in-plane shear behavior of reinforced concrete elements with...

공학석사 학위논문

In-Plane Shear Behavior of

Reinforced Concrete Elements with

High-Strength Materials

고강도 재료가 사용된

철근콘크리트 요소의 면내 전단 거동

2014년 2월

서울대학교 대학원

건설환경공학부 구조전공

배 광 민

In-Plane Shear Behavior of

Reinforced Concrete Elements with


지도 교수 조 재 열

이 논문을 공학석사 학위논문으로 제출함

2014 년 1 월

서울대학교 대학원

건설환경공학부 구조전공

배 광 민

배광민의 석사 학위논문을 인준함

2014 년 1 월

위 원 장 (인)

부위원장 (인)

위 원 (인)

i

Abstract

In-Plane Shear Behavior of Reinforced Concrete Elements with


Bae, Gwang-Min

Department of Civil and Environmental Engineering

The Graduate School

Seoul National University

This thesis presents the results of twelve reinforced concrete elements

subjected to shear and biaxial stresses. These elements were constructed by

one-third scale of real nuclear power plant wall elements. And the load

conditions were determined by considering earthquake and accidental inner

pressure when the nuclear power plant is overheated. Elements were loaded

until failure using University of Toronto’s Shell Element Tester. The concrete

compressive strength, steel yield strength and reinforcement ratio of APR

1400 that is current model of nuclear power plant in Korea were used for

reference element. And the high strength concrete, high yield strength steel

and decreased reinforcement ratio were used for other elements to compare

with the shear behavior of reference elements. On the other hand, in recent

years, design codes have incorporated compression field theory for the design

of reinforced concrete structures subjected to shear. Especially the Modified

Compression Field Theory has become the basis of the shear provisions in

CSA Standards, AASHTO LRFD, fib Model code and Eurocode 2. It is

expected that ASME, ACI 318 and ACI 349 design codes that commonly used

ii

in the design of nuclear power plant structures will implement Modified

Compression Field Theory based provisions in the near future. The ultimate

load was accurately predicted with a mean test to predicted ratio of 1.03 and a

coefficient of variation of 6.4 %. The shear strains at peak shear stress were

also accurately predicted with a mean test to predicted ratio of 1.04 and a

coefficient of variation of 13.5 %. The Modified Compression Field Theory

also well predicted the cracked shear stiffness of elements. These results show

the applicability of the Modified Compression Field Theory to shear design of

nuclear power plant wall. And the new tension stiffening equation for large

reinforced concrete elements is proposed based on the test results.

Keywords: Concrete Shear, High-Strength Materials, Nuclear Power

Plant, Modified Compression Field Theory, Tension Stiffening

Student Number: 2011-20982

iii

Contents

Chapter 1 Introduction........................................................... 1

1.1 General ................................................................................ 1

1.2 Modified Compression Field Theory .................................... 4

1.3 Objective and Scope............................................................. 9

Chapter 2 Experimental Program ........................................ 10

2.1 Test Variables ..................................................................... 10

2.2 Specimen Descriptions ....................................................... 16

2.3 Shell Element Tester .......................................................... 21

2.4 Instrumentation .................................................................. 24

Chapter 3 Experimental Results .......................................... 30

3.1 N420A Series ..................................................................... 32

3.2 N550B Series ..................................................................... 41

3.3 N550A Series ..................................................................... 50

3.4 H550B Series ..................................................................... 58

3.5 H550A Series ..................................................................... 66

Chapter 4 Observations and Analysis .................................. 74

4.1 Applicability of High-Strength Materials............................ 74

4.2 Applicability of Modified Compression Field Theory......... 79

4.3 Modification of Tension Stiffening Equation ...................... 88

iv

Chapter 5 Conclusion ........................................................ 124

References ......................................................................... 125

Abstract ............................................................................. 128

v

List of Tables

Table 2.1 Reinforcement ratio of APR 1400 NPP wall ............................. 11

Table 2.2 Test variables ........................................................................... 12

Table 2.3 Instrumentation for data acquisition per each specimen ............. 24

Table 3.1 Summary of experimental results.............................................. 31

Table 4.1 Comparison of N420A-PS and N550B-PS ................................ 76

Table 4.2 Comparison of N420A-PS, N550B-PS and H550B-PS ............. 78

Table 4.3 Comparsion of observed and MCFT predicted values ............... 84

vi

List of Figures

Figure 1.1 Reinforcing bars in construction field of nuclear power plant ...... 1

Figure 1.2 RC element and NPP containment structure ................................ 2

Figure 1.3 Compression softening effect of concrete ................................... 4

Figure 1.4 Tension stiffening effect of concrete ........................................... 5

Figure 1.5 Secant stiffness in the direction of principal tension of concrete .. 5

Figure 1.6 Secant stiffness in the direction of principal compression of

concrete ..................................................................................... 6

Figure 1.7 Secant stiffness in the direction of reinforcement ........................ 6

Figure 2.1 RC element and NPP containment structure .............................. 10

Figure 2.2 Previous in-plane shear tets of RC elements.............................. 14

Figure 2.3 Large RC element specimen ..................................................... 16

Figure 2.4 A Series reinforcement mesh .................................................... 18

Figure 2.5 B Series reinforcement mesh .................................................... 19

Figure 2.6 Shell Element Tester ................................................................. 21

Figure 2.7 The principle of Shell Element Tester ....................................... 22

Figure 2.8 LVDTs locations....................................................................... 25

Figure 2.9 LEDs locations ......................................................................... 27

Figure 2.10 Real pictures of LVDTs and LEDs ............................................ 28

Figure 2.11 ERSGs locations ...................................................................... 29

Figure 3.1 Experimental results of N420A Series ...................................... 40

Figure 3.2 Experimental results of N550B Series ...................................... 49

Figure 3.3 Experimental results of N550A Series ...................................... 57

Figure 3.4 Experimental results of H550B Series ...................................... 65

Figure 3.5 Experimental results of H550A Series ...................................... 73

Figure 4.1 Shear stress – shear strain of N420A and N550B Series ............ 75

Figure 4.2 Shear stress – maximum crack width of N420A and N550B

Series ....................................................................................... 77

vii

Figure 4.3 Shear stress – average crack width of N420A and N550B

Series ....................................................................................... 77

Figure 4.4 Shear stress – shear strain of N420A-PS, N550B-PS and H550B-

PS ............................................................................................ 78

Figure 4.5 Comparison of predicted and observed shear stress – shear

strain ........................................................................................ 83

Figure 4.7 Tension stiffening denominator versus bond parameter ............. 88

Figure 4.8 Tension stiffening denominator of individual Toronto Large

Elements experiments versus bond parameter ........................... 89

Figure 4.9 Comparison of predicted and observed principal tensile stress –

principal tensile strain with Bentz tension stiffening equation ... 90

Figure 4.10 Comparison of test, Bentz, and modified Bentz with A = 8.0 in

principal tensile behavior........................................................ 101

Figure 4.11 Comparison of test, Bentz, and Eq. (4.4) with best coefficient A

for each speciemen ................................................................. 112

Figure 4.12 Tension stiffening denominator versus bond parameter by new

equation ................................................................................. 113

Figure 4.13 Comparison of test, Bentz, and proposed equation in this

study ...................................................................................... 123

1

Chapter 1 Introduction

1.1 General

Design codes for nuclear power plant such as ASME Sec.III Div. 2, ACI 349,

and ACI 318 restrict the yield strength of reinforcing bars to 420 MPa. For

these reasons, excessive amount of reinforcing bars are used for construction

of nuclear power plant (NPP) as shown in Fig. 1.1. Due to using of excessive

amount of reinforcing bars, many problems are occurred such as poor

constructability, careful quality control of concrete, and uneconomical design.

To solve these problems, high-strength materials are required for nuclear

power plant structures.

Fig. 1.1 Reinforcing bars in construction field of nuclear power plant

But, due to high levels of conservatism and cautiousness for design and

construction of nuclear power plant structure, a lot of researches are required

to apply high-strength materials such as beam shear and torsion test, headed

2

bar test, wall test, column shear test, reinforcing bar development test, and

crack behavior test. This study focused on the shear behavior evaluation of

nuclear power plant containment wall that is applied with high-strength rebars

and high-strength concrete.

