.80904 0.1628 No

A 3502.083 1 3502.083 4.986947 0.2680 No

B 34225 1 34225 48.73621 0.0906 Yes

C 6480.25 1 6480.25 9.227839 0.2025 No

AB 812.25 1 812.25 1.156639 0.4769 No

Residual 702.25 1 702.25

Cor Total 59154.83 5

Figure 1 shows the normal probability plot of the effects of variables in this study. It can be seen

that effect B (slab depth) is well off the line indicating its significance, furthermore, the effect A

(concrete strength) is on the line and thus not

significant on its own. This is confirmed by the

results shown in Table 4 and Figure 2.

Unfortunately, partly because of loss of two

specimens (treatments), the model for this study is

insignificant, which implies that the interaction of

variables can not be properly shown with at least

95% confidence. However, the results prove that fc’

has a relatively less effect on punching strength of

DESIGN-EXPERT Plot

Ultimate loadX = A: concrete strengthY = B: slab depth

Actual FactorC: reinf orcement ratio = 0.00

Ultimate load

A: concrete strength

B: s

lab d

epth

-1.00 -0.50 0.00 0.50 1.00

-1.00

-0.50

0.00

0.50

1.00

319.125

358.5

397.875

437.25

476.625

Figure.2: Group 1, Interaction contour plot of d and

fc’ when p is in the middle level


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HSC flat slabs. In practice, since the punching strength of HSC flat slabs depends on a power of

fc’ less than 0.5, the significant effect of fc’ requires more difference of fc’ between low level and

high level. On the other hand, slab depth approximately has a square relationship with punching

strength of HSC flat slabs so that a small change of slab depth would have a considerable effect

on punching strength.

Other than analysis by the Design-Expert software, the comparison of the three approaches,

based on the relationship of punching strength and concrete strength, is also noteworthy and

shown in Figure3.1, Figure 3.2 and Figure 3.3. The principal variable was the concrete strength

in two series of slabs: NS2 and HS6, NS1 and HS3. All the specimens were punching shear

failure. The test data are summarized in Table 3. Figure 3 shows the graphs of ultimate loads

against concrete strength and sets the experimental results compared with the curves

determined by ACI 315-95, BS8110 and Rankin’s approach.

It is apparent from Figure 3 that the BS8110 assumption that punching strength is proportional to

the cube root of the concrete compressive strength can be seen to reasonable, especially when

the concrete strength is beyond the limit of 40 MPa of maximum useful cube strength in BS8110.

The ACI code, although overestimates the effect of concrete strength and neglects the effect of

reinforcement ratio, is safe for all concrete strength in this study, The Rankin’s approach could

not reflect the tendency of punching strength against concrete strength; however, it predicts the

punching resistance of slabs most close to the actual ultimate load.


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Figure 3.1: Group1 relationship of punching strength to concretecompression strength, determined by ACI 315-95

0

100

200

300

400

500

600

0 20 40 60 80 100

fc' (MPa)

Pu

(KN

)

Experiment data:NS2 and HS6ACI based on NS2and HS6Experiment data:NS1 and HS3ACI based on NS1and HS3

Figure 3.2: Group1 relationship of punching strength to concretecompression strength, determined by BS8110

0

100

200

300

400

500

600

0 20 40 60 80 100

fc' (MPa)

Pu

(KN

)

Experiment data:NS2 and HS6BS8110 based onNS2 and HS6Experiment data:NS1 and HS3BS8110 based onNS1 and HS3


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Figure 3.3: Group1 relationship of punching strength to concretecompression strength, determined by Rankin's approach

0

100

200

300

400

500

600

0 20 40 60 80 100

fc' (MPa)

Pu

(KN

)

Experiment data:NS2 and HS6Rankin based onNS2 and HS6Experiment data:NS1 and HS3Rankin based onNS1 and HS3


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Group 2, Load area and slab depth