To investigate the shear behavior of nuclear power plant containment

structures, in-plane shear tests of reinforced concrete element from the shear

critical region of nuclear power plant wall as shown in Fig. 1.2 were

conducted. Structures like nuclear power plant containment can be considered

as an assemblage of reinforced concrete elements. And the shear behavior of a

reinforced concrete element is the basis for the prediction of shear behavior of

whole structures by finite element analysis.

Fig. 1.2 RC element and NPP containment structure

3

On the other hand, in recent years, design codes have implemented

compression field approaches for the design of reinforced concrete structures

subjected to shear. In particular, the Modified Compression Field Theory

(MCFT) has become the basis of the shear design such as CSA Standard,

AASHTO LRFD, fib Model Code, and Eurocode 2. It is expected that codes

used for the design of nuclear power plant structures, such as ASME, ACI 349,

and ACI 318 will adopt MCFT based shear design in the near future.

4

1.2 Modified Compression Field Theory

MCFT regards the cracked concrete as an orthotropic material by smeared

cracking. In smeared cracking model, cracked concrete is assumed to remain a

continuum. Cracks are assumed an average deformation spread out over an

area. And MCFT uses rotating cracking model. In rotating cracking model, the

crack direction rotates as loading conditions change. New cracking and crack

extensions result in a change in direction of total crack condition.

MCFT considered the compression softening effect of concrete when

tension stresses existed in the direction of principal tension as shown in Fig.

1.3.

Fig. 1.3 Compression softening effect of concrete

From a lot of test data, cracked concrete in compression has a reduced

strength and stiffness compared to a uniaxially compressed concrete. This

5

behavior is known as the compression softening effect.

MCFT also considered the tension stiffening effect of concrete. From a

lot of test data, concrete between cracks resist tensile stresses because of bond

effects with the reinforcement as shown in Fig. 1.4.

Fig. 1.4 Tension stiffening effect of concrete

Fig. 1.5 Secant stiffness in the direction of principal tension of concrete

6

Fig. 1.6 Secant stiffness in the direction of principal compression of concrete

Fig. 1.7 Secant stiffness in the direction of reinforcement

MCFT uses secant stiffness of each material in shear analysis of

reinforced concrete elements as shown in Fig. 1.5 to 1.7. Then, shear secant

stiffness of concrete is calculated like Eq. (1.1) because MCFT regards

concrete as an orthotropic material.

1 2

1 2

c cc

c c

E EG

E E

×=

+ (1.1)

From secant stiffness in the direction of principal tension, principal

7

compression, and shear secant stiffness of concrete, material secant stiffness

of concrete like Eq. (1.2) can be constructed.

1

2

0 0

[ ] 0 0

0 0

c

c c

c

E

D E

G

é ùê ú¢ = ê úê úë û

(1.2)

In the same manner, material secant stiffness of reinforcement can be

constructed like Eq. (1.3).

0 0

[ ] 0 0 0

0 0 0

si si

si

E

D

ré ùê ú¢ = ê úê úë û

(1.3)

By using of transpose matrix like Eq. (1.4) where y = the angle of the

direction of principal tension of concrete for transpose matrix for concrete

and y = the angle of the direction of each reinforcement from x axis for

transpose matrix for reinforcement, secant stiffness matrix of reinforced

concrete element like Eq. (1.5) can be constructed.

2 2

2 2

2 2

cos sin cos sin

[ ] sin cos cos sin

2cos sin 2cos sin cos sin

T

y y y y

y y y y

y y y y y y

é ùê ú

= -ê úê ú- -ë û

(1.4)

8

[ ] [ ] [ ] [ ]

[ ] [ ] [ ] [ ]

[ ] [ ] [ ]

Tc c c c

Tsi si si si

c si

D T D T

D T D T

D D D

¢=

¢=

= +å

(1.5)

From the secant stiffness matrix of reinforced concrete element, in-plane

strains of reinforced concrete element can be achieved under any in-plane

stresses like Eq. (1.6) by typically 20 to 30 iterations.

1{ } [ ]

x x

y y

xy xy

f

D f

v

e

e e

g

-

ì ü ì üï ï ï ï

= =í ý í ýï ï ï ïî þ î þ

(1.6)

9

1.3 Objective and Scope

The objective of this thesis is investigation of the influence of 550 MPa high

design yield strength rebars on the shear behavior of reinforced concrete

nuclear power plant wall elements subjected to in-plane shear and axial

stresses. And an investigation of the applicability of 70 MPa high design

compressive strength concrete with 550 MPa reinforcing bars in the nuclear

power plant design will be discussed.

Also, an investigation of the applicability of Modified Compression Field

Theory for the shear behavior of reinforced concrete elements with high-

strength materials will be discussed and modification of MCFT formulation

will be conducted if needed.

10

Chapter 2 Experimental Program

2.1 Test Variables

Fig. 2.1 RC element and NPP containment structure

When a seismic event occurred to NPP containment structure, huge shear

stress will be induced near the base of the NPP containment wall that is shear

critical region. In the event that a nuclear reactor overheats, large pressures

can build inside the containment structure inducing biaxial tension into the

RC element of NPP containment wall. And also the existence of biaxial

compression is common since large amounts of prestressing are often used in

both the vertical and horizontal direction. So the test specimens are

constructed by considering the RC elements of NPP low level wall which

11

shear and biaxial stresses are induced when a seismic event occurred as shown

in Fig 2.1.

RC element test specimens’ reinforcement ratio is decided by that of APR

1400 NPP containment low level wall which is shear critical region. APR

1400 is current NPP model of Shin-Kori NPP 3 and 4 units that are being

constructed in Korea. The vertical and horizontal reinforcement ratio of APR

1400 NPP wall is shown in Table 2.1.

Table 2.1 Reinforcement ratio of APR 1400 NPP wall

Location Reinforcements

Reinforcement ratio

(%)

Vertical Horizontal Vertical Horizontal

Dome Inside #14 @0.9˚ #14 @0.9˚

0.56 0.56 Outside #11 @0.9˚ #11 @0.9˚

Wall (Spring line)

Inside #14 & #18 @

0.9˚

#11 & #18 @

12" 1.84 1.93

Outside #14 & #18 @

0.9˚

#11 & #18 @

12"

Wall

(Mid. level)

Inside #14 @0.9˚ #18 @12" 0.66 1.39

Outside #14 @0.9˚ #18 @12"

Wall

(Low level)

Inside 2-#18 & #14

@0.9˚ #18 @12"

2.10 1.39

Outside #18 @0.9˚ #18 @12"

Vertically 2.10 % and horizontally 1.39 % reinforcement ratio of APR

1400 NPP low level wall are considered to RC element test specimens.

12

Table 2.2 Test variables

Specimens fn / v fc'

(MPa)

fyx

(MPa)

fyy

(MPa)

ρx

(%)

ρy

(%)

ρxfyx

(MPa)

ρyfyy

(MPa) Remarks

N420A-PS 0 35.2

448 477 2.09 1.35 9.36 6.44 Reference specimens N420A-SBT +0.4 35.2

N420A-SBC -0.4 35.2

N550B-PS 0 35.2

631 631 1.56 1.04 9.84 6.56 Increased fy

with ρfy maintained N550B-SBT +0.4 39.0

N550B-SBC -0.4 39.0

N550A-PS 0 39.0 631 653 2.09 1.35 13.19 8.82

Increased fy

with the same ρ N550A-SBT +0.4 39.0

H550B-PS 0 55.8 631 631 1.56 1.04 9.84 6.56

Increased fy and fc'

with ρfy maintained H550B-SBC -0.3 55.8

H550A-PS 0 55.8 631 653 2.09 1.35 13.19 8.82

Increased fy and fc'

with the same ρ H550A-SBC -0.2 55.8

13

Considering the APR 1400 NPP low level wall reinforcement ratio and

the loading conditions of RC element of NPP wall when seismic event occur,

twelve RC elements shown in Table. 2.2 were constructed. Considering size

effect of concrete, 1626 × 1626 mm square and 355 mm thick large RC

elements were constructed. 355 mm thick is almost one third scale of APR

1400 NPP wall thickness 1.2 m.

The major test variables for the in-plane shear tests of RC elements are

concrete compressive strength, rebar yield strength, reinforcement ratio, and

loading conditions. For the concrete compressive strength, 42 MPa and 70

MPa concrete design compressive strength were used. 42 MPa concrete

strength is currently being used in APR 1400 NPP structures, and 70 MPa

concrete strength was used to represent high-strength concrete. For the rebar

yield strength, 420 MPa and 550 MPa design yield strength were used. 420

MPa yield strength is currently being used in NPP structure and 550 MPa

yield strength is the goal of this study. Longitudinally (x) 2.09 % and

transversely (y) 1.35 % reinforcement ratio was chosen to represent the APR

1400 NPP’s vertically 2.10 % and horizontally 1.39 % reinforcement ratio

respectively. And longitudinally 1.56 % and transversely 1.04 %

reinforcement ratio that are reduced by 420 / 550 were used. 420 / 550 is the

ratio of rebar yield strength to represent the applying high-strength rebar and

reduced reinforcement ratio. For the loading conditions, pure shear, shear and

biaxial tension, and shear and biaxial compression are used.