Long and Bond (1967) have shown that the critical stress is on the neutral plane as there is no

beneficial influence of direct compression at this level. The vertical shear stress is also dispersed

before reaching the neutral plane and the critical section is therefore at some distance from the

column periphery. This dispersion is dependent on the ratios of the size of column to the slab

effective depth. Moe (1961) also recognized this dependence and assumed a linear change in

shear strength with c / d in his equation for predicting the shear strength of slabs. In the current

codes, this ratio has been taken into account by assuming a pseudo-critical section at one half

(ACI code) or one and a half (BS8110) of the slab effective depth from the column periphery. This

would seem reasonable because of the fact that the depth of the compression zone may well

approach one half of the slab effective depth in the shear mode of punching failure.

Since the inconsistencies expressing the critical section between ACI code and BS8110 code,

the actual relationship between punching strength and critical section is demonstrated in the

second group. In this group, consisting three series of eight specimens, the principal variable is

the critical section in terms of the variable of slab effective depth or column size. All the slabs

failed by punching and the detailed series are given in Table 5.


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Table 5. Group 2 test data

Pk / Pu Series

No.

Slab

No.

concrete

strength

(MPa)

column

size

(mm)

Slab

thickness

(mm)

Average

depth

(mm)

Critical

perimeter

4(c+d)

(mm)

Steel

ratio p%

Ultimate

load

Pu (KN) ACI BS8110 Rankin

Failure

mode

� HS3 69 150 120 95 980 1.473 356 0.72 0.90 0.99 shear

1 HS14 72 220 120 95 1260 1.473 498 0.68 0.76 0.93 shear

� HS15 71 300 120 95 1580 1.473 560 0.75 0.78 0.97 flexure

� HS12 75 150 90 70 880 1.524 258 0.69 0.85 0.95 shear

2 HS3 69 150 120 95 980 1.473 356 0.72 0.90 0.99 shear

� HS9 74 150 150 120 1080 1.611 543 0.68 0.87 0.96 shear

� HS13 68 150 90 70 880 2.000 267 0.63 0.87 0.94 shear

3 HS4 66 150 120 90 960 2.370 418 0.56 0.82 0.86 shear

� HS10 80 150 150 120 1080 2.333 645 0.60 0.85 0.92 shear

In the first series, the column size is changed from 150 mm to 300 mm while the effective depth

of slabs is fixed. The concrete compression strength is around 70 Mpa, and the level of

reinforcement ratio is the same as 1.473%. Figure 4.1 shows the test results as a graph of (Pu / d)

plotted against (c +d). If the relationship between the punching strength and critical perimeter

(c+d) is in accordance with the definition in ACI code, the experimental data should have similar

scatter along the curve determined by ACI code. On the other hand, they should have unequal

scatter along the curve determined by BS8110. Figure 4.1 proves this assumption. It could also

be seen that the line based on Rankin’s approach is closer to the test result, and the critical

section (c+d) is proportional to the corrected punching strength.


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Figure 4.1: Group2 relationship of punching strength tocritcial perimeter determined by different codes

0

1

2

3

4

5

6

7

8

9

10

700 1200 1700 2200

Critical perimeter (mm)

Pu/

d (K

N)

Rankin

Experiment data (HS3,HS14, HS15)

BS8110

ACI

In order to verify the results of the first series of specimens, the second and third series are

investigated as the main variable is the slab effective depth. When compared with the prediction

of Rankin approach, Figure 4.2 and Figure 4.3 show the relationship between the critical section

(c+d) and punching loads, which are corrected for the small variations of the concrete

compression strength and the reinforcement ratio. The assumption is proved again.


- 22 -

Figure 4.2: Group2 relationship of punching strength tocritcial perimeter determined byRankin's approach

0

100

200

300

400

500

600

700

800 1100 1400 1700


P. c

orr

= P

u / (

d*fc

^0.5

*p^0

.25)

Rankin

Experiment data (HS12,HS3, HS9)

Figure 4.3: Group2 relationship of punching strength tocritcial perimeter determined by Rankin's approach

0

100

200

300

400

500

600

700

800 1100 1400 1700


P. c

orr

= P

u / (

d*fc

^0.5

*p^0

.25)

Rankin

Experiment data(HS13, HS4, HS10)


- 23 -

Group III, Reinforcement ratio and slab depth

Nine specimens with the main variables of the reinforcement ratio and the slab depth are

included in this group. The concrete compression strength is around 70 MPa, and the column

size is fixed at 150 mm. A two-numeric-factor factorial design is used in this group, and each

factor is set at three levels, which is shown in Table 6. The 3 X 3 experimental runs are given in

Table 7.

Table 6. Factors and Levels for Flat Slabs in Group 3

Factor Name Unit Low level Middle Level High level

A Slab effective depth (d) mm 70 95 120

B Reinforcement ratio (p) % 0.95 1.50 2.00

Table 7: Treatment combinations and test results in Group 3

Pk / Pu Slab No.

column size (mm)

Slab thickness

(mm)

Average depth (mm)

Steel ratio p%

Ultimate load Pu

(KN) ACI BS8110 Rankin

Failure mode

HS11 150 90 70 0.952 196 0.87 0.94 0.88 flexure

HS12 150 90 70 1.524 258 0.69 0.85 0.95 shear

HS13 150 90 70 2.000 267 0.63 0.87 0.94 shear

HS2 150 120 95 0.842 249 1.04 1.08 1.15 flexure

HS7 150 120 95 1.193 356 0.75 0.86 0.98 shear

HS4 150 120 90 2.370 418 0.56 0.82 0.86 shear

HS6 150 150 120 0.944 489 0.74 0.80 0.91 shear

HS9 150 150 120 1.611 543 0.68 0.87 0.96 shear

HS10 150 150 120 2.333 645 0.60 0.85 0.92 shear


- 24 -

The procedure of ANOVA using the Design-Expert software is shown in the Table 8.

Table 8: Analysis of variance table for Group 3

Source Sum of

Squares DF

Mean

Square

F

Value Prob > F

Model 180281.16 3 60093.72 33.078 0.0010 significant

A (effect of d) 151633.78 1 151633.78 83.464 0.0003 significant

B (effect of p) 26221.05 1 26221.05 14.433 0.0126 significant

AB (interaction

effect of d and p 1737.44 1 1737.44 0.9563 0.3730

Residual 9083.73 5 1816.75

Cor Total 189364.89 8

The values of "Prob > F" less than 0.0500 indicate

that the model terms are significant. The effect of

the slab effective depth (d) and the effect of

reinforcement ratio (p) in this group are significant

for the punching strength of HSC flat slabs. Thus,

it is unacceptable to predict punching resistance

with ACI code in this group because the

reinforcement ratio is not taken into consideration

considered in the ACI code.

The interaction effect of d and is shown in Figure 5. In the first place, the punching strength is

DESIGN-EXPERT Plot

utimate load

X = A: slab thicknessY = B: reinf orcement ratio

Design Points

B- 0.950B+ 2.000

B: reinforcement ratioInteraction Graph

A: slab thickness

utim

ate

load

90.00 105.00 120.00 135.00 150.00

110.053

254.872

399.691

544.51

689.328

Figure.5: Group 3, Interaction graph of d and p


- 25 -

higher with a larger depth. Furthermore, the increase of punching strength in the high level of is

slightly faster than that in the low level of as d increases. The punching strength in the high

level of is significantly higher than that in low level of as d is in the high level, although it has

no significant difference in the low level of d regardless of whether is at 0.95% or 2.0%.