Specimens labelled ‘N’ used 42 MPa normal design compressive

concrete strength, while specimens labelled ‘H’ used 70 MPa high design

14

compressive strength concrete. The ‘420’ label indicates that 420 MPa normal

design yield strength rebar, while the ‘550’ label indicates that 550 MPa high

design yield strength rebar. The ‘A’ label indicates that the specimens were

constructed with 2.09 % reinforcement ratio in the longitudinal direction and

1.35 % reinforcement ratio in the transverse direction to represent the

reinforcement ratio of APR 1400 NPP low level wall. The ‘B’ label indicates

that the specimens were constructed with 1.56 % reinforcement ratio in the

longitudinal direction and 1.04 % reinforcement ratio in the transverse

direction. The label ‘PS’ indicates pure shear, the label ‘SBT’ indicates shear

and biaxial tension, and the label ‘SBC’ indicates shear and biaxial

compression. The specimens were divided into five series: N420A, N550B,

N550A, H550B, and H550A.

Fig. 2.2 Previous in-plane shear tests of RC elements

15

Selected test variables are not duplicated to those variables tested

previously. 890 × 890 mm square and 70 mm thick small RC elements and

1626 × 1626 mm square and 216 to 310 mm thick large RC elements were

tested with certain concrete compressive strength and rebar yield strength as

shown in Fig. 2.2. Especially, large RC elements with high-strength rebar in-

plane shear tests were not performed so far.

16

2.2 Specimen Descriptions

To perform in-plane shear test of RC elements representing one third scale of

NPP low level wall, 1626 × 1626 × 355 mm large RC element specimens like

Fig. 2.3 were constructed.

(mm)

Fig. 2.3 Large RC element specimen

All specimens have same dimensions and two orthogonally welded

reinforcement meshes were embedded in the concrete for each specimen. And

twenty anchor blocks are required for each reinforcement mesh.

17

(a) A Series reinforcement mesh of bottom layer

(b) A Series reinforcement mesh of top layer

18

(c) A Series reinforcement drawing

Fig. 2.4 A Series reinforcement mesh

(a) B Series reinforcement mesh of bottom layer

19

(b) B Series reinforcement mesh of top layer

(c) B Series reinforcement drawing

Fig. 2.5 B Series reinforcement mesh

20

Twenty anchor blocks were placed in the edge of reinforcement mesh and

rebars were welded to the anchor blocks. For A Series specimens, 2 layers of

#5 rebars were reinforced to the longitudinal direction spaced at 54 mm, and 2

layers of #4 rebars were reinforced to the transverse direction spaced at 54

mm as shown in Fig. 2.4. For B Series specimens, 2 layers of #5 rebars were

reinforced to the both longitudinal direction spaced at 72 mm, and 2 layers of

#5 rebars were reinforced to the transverse direction spaced at 108 mm as

shown in Fig. 2.5.

21

2.3 Shell Element Tester

To apply uniform stress to the RC element specimens, the Shell Element

Tester at the University of Toronto, shown in Fig. 2.6, was used. The Shell

Element Tester is capable of loading 1626 × 1626 mm square and 200 to 400

mm thick large scale reinforced concrete elements.

Fig. 2.6 Shell Element Tester

22

( ) / 2h vv f f= + , ( ) / 2n h vf f f= -

Fig. 2.7 The principle of Shell Element Tester

The reinforcement in a specimen was oriented at 45 degrees to the

direction of applied principal stresses, so the elements are subjected to in-

plane shear and biaxial stresses to the direction of reinforcement (x, y

23

directions). By adjusting the magnitude of horizontal and vertical stresses, a

variety of normal stress to shear stress ratio can be achieved as shown in Fig.

2.7.

Furthermore, the tester can apply any combination of the eight shell

stress resultants that are three in-plane forces, three moments and two out-of-

plane shear forces. The tester consists of forty in-plane double acting

hydraulic jacks and twenty out-of-plane double acting hydraulic jacks. The in

–plane jacks are used to apply in-plane forces and are arranged in two layers

to apply bending moments. The out-of-plane jacks are used to apply torsional

moment and out-of-plane shear. A more detailed description is presented in

the theses of Khalifa (1986) and Kirschner (1986).

24

2.4 Instrumentation

To obtain strain information of RC element, 12 linearly variable differential

transformers (LVDTs), 35 light emitting diodes (LEDs), and 16 electrical

resistance strain gauges (ERSGs) were installed to each specimen as shown

in Table 2.3.

Table 2.3 Instrumentation for data acquisition per each specimen

Type Description Amount Interval Purpose

LVDT

Linearly variable

differential transformers

0.001 mm resolution

12 EA 10 Hz Observe the strains

of elements

LED

Light emitting diode

three dimensional

position tracking targets

35 EA 10 Hz

Observe the strains

of elements and

measure several

crack widths

ERSG Electrical resistance

strain gauges 16 EA 10 Hz

Observe the strains

of longitudinal and

transverse rebars

LVDTs were installed both on northface and southface of the specimens

as shown in Fig. 2.8. On each face of the specimen, two LVDTs were installed

in the horizontal direction, two in the vertical direction, one in the longitudinal

(x) direction, and one in the transverse (y) direction. ‘N’ indicates northface,

‘S’ indicates southface, ‘H’ indicates horizontal, ‘V’ indicates vertical, ‘D’

indicated diagonal, ‘T’ indicates top, ‘B’ indicates bottom, ‘E’ indicates east,

and ‘W’ indicates west.

25

(a) 6 LVDTs on northface

(b) 6 LVDTs on southface

Fig. 2.8 LVDTs locations

35 LEDs were installed only on the southface per each specimen. 25

26

LEDs were arranged in a grid of 5 × 5 spaced 300 mm apart. After cracking,

the remaining 10 LEDs were attached across cracks in 5 pairs as shown in Fig.

2.9. The LVDTs and the grid of 25 LEDs were used to obtain the average

strains of each specimen and the 5 pairs of LEDs were used to continuously

measure several crack widths. 16 ERSGs were attached to selected rebars of

each specimen. For each top and bottom reinforcement layers, 4 ERSGs were

attached to longitudinal rebars and 4 ERSGs were attached to transverse

rebars as shown in Fig. 2.11. After first cracking and at the key intervals, the

loading was halted and the loads were reduced by about 10 % so that cracks

could be safely marked and measured with crack sheets. During these load

stages photographs were also taken.

(a) A grid of 25 LEDs on southface

27

(b) 5 pairs of LEDs on southface beside several cracks

Fig. 2.9 LEDs locations

(a) 6 LVDTs on northface

28

(b) 6 LVDTs and 35 LEDs on southface

Fig. 2.10 Real pictures of LVDTs and LEDs

(a) ERSGs on A Series specimen’s top and bottom reinforcement layers

29

(b) ERSGs on B Series specimen’s top and bottom reinforcement layers

Fig. 2.11 ERSGs locations

30

Chapter 3 Experimental Results

All RC element specimens were tested by increasing the shear stress in

increments of 0.1 MPa. The biaxial stresses were increased in certain

proportion to the shear stress for each specimen. Load cells mounted at the

base of each hydraulic actuator were used to determine the applied stress

magnitude. LVDTs, LEDs, and ERSGs were continuously measured strains

during for each test at 10 Hz interval. Specimen’s northface were recorded by

digital camcorder and its photographs were continuously taken during the

tests. At four to six load stages, including right after first cracking, the loading

was halted and the loads were reduced by about 10 %. During load stages,

cracks were marked and measured, and detailed photographs of specimen

were taken. Although the tests were intended to be monotonic, some

specimens were unloaded and the out-of-plane alignment was adjusted to

minimize second order effects. Some specimens also were unloaded

intentionally after the peak load to capture the post peak behavior.

The specimens were divided into five series by concrete compressive

strength, rebar yield strength, and reinforcement ratio. The five series of tests

will be called as N420A, N550B, N550A, H550B, and H550A Series. For

each series of tests, two to three RC elements were tested, one in pure shear

(PS) and the remainder with different combinations of shear and biaxial

tension (SBT) or shear and biaxial compression (SBC). Table 3.1 summarizes

the experimental results of the twelve specimens.

31

Table 3.1 Summary of experimental results

Specimens fn / v vcr

(MPa)

vu

(MPa)

fnu

(MPa)

Strains at vu (×10-3) fc1

(MPa)

fc2

(MPa)

θuε

(Deg.)

θuσ

(Deg.) εx εy γxy ε1 ε2

N420A-PS 0 2.10 7.70 0 2.58 5.43 10.95 9.66 -1.65 -0.06 -15.7 37.7 39.7

N420A-SBT +0.4 1.60 5.87 2.35 3.28 13.90 17.34 18.75 -1.58 0.37 -11.6 29.3 38.0

N420A-SBC -0.4 3.07 9.56 -3.82 1.68 2.42 7.09 5.61 -1.51 -0.58 -20.1 42.0 44.2

N550B-PS 0 2.01 7.68 0 2.64 4.30 9.64 8.36 -1.42 -0.15 -15.1 40.1 41.9

N550B-SBT +0.4 1.29 5.97 2.39 3.61 15.21 21.65 21.69 -2.87 -0.10 -12.0 30.9 37.3

N550B-SBC -0.4 2.78 10.47 -4.19 2.29 3.04 8.26 6.81 -1.48 0.32 -21.4 42.4 43.9

N550A-PS 0 1.88 9.64 0 2.60 4.21 9.98 8.46 -1.65 0.25 -19.5 40.4 42.0

N550A-SBT +0.4 1.39 6.93 2.77 2.62 4.57 8.29 7.85 -0.66 -0.44 -14.1 38.4 40.6

H550B-PS 0 1.29 8.08 0 3.85 10.86 17.94 16.99 -2.28 -0.13 -16.4 34.4 39.3

H550B-SBC -0.3 1.39 10.48 -3.14 3.61 5.83 12.56 11.10 -1.66 -0.58 -22.0 40.0 40.6

H550A-PS 0 1.58 9.84 0 3.03 6.08 11.43 10.47 -1.36 0.04 -20.8 37.6 39.5

H550A-SBC -0.2 1.59 11.27 -2.25 3.09 4.26 10.16 8.79 -1.44 -0.74 -24.6 41.7 39.8

32

3.1 N420A Series

N420A Series are reference specimens which are representative of APR 1400

nuclear power plant’s low level wall element. 42 MPa design compressive

strength concrete and 420 MPa design yield strength rebar were used to

construct N420A Series specimens. The actual concrete strength is 35.2 MPa

and the actual rebar yield strength for longitudinal (x) direction is 448 MPa

and for transverse (y) direction is 477 MPa. #5 rebar of ASTM A615 is used

for longitudinal direction spaced at 54 mm, #4 rebar of ASTM A615 is used

for transverse direction spaced at 54 mm. The reinforcement ratio is almost

same with that of APR 1400 nuclear power plant’s low level wall which is

shear critical region.

Fig. 3.1 shows the shear stress – shear strain, principal concrete

compressive stress – principal compressive strain, principal concrete tensile

stress – principal tensile strain, shear stress – shear strain by LVDTs, shear

stress – shear strain by LEDs, shear stress – longitudinal strain, shear stress –

transverse strain, shear stress – maximum crack width, and shear stress –

average crack width graphs of N420A Series. The shear strain obtained by

LVDTs and LEDs are coincided each other. Especially prior to failure, the

LVDTs and LEDs measurements showed excellent agreement. The LEDs data

of N420A-SBC was lost.

33

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A Series

ρx = 2.09% fyx = 448 MPa

ρy = 1.35% fyy = 477 MPa

sx = 54 mm sy = 54 mm

fc' = 35.2 MPa ag = 20 mm

N420A-SBC: fn/v = -0.4

N420A-SBT: fn/v = +0.4

N420A-PS: fn/v = 0

(a) Shear stress – shear strain of N420A Series

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A Series

ρx = 2.09% fyx = 448 MPa

ρy = 1.35% fyy = 477 MPa

sx = 54 mm sy = 54 mm

fc' = 35.2 MPa ag = 20 mm

N420A-SBC: fn/v = -0.4

N420A-SBT: fn/v = +0.4

N420A-PS: fn/v = 0

(b) Shear stress – shear strain of N420A Series with unloading part deleted

34

(c) Principal concrete compressive stress – principal compressive strain of

N420A Series

(d) Principal concrete tensile stress – principal tensile strain of N420A-PS

35

(e) Principal concrete tensile stress – principal tensile strain of N420A-SBT

(f) Principal concrete tensile stress – principal tensile strain of N420A-SBC

36

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A-PS

Average

Northface

Southface

(g) Shear stress – shear strain by LVDTs of N420A-PS

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A-SBT

Average

Northface

Southface

(h) Shear stress – shear strain by LVDTs of N420A-SBT

37

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A-SBC

Average

Northface

Southface

(i) Shear stress – shear strain by LVDTs of N420A-SBC

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A-PS

LVDT

LED

(j) Shear stress – shear strain by LVDTs and LEDs of N420A-PS

38

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A-SBT

LVDT

LED

(k) Shear stress – shear strain by LVDTs and LEDs of N420A-SBT

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N420A-SBC

LVDT

LED

(l) Shear stress – shear strain by LVDTs and LEDs of N420A-SBC (The LEDs

data of N420A-SBC was lost)

39

(m) Shear stress – longitudinal strain of N420A Series

0 4 8 12 16

Transverse Strain, mm/m

0

2

4

6

8

10

12

N420A SeriesLVDT

ERSG Average

ERSG Top

ERSG Bottom

N420A-PS: fn/v = 0

N420A-SBT: fn/v = +0.4

N420A-SBC: fn/v = -0.4

(n) Shear stress – transverse strain of N420A Series

40

(o) Shear stress – maximum crack width of N420A Series

(p) Shear stress – average crack width of N420A Series

Fig. 3.1 Experimental results of N420A Series

41

3.2 N550B Series

N550B Series specimens used 550 MPa high design yield strength rebars and

reduced reinforcement ratio according to 420 / 550. So, N550B Series

specimens’ ρfy values are similar with those of N420A Series specimens.

N550B Series specimens are constructed to research the behavior when high-

strength rebar used and reinforcement ratio decreased according to inverse

ratio of increased rebar yield strength. 42 MPa design compressive strength

concrete and 550 MPa design yield strength rebar were used to construct

N550B Series specimens. The actual concrete strength is 39.0 MPa except

N550B-PS and the actual rebar yield strength for longitudinal (x) direction is

631 MPa and for transverse (y) direction is 631 MPa. The actual concrete

strength of N550B-PS is 35.2 MPa that is same with N420A Series. N420A

Series and N550B-PS used same concrete batch. N550B-SBT, N550B-SBC

and N550A Series used same concrete batch. #5 rebar of ASTM A615 is used

for longitudinal direction spaced at 72 mm, #5 rebar of ASTM A615 is used

for transverse direction spaced at 108 mm. The reinforcement ratio is

decreased by 420 / 550 ratio than N420A Series specimens.






average crack width graphs of N550B Series.