Figure 6.1: Rank in punching strength against reinforcement ratio

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Reinforcement ratio (%)

Pu

(KN

) Rankin punchingstrength

Experimentaldata (HS11,HS12 and HS13)

Figure 6.2 Rank in punching strength against reinforcement ratio

0

50

100

150

200

250

300

350

400

450

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Pu

(KN

)

Rankinpunchingstrength

Experimentaldata (HS2,HS7,HS4)


- 26 -

Figure 6.3 Rank in punching strength against reinforcement ratio

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0


Pu

(KN

)

Rankinpunchingstrength

Experimentaldata (HS6, HS9and HS10)

This interaction effect is reasonable in practice. In this group, only HS2 and HS11 failed in the

mode of punching flexure with the relatively lower level of and d. Accompanied with the

increase of and d, the failure mode of slabs is transformed to punching shear failure. In addition,

dowel force, developed at the apex of the inclined crack crossing or extending along the slab

reinforcement, is significantly increased in this condition. Kinnunen (1963) concluded that dowel

forces carry about 30 percent of the total shear. Therefore, the reinforcement ratio would have a

considerable effect on the punching strength. Rankin approach shows the effect of as depicted

in Figure 6.1, Figure 6.2 and Figure 6.3 and predicts accurately the punching strength compared

with the ACI code and BS8110 code as shown in Table 7.


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Discussion and Recommendation

According to the above analysis based on Hussein’s experiment, the relationship between the

variables and the punching shear strength of HSC flat slabs could be defined as below:

( )ddcfP cvs +⋅∝ 3 '4 100ρ

Compared with all approach for predicting the punching strength, the Rankin approach gives

good correlation with the test, although it could not express the proper relationship between

punching shear and concrete compression strength. Therefore, a modified approach, modeled

from Rankin’s, is proposed to predict the punching shear strength of HSC flat slabs.

( )ddcfP cvs +⋅⋅= 3 '4 10012.3 ρ

This modified equation accurately shows that the punching shear strength is proportional to the

cube root of concrete compression strength, the quartic root of reinforcement ratio, the effective

slab depth and the critical perimeter assuming the width of load area plus the effective slab depth

each side. To verify the proposed approach, its validity is checked by comparing it with Hussein’s

test results of this test and another data from Ramdane (1996) and Tomaszewicz (1993). Table 9

shows the comparisons of the test results with ACI code, BS8110 and the proposed approach.


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The mean values of (Pk / Pu) are 0.99 and the coefficient of variation is 9%. This coefficient of

variation corresponds to an improvement of approximately 37% over the next coefficient of

variation (14%) given by BS8110. Therefore, the adoption of this proposed approach for

predicting the punching strength of HSC flat slabs would provide a more accurate prediction.

Furthermore, it could efficiently use the reinforcement and the concrete.

Table 9: Comparison of experimental and predicted punching strength

Pk / Pu Series No. Slab No.

Compressive

strength

(MPa)

Slab

effective

length,a

(mm)

column

size

(mm)

Averag

e depth

(mm)

Steel

ratio �

%

Ultimate

load

(KN)

Pmod

Modify ACI BS8110

NS1 42 1500 150 95 1.473 320 286 0.89 0.63 0.85

HS1 67 1500 150 95 0.491 178 175 0.98 1.42 1.24

HS2 70 1500 150 95 0.842 249 286 1.15 1.04 1.08

HS7 74 1500 150 95 1.193 356 328 0.92 0.75 0.86

HS3 69 1500 150 95 1.473 356 338 0.95 0.72 0.90

HS4 66 1500 150 90 2.370 418 348 0.83 0.56 0.82

NS2 30 1500 150 120 0.944 396 319 0.80 0.60 0.74

HS5 68 1500 150 120 0.640 365 356 0.98 0.97 0.93

HS6 70 1500 150 120 0.944 489 422 0.86 0.74 0.80

HS8 69 1500 150 120 1.111 436 438 1.00 0.82 0.94

HS9 74 1500 150 120 1.611 543 492 0.91 0.68 0.87

HS10 80 1500 150 120 2.333 645 554 0.86 0.60 0.85

HA (1991)

HS11 70 1500 150 70 0.952 196 173 0.88 0.87 0.94


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HS12 75 1500 150 70 1.524 258 232 0.90 0.69 0.85