42

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B Series

ρx = 1.56 % fyx = 631 MPa

ρy = 1.04 % fyy = 631 MPa

sx = 72 mm sy = 108 mm

fc' = 39.0 MPa ag = 20 mm

N550B-PS: fc' = 35.2 MPa

N550B-PS: fn/v = 0

N550B-SBT: fn/v = +0.4

N550B-SBC: fn/v = -0.4

(a) Shear stress – shear strain of N550B Series

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B Series

ρx = 1.56 % fyx = 631 MPa

ρy = 1.04 % fyy = 631 MPa

sx = 72 mm sy = 108 mm

fc' = 39.0 MPa ag = 20 mm

N550B-PS: fc' = 35.2 MPa

N550B-PS: fn/v = 0

N550B-SBT: fn/v = +0.4

N550B-SBC: fn/v = -0.4

(b) Shear stress – shear strain of N550B Series with unloading part deleted

43


N550B Series

0 4 8 12 16

Principal Tensile Strain, ×10-3

-1

0

1

2

3N550B-PS

(d) Principal concrete tensile stress – principal tensile strain of N550B-PS

44

0 4 8 12 16


-1

0

1

2

3N550B-SBT

(e) Principal concrete tensile stress – principal tensile strain of N550B-SBT

(f) Principal concrete tensile stress – principal tensile strain of N550B-SBC

45

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B-PS

Average

Northface

Southface

(g) Shear stress – shear strain by LVDTs of N550B-PS

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B-SBT

Average

Northface

Southface

(h) Shear stress – shear strain by LVDTs of N550B-SBT

46

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B-SBC

Average

Northface

Southface

(i) Shear stress – shear strain by LVDTs of N550B-SBC

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B-PS

LVDT

LED

(j) Shear stress – shear strain by LVDTs and LEDs of N550B-PS

47

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B-SBT

LVDT

LED

(k) Shear stress – shear strain by LVDTs and LEDs of N550B-SBT

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550B-SBC

LVDT

LED

(l) Shear stress – shear strain by LVDTs and LEDs of N550B-SBC

48

(m) Shear stress – longitudinal strain of N550B Series

0 4 8 12 16


0

2

4

6

8

10

12

N550B SeriesLVDT

ERSG Average

ERSG Top

ERSG Bottom

N550B-PS: fn/v = 0

N550B-SBT: fn/v = +0.4

N550B-SBC: fn/v = -0.4

(n) Shear stress – transverse strain of N550B Series

49

(o) Shear stress – maximum crack width of N550B Series

(p) Shear stress – average crack width of N550B Series

Fig. 3.2 Experimental results of N550B Series

50

3.3 N550A Series

N550A Series specimens used 550 MPa high design yield strength rebars and

same reinforcement ratio with N420A Series. N550A Series specimens are

constructed to research the behavior when high-strength rebar used with same

reinforcement ratio of current APR 1400 nuclear power plant wall. 42 MPa

design compressive strength concrete and 550 MPa design yield strength rebar

were used to construct N550A Series specimens. The actual concrete strength

is 39.0 MPa and the actual rebar yield strength for longitudinal (x) direction is

631 MPa and for transverse (y) direction is 653 MPa. N550B-SBT, N550B-

SBC and N550A Series used same concrete batch. #5 rebar of ASTM A615 is

used for longitudinal direction spaced at 54 mm, #4 rebar of ASTM A615 is

used for transverse direction spaced at 54 mm. The reinforcement ratio is

same with N420A Series specimens.






average crack width graphs of N550A Series. N550A-SBT specimen suffered

from edge failure.

51

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550A Series

ρx = 2.09 % fyx = 631 MPa

ρy = 1.35 % fyy = 653 MPa

sx = 54 mm sy = 54 mm

fc' = 39.0 MPa ag = 20 mm

N550A-PS: fn/v = 0

N550A-SBT: fn/v = +0.4

edge failure

(a) Shear stress – shear strain of N550A Series

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550A Series

ρx = 2.09 % fyx = 631 MPa

ρy = 1.35 % fyy = 653 MPa

sx = 54 mm sy = 54 mm

fc' = 39.0 MPa ag = 20 mm

N550A-PS: fn/v = 0

N550A-SBT: fn/v = +0.4

edge failure

(b) Shear stress – shear strain of N550A Series with unloading part deleted

52


N550A-Series

(d) Principal concrete tensile stress – principal tensile strain of N550A-PS

53

(e) Principal concrete tensile stress – principal tensile strain of N550A-SBT

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550A-PS

Average

Northface

Southface

(f) Shear stress – shear strain by LVDTs of N550A-PS

54

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550A-SBT

Average

Northface

Southface

edge failure

(g) Shear stress – shear strain by LVDTs of N550A-SBT

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550A-PS

LVDT

LED

(h) Shear stress – shear strain by LVDTs and LEDs of N550A-PS

55

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12N550A-SBT

LVDT

LED

(i) Shear stress – shear strain by LVDTs and LEDs of N550A-SBT

(j) Shear stress – longitudinal strain of N550A Series

56

0 4 8 12 16


0

2

4

6

8

10

12

N550A SeriesLVDT

ERSG Average

ERSG Top

ERSG Bottom

N550A-PS: fn/v = 0

N550A-SBT: fn/v = +0.4

(k) Shear stress – transverse strain of N550A Series

(l) Shear stress – maximum crack width of N550A Series

57

(m) Shear stress – average crack width of N550A Series

Fig. 3.3 Experimental results of N550A Series

58

3.4 H550B Series

H550B Series specimens used 550 MPa high design yield strength rebars and

70 MPa high design compressive strength concrete with 420 / 550 decreased

reinforcement ratio to N420A Series. H550B Series specimens are constructed

to research the behavior when high-strength rebar and high-strength concrete

used with decreased reinforcement ratio. The actual concrete strength is 55.8

MPa and the actual rebar yield strength for longitudinal (x) direction is 631

MPa and for transverse (y) direction is 631 MPa. H550B and H550A Series

used same concrete batch. #5 rebar of ASTM A615 is used for longitudinal

direction spaced at 72 mm, #5 rebar of ASTM A615 is used for transverse

direction spaced at 108 mm. The reinforcement ratio is decreased by 420 / 550

to those of N420A Series specimens.






average crack width graphs of H550B Series.

59

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550B Series

ρx = 1.56 % fyx = 631 MPa

ρy = 1.04 % fyy = 631 MPa

sx = 72 mm sy = 108 mm

fc' = 55.8 MPa ag = 20 mm

H550B-PS: fn/v = 0

H550B-SBC: fn/v = -0.3

(a) Shear stress – shear strain of H550B Series

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550B Series

ρx = 1.56 % fyx = 631 MPa

ρy = 1.04 % fyy = 631 MPa

sx = 72 mm sy = 108 mm

fc' = 55.8 MPa ag = 20 mm

H550B-PS: fn/v = 0

H550B-SBC: fn/v = -0.3

(b) Shear stress – shear strain of H550B Series with unloading part deleted

60


H550B Series

(d) Principal concrete tensile stress – principal tensile strain of H550B-PS

61

(e) Principal concrete tensile stress – principal tensile strain of H550B-SBC

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550B-PS

Average

Northface

Southface

(f) Shear stress – shear strain by LVDTs of H550B-PS

62

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550B-SBC

Average

Northface

Southface

(g) Shear stress – shear strain by LVDTs of H550B-SBC

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550B-PS

LVDT

LED

(h) Shear stress – shear strain by LVDTs and LEDs of H550B-PS

63

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550B-SBC

LVDT

LED

(i) Shear stress – shear strain by LVDTs and LEDs of H550B-SBC

(j) Shear stress – longitudinal strain of H550B Series

64

0 4 8 12 16


0

2

4

6

8

10

12

H550B SeriesLVDT

ERSG Average

ERSG Top

ERSG Bottom

H550B-PS: fn/v = 0

H550B-SBC: fn/v = -0.4

(k) Shear stress – transverse strain of H550B Series

(l) Shear stress – maximum crack width of H550B Series

65

(m) Shear stress – average crack width of H550B Series

Fig. 3.4 Experimental results of H550B Series

66

3.5 H550A Series

H550A Series specimens used 550 MPa high design yield strength rebars and

70 MPa high design compressive strength concrete with same reinforcement

ratio of N420A Series. H550A Series specimens are constructed to research

the behavior when high-strength rebar and high-strength concrete used with

same reinforcement ratio with APR 1400 nuclear power plant wall. The actual

concrete strength is 55.8 MPa and the actual rebar yield strength for

longitudinal (x) direction is 631 MPa and for transverse (y) direction is 653

MPa. H550B and H550A Series used same concrete batch. #5 rebar of ASTM

A615 is used for longitudinal direction spaced at 54 mm, #4 rebar of ASTM

A615 is used for transverse direction spaced at 54 mm. The reinforcement

ratio is same with N420A Series specimens.






average crack width graphs of H550A Series. H550A-PS specimen suffered

from edge failure.

67

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550A Series

ρx = 2.09% fyx = 631 MPa

ρy = 1.35% fyy = 653 MPa

sx = 54 mm sy = 54 mm

fc' = 55.8 MPa ag = 20 mm

H550A-PS: fn/v = 0

H550A-SBC: fn/v = -0.2

edge failure

(a) Shear stress – shear strain of H550A Series

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550A Series

ρx = 2.09 % fyx = 631 MPa

ρy = 1.35 % fyy = 653 MPa

sx = 54 mm sy = 54 mm

fc' = 55.8 MPa ag = 20 mm

H550A-PS: fn/v = 0

H550A-SBC: fn/v = -0.2

edge failure

(b) Shear stress – shear strain of H550A Series with unloading part deleted

68


H550A Series

(d) Principal concrete tensile stress – principal tensile strain of H550A-PS

69

(e) Principal concrete tensile stress – principal tensile strain of H550A-SBC

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550A-PS

Average

Northface

Southface

edge failure

(f) Shear stress – shear strain by LVDTs of H550A-PS

70

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550A-SBC

Average

Northface

Southface

(g) Shear stress – shear strain by LVDTs of H550A-SBC

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550A-PS

LVDT

LED

(h) Shear stress – shear strain by LVDTs and LEDs of H550A-PS

71

0 20 40 60 80

Shear Strain, mm/m

0

2

4

6

8

10

12H550A-SBC

LVDT

LED

(i) Shear stress – shear strain by LVDTs and LEDs of H550A-SBC

(j) Shear stress – longitudinal strain of H550A Series

72

0 4 8 12 16


0

2

4

6

8

10

12

H550A SeriesLVDT

ERSG Average

ERSG Top

ERSG Bottom

H550A-PS: fn/v = 0

H550A-SBC: fn/v = -0.4

(k) Shear stress – transverse strain of H550A Series

(l) Shear stress – maximum crack width of H550A Series

73

(m) Shear stress – average crack width of H550A Series

Fig. 3.5 Experimental results of H550A Series

74

Chapter 4 Observations and Analysis

4.1 Applicability of High-Strength Materials

To investigate the applicability of high-strength materials to shear design of

nuclear power plant structure, the twelve specimens were divided into five

series. Among them, N420A Series, N550B Series and H550B Series were

compared in more detail in this chapter. N420A Series specimens are

representative of APR 1400 nuclear power plant low level wall element that

currently used in the field. N420A Series used 42 MPa design compressive

strength concrete, 420 MPa design yield strength rebar and APR 1400 nuclear

power plant low level wall reinforcement ratio. N550B Series used 42 MPa

design compressive strength concrete, 550 MPa high design yield strength

rebar and decreased reinforcement ratio according to the ratio of 420 over 550.

H550B Series used same properties with N550B Series except concrete

strength. H550B Series used 70 MPa high design compressive strength

concrete.

Fig. 4.1 shows the comparison of N420A Series and N550B Series shear

stress – shear strain relationships. The N550B Series specimens shows almost

same shear behavior with N420A Series except specimens with biaxial

compression stresses as can be seen in Fig. 4.1. Once the peak load was

reached, N420A-SBC and N550B-SBC specimens failed explosively. N550B-

SBC specimen failed with no yielding of reinforcement and N420A-SBC

specimen failed as soon as the longitudinal rebar yielded.

75

Fig. 4.1 Shear stress – shear strain of N420A and N550B Series

N550B Series showed somewhat low shear stiffness than N420A Series

because the steel stiffness was decreased with decreased reinforcement ratio.

The reinforcement ratio of N550B Series was decreased by 420 over 550 to

make the almost same ρfy values with N420A Series. But the decreased

reinforcement ratio ρ made decreased steel stiffness ρEs, and the decreased

steel stiffness made the decreased shear stiffness of N550B Series. Especially,

N420A-PS and N550B-PS specimens used same concrete. Even the ρfy

value of N550B-PS are larger than N420A-PS as you can see in Table 4.1,

N550B-PS shows low shear stiffness and shear strength than N420A-PS.

76

Table 4.1 Comparison of N420A-PS and N550B-PS

N420A-PS N550B-PS

fc' (MPa) 35.2

vu (MPa) 7.70 7.68

fyx (MPa) 448 631

fyy (MPa) 477 631

ρx (%) 2.09 1.56

ρy (%) 1.35 1.04

ρxfyx (MPa) 9.36 9.84

ρyfyy (MPa) 6.44 6.56

ρxEs (MPa) 4180 3120

ρyEs (MPa) 2700 2080

Because of decreased ρEs values, N550B Series showed larger shear

strain than N420A Series as can be seen in Fig. 4.1. And also N550B Series

showed larger maximum crack width and average crack width as can be seen

in Fig. 4.2 and Fig. 4.3. These large shear strains and crack widths are

softening the concrete. The shear strength is decreased by large shear strains

and crack widths. This is called by strain effect. The effect is small in service

load level, but the additional research will be required.

77

Fig. 4.2 Shear stress – maximum crack width of N420A and N550B Series

Fig. 4.3 Shear stress – average crack width of N420A and N550B Series

78

Fig. 4.4 Shear stress – shear strain of N420A-PS, N550B-PS and H550B-PS

H550B-PS specimen used 70 MPa high design compressive strength

concrete. H550B-PS behaved in a ductile manner with the shear strain

exceeding 0.048 before the load carrying capacity was significantly reduced

as can be seen in Fig. 4.4. H550B-PS specimen failed after yielding of both

rebars sufficiently as can be seen in Table 4.2.

Table 4.2 Comparison of N420A-PS, N550B-PS and H550B-PS

Specimens fc' (MPa) vu (MPa) γxy (10-3) εx / εsyx (%) εy / εsyy (%)

N420A-PS 35.2 7.70 10.95 115.2 227.7

N550B-PS 35.2 7.68 9.64 83.7 136.3

H550B-PS 55.8 8.08 17.94 122.0 344.2

79

4.2 Applicability of Modified Compression Field Theory

The Modified Compression Field Theory (MCFT) uses equilibrium,

compatibility and constitutive relations to predict the stress – strain response

of reinforced concrete members subjected to shear as discussed in chapter 1.2.

For the analysis of shear behavior of the reinforced concrete elements by

MCFT in this study, CAN CSA A23.3 M84 compression softening equation

and Bentz 1999 tension stiffening equation were used. And for the concrete

stress – strain curve, the Popovich (HSC) formulation was used to analyze the

shear behavior of reinforced concrete elements.

1

11

0.8 170

p c

p c

c

f fb

e e

be

¢=

¢=

= £-

(4.1)

1

11 3.6t

c

c

b

ff

M

AM

d

e

p

=+

=å

(4.2)

Eq. (4.1) is CAN CSA A23.3 M84 compression softening model. This

model is strength only softened version. Eq. (4.2) is Bentz 1999 tension

stiffening model. M is bond parameter to indicate the bond characteristics of

different arrays of reinforcement is to divide the area of concrete in tension by

80

the perimeter of all the reinforcing bars bonded to the area. Ac is are of

concrete reinforced by the bar and db is the diameter of reinforcing bar. In a

case that the different reinforcement is used by directions, the selected value

of the M parameter will be the lowest value for each of the orthogonal

reinforcement directions.

Fig. 4.5 shows the observed shear stress – shear strain response for each

test series along with the corresponding MCFT predictions. The mean MCFT

predicted to test ratio for the peak shear stress was 1.03 with a coefficient of

variation of only 6.4 %. The strains at peak stress were also well predicted

with a mean predicted to test ratio of 1.04 and a coefficient of variation of

13.5 %. The concrete principal compressive stresses at peak stress were also

well predicted with a mean predicted to test ratio of 0.98 and a coefficient of

variation of 5.5 %. Table 4.3 provides a summary of the observed and

predicted values of twelve reinforced concrete elements.