HS13 68 1500 150 70 2.000 267 240 0.90 0.63 0.87

HS14 72 1500 220 95 1.473 498 440 0.88 0.68 0.76

HS15 71 1500 300 95 1.473 560 544 0.97 0.75 0.78

slab5 54.4 1372 150 100 0.580 190 194 1.02 1.29 1.23

slab12 60.4 1372 150 100 1.280 319 335 1.05 0.81 0.99

slab15 68.4 1372 150 100 1.280 276 349 1.26 1.00 1.19

slab16 99.2 1372 150 100 1.280 362 395 1.09 0.91 1.03

slab22 84.2 1372 150 100 1.280 405 374 0.92 0.75 0.87

RK (1996)

slab23 56.4 1372 150 100 0.870 341 277 0.81 0.73 0.80

nd65-1-1 64.3 2500 200 290 1.420 2050 1995 0.97 0.74 0.86

nd95-1-1 83.7 2500 200 290 1.420 2250 2178 0.97 0.77 0.86

nd95-1-3 89.9 2500 200 290 2.430 2400 2551 1.06 0.75 0.98

nd115-1-1 112 2500 200 290 1.420 2450 2400 0.98 0.82 0.87

nd65-2-1 70.2 2200 150 210 1.660 1200 1136 0.95 0.70 0.91

nd95-2-1 88.2 2200 150 210 1.660 1100 1226 1.11 0.86 1.07

nd95-2-3 89.5 2200 150 210 2.490 1250 1364 1.09 0.76 1.09

nd115-2-1 119 2200 150 210 1.660 1400 1355 0.97 0.78 0.93

nd115-2-3 108.1 2200 150 210 2.490 1550 1452 0.94 0.67 0.93

TA (1993)

nd95-3-1 85.1 1100 100 95 1.720 330 300 0.91 0.69 0.97

Mean 0.992 0.794 0.93

Coefficient of variation 0.09 0.346 0.14

The interaction of reinforcement ratio and slab depth was revealed in the Group 3. It is

reasonably convincing that more interaction of variables could be discovered. Then, the


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punching behavior of slabs would be fully understood in the range of specified level, if this

experiment had been designed on the statistical basis and in accordance with the methods of

design of experiment. With the consideration of reducing the number of experimental runs and

possible quadratic or curvature effects, a one half fraction of a 24 experiment combined with a

face centered central composite response surface design could be used to investigate the

punching strength of HSC flat slabs. Half of a 24 factorial experiment requires only eight runs and

the central composite design requires another eight axial and one center points. Thus, 17

(2K+2K+1) runs, which is the same as the number of specimens in the Hussein’s experiment, are

required to fit a second order model without losing too much information; hence, it would

estimate the main effects and two-factor interaction effects efficiently. The factors and their

ranges of interest are shown in Table 10,

Table 10. Factors and Levels for the recommended experiment

Factor Name Unit Low level (-1) Mid level (0) High level (+1)

A Concrete strength (fc’) MPa 40 60 80

B Reinforcement ratio (p) % 0.5 1.0 1.5

C Slab effective depth (d) mm 100 150 200

D Column size (d) mm 150 200 250

Each factor would be set at three levels for a face centered response surface design. In the first

place, the range of the concrete strength is selected between 40 Mpa and 80 Mpa to investigate

the effect of the high-concrete strength. Secondly, reinforcement ratio equal to 0.5% has been


- 31 -

widely used for two-way slabs, as well as, the high level of reinforcement ratio, 1.5% or more,

has been used for footings or transfer plates. Moreover, the slab effective depth set from 100 mm

to 200 mm would show the change of failure mode from flexure to shear. Finally, the column size

reflects the actual size in accordance with the slab depth. seventeen experimental runs are laid

out in Table 11.