81

(a) N420A Series

(b) N550B Series

82

(c) N550A Series

(d) H550B Series

83

(e) H550A Series

Fig. 4.5 Comparison of predicted and observed shear stress – shear strain

84

Table 4.3 Comparison of observed and MCFT predicted values

Specimens fn / v

Observed MCFT Prediction Predicted / Observed

vu

(MPa)

Values at vu vu

(MPa)

Values at vu

vu

Values at vu

fc1

(MPa)

fc2

(MPa)

γxy

(10-3)

fc1

(MPa)

fc2

(MPa)

γxy

(10-3) fc2 γxy

N420A-PS 0 7.70 -0.06 15.74 10.95 7.80 0 15.80 11.66 1.01 1.00 1.02

N420A-SBT +0.4 5.87 0.37 11.61 17.34 5.55 0 11.40 17.03 0.95 0.98 0.94

N420A-SBC -0.4 9.56 -0.58 21.01 7.09 10.52 0.68 20.39 7.13 1.10 0.97 1.01

N550B-PS 0 7.68 0.32 15.87 9.64 7.95 0.51 15.49 10.05 1.04 0.98 1.04

N550B-SBT +0.4 5.97 0.25 12.00 21.65 5.71 0 11.85 18.80 0.96 0.99 0.81

N550B-SBC -0.4 10.47 -0.44 22.75 8.26 10.08 0.49 19.71 8.97 0.96 0.87 1.09

N550A-PS 0 9.64 -0.15 20.33 9.98 9.37 0.54 18.26 9.88 0.97 0.90 0.99

N550A-SBT +0.4 6.93 -0.10 14.22 8.29 7.63 0.52 15.02 11.94 1.10 1.06 1.44

H550B-PS 0 8.08 0.04 16.44 17.94 8.05 0 16.41 18.40 1.00 1.00 0.96

H550B-SBC -0.3 10.48 -0.74 21.95 12.56 11.43 0.28 22.71 11.80 1.09 1.03 0.94

H550A-PS 0 9.84 -0.13 20.93 11.43 10.80 0.53 21.47 11.01 1.10 1.03 0.96

H550A-SBC -0.2 11.27 -0.58 24.73 10.16 12.60 0.42 24.84 10.66 1.12 1.00 1.05

Average 1.03 0.98 1.04

Coefficient of variation, % 6.4 5.5 13.5

85

As can be seen in Table 4.3, most specimens’ shear behavior is quite well

predicted by MCFT. Especially, the shear strength and the concrete principal

compressive stresses at peak stress of N420A-PS, N420A-SBT, N550B-PS,

N550B-SBT, and H550B-PS were predicted by only less than 5 % error. The

MCFT is also able to predict the full load deformation response with good

accuracy. In particular, the cracked elastic stiffness was well predicted for all

elements. But the shear strength and the concrete principal compressive

stresses at peak stress of N420A-SBC, N550B-SBC, N550A-PS, N550A-SBT,

H550B-SBC, H550A-PS and H550A-SBC were predicted by over then 5 %

error. The concrete principal tensile stresses at peak stress of these specimens

show somewhat big difference over than 0.62 MPa. Fig. 4.6 shows the

comparison of concrete principal compressive stresses of all tests.

(a) N420A Series

86

(b) N550B Series

(c) N550A Series

87

(d) H550B Series

(e) H550A Series

Fig. 4.6 Comparison of predicted and observed principal compressive stress –

principal compressive strain

88

4.3 Modification of Tension Stiffening Equation

According to Bentz (2005) paper, the coefficient of factor for ε1 strain in

denominator in tension stiffening equations was determined from Fig. 4.7.

Fig. 4.7 Tension stiffening denominator versus bond parameter

By the way, the solid square marker was obtained from only three

specimens of Toronto Large Elements SE1, SE6, and SE12 as can be seen by

Fig. 4.8. And Fig. 4.9 shows comparisons between the test data and Bentz

tension stiffening equation as shown in Eq. (4.2).

89

Fig. 4.8 Tension stiffening denominator of individual Toronto Large Elements

experiments versus bond parameter

(a) SE1

90

(b) SE6

(c) SE12

Fig. 4.9 Comparison of predicted and observed principal tensile stress –

principal tensile strain with Bentz tension stiffening equation

91

From Fig. 4.9, the difference between the test and the MCFT prediction

by the Bentz tension stiffening equation can be regarded as acceptable. In the

same manner in the Bentz (2005) paper, the coefficients for large reinforced

concrete elements that have been reported so far including the twelve

specimens in this study were obtained.

As seen in Fig. 4.10, overall comparison between the test results and the

prediction by Bentz tension stiffening equation shows that Bentz equation

gives consistently overestimates the tension stiffening effect after cracking. As

the first trial, therefore, A = 8.0 which is almost twice greater than Bentz

tension stiffening equation’s coefficient 3.6 is applied to Eq. (4.3)

1

11t

c

ff

A M e=

+ × × (4.3)

Fig. 4.10 also includes the estimations by applying 8.0 to A in the Eq.

(4.3). From the comparison of MCFT prediction by Bentz tension stiffening

equation and an example prediction with A = 8.0 in Eq. (4.3), the modification

of A is required.

92

(a) N420A-PS

(b) N420A-SBT

93

(c) N420A-SBC

0 4 8 12 16


-1

0

1

2

3N550B-PS

Test

Bentz

A = 8.0

(d) N550B-PS

94

0 4 8 12 16


-1

0

1

2

3N550B-SBT

Test

Bentz

A = 8.0

(e) N550B-SBT

(f) N550B-SBC

95

(g) N550A-PS

(h) N550A-SBT

96

(i) H550B-PS

(j) H550B-SBC

97

(k) H550A-PS

(l) H550A-SBC

98

(m) SE1

(n) SE5

99

(o) SE6

(p) SE11

100

(q) SE12

(r) SE13

101

(s) SE13

(t) SE13

Fig. 4.10 Comparison of test, Bentz, and modified Bentz with A = 8.0 in

principal tensile behavior

102

By the way, only the modification of A could not be satisfactory. Right

after cracking the Bentz tension stiffening equation underestimates and after

some point, the Bentz equation overestimates the test results. The difference

between the test and estimation is not a matter of coefficient value. In other

words, it is matter of form of equation.

Through several trials, removing of square root in the denominator like

Eq. (4.4) gives better correlation with the large elements test results.

1

11t

c

ff

A M e=

+ × × (4.4)

Fig. 4.11 shows comparison of Bentz tension stiffening equation and Eq.

(4.4) with the best coefficient A which were found for each specimen. As

shown in Fig. 4.11, removing of square root could simulates better the

descending branch immediately after cracking as well as overall response.

103

(a) N420A-PS

(b) N420A-SBT

104

(c) N420A-SBC

0 4 8 12 16


-1

0

1

2

3N550B-PS

Test

Bentz

A = 3.6

(d) N550B-PS

105

0 4 8 12 16


-1

0

1

2

3N550B-SBT

Test

Bentz

A = 3.7

(e) N550B-SBT

(f) N550B-SBC

106

(g) N550A-PS

(h) N550A-SBT

107

(i) H550B-PS

(j) H550B-SBC

108

(k) H550A-PS

(l) H550A-SBC

109

(m) SE1

(n) SE5

110

(o) SE6

(p) SE11

111

(q) SE12

(r) SE13

112

(s) SE14

(t) EZ9

Fig. 4.11 Comparison of test, Bentz, and Eq. (4.4) with best coefficient A for

each specimen

113

In the same manner with Bentz (2005), all best coefficient of A for each

specimen was averaged and A = 4.5 was obtained as shown in Fig. 4.12.

Fig. 4.12 Tension stiffening denominator versus bond parameter by new

equation

Consequently, a new equation for tension stiffening equation after

cracking is proposed like Eq. (4.5).

1

11 4.5t

c

ff

Me=

+ (4.5)

Following Fig. 4.13 are comparison of the test results, Bentz equation,

and the Eq. (4.5).

114

(a) N420A-PS

(b) N420A-SBT

115

(c) N420A-SBC

0 4 8 12 16


-1

0

1

2

3N550B-PS

Test

Bentz

This study

(d) N550B-PS

116

0 4 8 12 16


-1

0

1

2

3N550B-SBT

Test

Bentz

This study

(e) N550B-SBT

(f) N550B-SBC

117

(g) N550A-PS

(h) N550A-SBT

118

(i) H550B-PS

(j) H550B-SBC

119

(k) H550A-PS

(l) H550A-SBC

120

(m) SE1

(n) SE5

121

(o) SE6

(p) SE11

122

(q) SE12

(r) SE13

123

(s) SE14

(t) EZ9

Fig. 4.13 Comparison of test, Bentz, and proposed equation in this study

124

Chapter 5 Conclusion

In-plane shear tests of twelve large reinforced concrete elements representing

nuclear power plant low level wall element were performed. Shear behavior

of reinforced concrete elements with high-strength materials was compared

with reinforced concrete elements of APR 1400 nuclear power plant wall’s

shear critical region. N420A Series representing APR 1400 nuclear power

plant wall and N550B Series reinforced with high-strength reinforcing bars

showed almost same shear behavior. H550B Series that applied with high-

strength reinforcing bars and high-strength concrete showed quite ductile

shear response. These test results showed the applicability of high-strength

materials to the shear design of nuclear power plant structures.

Modified Compression Field Theory accurately predicted the ultimate

shear strength by the average of prediction to test ratio 1.03 and coefficient of

variation 6.4 %. Also MCFT accurately predicted the shear strain and

principal compressive concrete stress at ultimate shear strength by the average

of prediction to test ratio 1.04, coefficient of variation 13.5 % and the average

of prediction to test ratio 0.98, coefficient of variation 5.5 % respectively. But

the Bentz tension stiffening equation overestimates the test results of large

reinforced concrete elements. The proposed tension stiffening equation for

large reinforced concrete elements in this thesis made predictions better the

principal tensile concrete stress after cracking of large reinforced concrete

elements.

125

References

Bae, G-M, Proestos, G. T., Lee, S-C, Bentz, E. C., Collins, M. P., and Cho, J-Y

(2013), “In-Plane Shear Behavior of Nuclear Power Plant Wall Elements with

High-Strength Reinforcing Bars,” SMiRT-22 Transactions.

Bentz, E. C. (2005), “Explaining the Riddle of Tension Stiffening Models for

Shear Panel Experiments,” Journal of Structural Engineering, V. 131, No. 9,

pp. 1422-1425.

Bentz, E. C., Vecchio, F. J., and Collins, M. P. (2006), “The Simplified MCFT

for Calculating the Shear Strength of Reinforced Concrete Elements,” ACI

Structural Journal, V. 103, No. 4, pp. 614-624.

Biedermann, J. D. (1987), “The Design of Reinforced Concrete Shell

Elements an Analytical and Experimental Study,” M.A.Sc thesis, Department

of Civil Engineering, University of Toronto, Canada.

Collins, M. P., and Mitchell, D. (1991), Prestressed Concrete Structures,

Prentice Hall, 766 pp.

Hsu, T. T. C., and Mau, S. T. (1992), Concrete Shear in Earthquake, Elsevier

Applied Science, 518 pp.

126

Khalifa, J. (1986), “Limit Analysis and Design of Reinforced Concrete Shell

Elements,” PhD thesis, Department of Civil Engineering, University of

Toronto, Canada.

Kirschner, U. H. K. (1986), “Investigating the Behavior of Reinforced

Concrete Shell Elements,” PhD thesis, Department of Civil Engineering,

University of Toronto, Canada.

Kuchma, D. A. (1996), “The Influence of T-headed Bars on the Strength and

Ductility of Reinforced Concrete Wall Elements,” PhD thesis, Department of

Civil Engineering, University of Toronto, Canada.

Liping, X., Bentz, E. C., and Collins, M. P. (2011), “Influence of Axial Stress

on Shear Response of Reinforced Concrete Elements,” ACI Structural Journal,

V. 108, No. 6, pp. 745-754.

Porasz, A. (1989), “An Investigation of the Stress-Strain Characteristics of

High Strength Concrete in Shear,” M.A.Sc thesis, Department of Civil

Engineering, University of Toronto, Canada.

Stevens, N. J., Uzumeri, S. M., and Collins, M. P. (1991), “Constitutive Model

for Reinforced Concrete Finite Element Analysis,” ACI Structural Journal, V.

88, No. 1, pp. 49-59.

127

Vecchio, F. J., and Collins, M. P. (1986), “The Modified Compression-Field

Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal,

V. 83, No. 2, pp. 219-231.

Vecchio, F. J., and Selby, R. G. (1991), “Toward Compression-Field Analysis

of Reinforced Concrete Solids,” Journal of Structural Engineering, V. 117,

No. 6, pp. 1740-1758.

Vecchio, F. J., and Collins, M. P. (1993), “Compression Response of Cracked

Reinforced Concrete,” Journal of Structural Engineering, V. 119, No. 12, pp.

3590-3610.

Vecchio, F. J., Collins, M. P., and Aspiotis, J. (1994), “High-Strength Concrete

Elements Subjected to Shear,” ACI Structural Journal, V. 91, No. 4, pp. 423-

433.

128

초 록

본 논문에서는 전단 및 이축 응력을 받는 12개 철근콘크리트

요소의 실험결과가 제시된다. 요소들은 실제 원전구조물 벽체

요소의 1/3 스케일로 제작되었고, 지진하중, 원전 사고시 내압의

증가를 고려하여 하중조건이 결정되었으며, 토론토대학교의 Shell

Element Tester를 이용하여 철근콘크리트 요소가 파괴될 때까지

가력되었다. 기준실험체에는 현 APR 1400 원전구조물에서

사용되는 콘크리트 압축강도, 철근 항복강도 및 철근비가

사용되었고, 고강도 콘크리트, 고강도 철근 및 감소된 철근비가

사용된 철근콘크리트 요소와 기준실험체의 전단 거동이 비교되었다.

한편, 최근 철근콘크리트 구조물의 전단 설계에는 압축장이론이

도입되고 있다. 특히 수정압축장이론은 CSA Standards, AASHTO

LRFD, fib Model code, Eurocode 2 전단 설계에 도입되었다. 향후

ASME, ACI 318, ACI 349와 같은 원전구조물 설계 관련

설계기준에도 수정압축장이론이 도입될 것으로 예측된다.

수정압축장이론은 예측값 대비 실험값을 평균 1.03, 변동계수

6.4 %로 매우 정확히 예측하였다. 최대 전단 응력에서의 전단

변형률 또한 평균 1.04, 변동계수 13.5 %로 정확히 예측되었다.

수정압축장이론은 균열 이후 요소의 전단 강성도 잘 예측하여

원전구조물의 전단 설계에 적용가능성을 보여주었다. 그리고 대형

철근콘크리트 요소에 대한 새로운 인장 경화 모델이 실험결과를

바탕으로 제안되었다.

129

주요어: 콘크리트 전단, 고강도 재료, 원전구조물, 수정압축장이론,

인장 경화

학 번: 2011-20982

Chapter 1 Introduction 1.1 General 1.2 Modified Compression Field Theory 1.3 Objective and Scope

Chapter 2 Experimental Program 2.1 Test Variables 2.2 Specimen Descriptions 2.3 Shell Element Tester 2.4 Instrumentation

Chapter 3 Experimental Results 3.1 N420A Series 3.2 N550B Series 3.3 N550A Series 3.4 H550B Series 3.5 H550A Series

Chapter 4 Observations and Analysis 4.1 Applicability of High-Strength Materials 4.2 Applicability of Modified Compression Field Theory 4.3 Modification of Tension Stiffening Equation

Chapter 5 Conclusion References Abstract

11Chapter 1 Introduction 1 1.1 General 1 1.2 Modified Compression Field Theory 4 1.3 Objective and Scope 9Chapter 2 Experimental Program 10 2.1 Test Variables 10 2.2 Specimen Descriptions 16 2.3 Shell Element Tester 21 2.4 Instrumentation 24Chapter 3 Experimental Results 30 3.1 N420A Series 32 3.2 N550B Series 41 3.3 N550A Series 50 3.4 H550B Series 58 3.5 H550A Series 66Chapter 4 Observations and Analysis 74 4.1 Applicability of High-Strength Materials 74 4.2 Applicability of Modified Compression Field Theory 79 4.3 Modification of Tension Stiffening Equation 88Chapter 5 Conclusion 124References 125Abstract 128

in-plane shear behavior of reinforced concrete elements with...

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