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Table 11: Run combinations and responses using response surface design

standard

order run type

Concrete strength (MPa)


Slab effective depth (mm)

Column size (mm)

1 13 *Fact 80 1.5 200 150

2 6 Fact 80 1.5 100 150

3 9 Fact 80 0.5 200 250

4 4 Fact 40 1.5 100 250

5 7 Fact 80 0.5 100 250

6 12 Fact 40 0.5 200 150

7 17 Fact 40 1.5 200 250

8 3 Fact 40 0.5 100 150

9 16 *Axial 40 1 150 200

10 2 Axial 80 1 150 200

11 1 Axial 60 0.5 150 200

12 8 Axial 60 1.5 150 200

13 5 Axial 60 1 100 200

14 10 Axial 60 1 200 200

15 11 Axial 60 1 150 150

16 15 Axial 60 1 150 250

17 14 *Center 60 1 150 200

*fact: factorial design

*Axial: axial points

*Center: center points, points with all levels set to the midpoint of each factor range


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Conclusion

1. The interaction among the variables, the major concern in HSC flat slabs, was not

demonstrated in Hussein’s study due to level choice of variables.

2. Shear strength depends on a power of fc’ less than 0.5 and more like the cube root

relationship. ACI code overestimates the effects of concrete compressive strength on the

punching resistance of HSC slabs.

3. The relationship between the punching strength and critical perimeter (c+d) is in accordance

with the definition in ACI code.

4. Dowel force developed along the slab reinforcement has a considerable influence on the

shear strength of HSC slab. ACI code is inconsistent with the ultimate punching load partly

because it neglects the effect of reinforcement.

5. The Rankin approach gives good correlation with the test. However, it overestimates the

effect of concrete compressive strength on the punching resistance of HSC slabs.

6. A proposed approach, based on the Rankin’s, is proposed

( )ddcfP cvs +⋅⋅= 3 '4 10012.3 ρ

7. A recommended experiment, a one half fraction of a 24 experiment combined with a face

centered central composite response surface design, could be used to investigate the

punching strength of HSC flat slabs.


- 34 -

Reference

American Concrete Institute (ACI), (1995) “Building code requirements for reinforced concrete

and reinforced concrete and commentary.” ACI 318-95/ACI 318R-95, Detroit.

British Standards Institution (BS8110), (1985) “Code of practice for design and construction.”

British Standard Institution, Part 1, London.

Rankin, G. I. B. “Predicting the punching strength of conventional slab-column specimens.” Proc.

Instn Civ. Engrs, Part1, 82, April, 1987, 327-346.

Kinnunen, S., “Punching of concrete slabs with two-way reinforcement with special reference to

dowel effect and deviation of reinforcement from polar symmetry,” Transactions, No. 198, 1963,

Royal Institute of Technology, Stockholm, Sweden.

Long A. E. and Bond D. “Punching failure of reinforced concrete slabs.” Proc. Inst Civ. Engrs, 37,

1967, 109-135.

Lye L. M., “Some applications of statistical design of experiment methodology in civil

engineering,” Annual conference of the Canadian Society for Civil Engineering, Moncton, June

2003.

Marzouk. H and Hussein A., “Experimental Investigation on the Behavior of High-Strength

Concrete Slabs,” ACI Structural Journal, V.88, No. 6, Nov-Dec 1991, pp 701-713.

Moe, J., “Shearing strength of reinforced concrete slabs and footings under concentrated loads,”

Development Department Bulletin D47, Portland Cement Association, April, 1961, 130pp.

Ramdane, K. E., “Punching shear of high performance concrete slabs.” 4th International

Symposium on Utilization of High-strength / High-performance concrete. Paris, 1996,

pp1015-1026

Tomaszewicz, A. “High-strength concrete SP2 – plate and shells.” Report 2.3, Punching shear

Capacity of Reinforced Concrete Slabs. Report No. STF70A93082, SINTEF, Trondheim, 1993.

˘ˇˆ - engr.mun.caqzhang/papers/punching_strength.pdf · fcu cube strength of concrete fy yield...

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