louis research report -rendu

8/3/2019 Louis Research Report -Rendu

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Louis de Fontenay Promotion 2012

EVALUATION OF MSJC PROVISIONS

FOR IN-PLANE SHEAR IN

MASONRY WALLS

Department of Civil and Environmental Engineering

WASHINGTON STATE UNIVERSITY- Pullman, 99163 WA

United States of America

Engineering internship from August 16th to December 16th, 2010


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Evaluation of MSJC (Masonry Standards Joint Committee)

provisions for in-plane shear in Masonry walls

Washington State University

Department of Civil & Environmental Engineering

Advisor and Department Chair: Dr. David McLean

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Acknowledgments

I would like to express my gratitude to my advisor Dr. David McLean for all

his patience, his advice and his backing throughout my internship. He has spent

countless hours to help me. I really enjoyed my internship working with him.

Thank you also to my officemate Jake Sherman. I could not have been

successful without his help, especially in the beginning of my internship.

Finally, I would like to thank Madam Bouzon from EPF for the efforts she

made to help the French interns go to WSU for a semester. It has been an

amazing experience.

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Abstract

Title of the internship

Study different hypothesis to evaluate the accuracy of MSJC (Masonry

Standards Joint Committee) provisions for in-plane shear in masonry walls.

Abstract in English

In this paper, a statistical analysis of MSJC provisions subjected to two new

different hypothesis were performed in order to improve the accuracy of the

equation. These shear stresses occur mainly in earthquakes (could be also due to

wind or any natural force) and predicting the response of walls under these

forces are particularly important. The statistical analysis is based on different

parameters: average, standard variation, coefficient of variation,

minimum/maximum value and 5th percentile. It was performed on a ratio V test/ Vn

which measures how close the reality (tests) and the predictions are. My work

during this internship was to do a literature review, perform an analysis on the

data and do statistics. Finally, I had to present the result of this research and

write a paper, future basis for incoming researches.

Titre du stage

Etude de diffrentes hypothses pour valuer la prcision des

recommandations du MSJC (comit de normalisation des standards de

maonnerie) concernant le cisaillement dans les murs de maonnerie.

Rsum en franais

Ce document expose lanalyse statistique des recommandations du MSJC,

mene avec deux nouvelles hypothses dans le but damliorer la prcision de

lquation prvoyant le comportement de murs de maonnerie sous des forces

de cisaillement. Ces forces se produisent principalement au cours de sismes.

Lanalyse statistique est fonde sur diffrents paramtres : moyenne, cart-type,

coefficient de variation, minimum, maximum et 5me centile. Elle a t effectue

sur le rapportVtest/ Vn qui mesure la proximit entre la ralit (tests) et les

recommandations. Mon travail durant ce stage a consist tudier la

documentation actuelle relative ce sujet, effectuer une analyse des donnes

et faire lanalyse statistique. A lissue de cette analyse, il ma t demand de

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prsenter les rsultats de mes recherches, comme pouvant constituer la base

future de nouvelles recherches plus labores en la matire.

TABLE OF CONTENTS

Acknowledgments .................................................................................................. 3

Abstract .................................................................................................................. 4

TABLE OF CONTENTS .............................................................................................. 5

CHAPTER 1 ............................................................................................................. 9

INTRODUCTION ....................................................................................................... 9

1.1 Background...................................................................................................9

1.2 Scope and Objectives.................................................................................10

1.3 Organization of this report..........................................................................11

CHAPTER 2 ........................................................................................................... 12

PRESENTATION OF WASHINGTON STATE UNIVERSITY ..........................................12

2.1 General presentation and History...............................................................12

2.2 Quick facts..................................................................................................13

2.3 Financial situation.......................................................................................14

2.4 Organization chart.......................................................................................14

CHAPTER 3 ........................................................................................................... 15

BACKGROUND AND PREVIOUS RESEARCH ........................................................... 15

3.1 MSJC Building Code.....................................................................................15

3.1.1 MSJC Strength Design (SD) .................................................................... 15

3.1.2 MSJC 2011 ............................................................................................. 19

3.1.3 Horizontal Reinforcement Ratio ............................................................ 19

3.1.4 MSJC Notation ........................................................................................ 21

3.2 Other Codes................................................................................................22

3.2.1 New Zealand Standards 4230:2004 ...................................................... 22

3.2.2 New Zealand Standard Notation ........................................................... 23

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3.2.3 Canadian Standards Association S304.1-04 ..........................................25

3.2.4 Canadian Standards Notation ................................................................ 26

3.3 Data tests....................................................................................................26

3.3.1 Shing et al............................................................................................. 27

3.3.2 Matsumura ............................................................................................ 27

3.3.3 Sveinsson et al. ..................................................................................... 28

3.3.4 Voon and Ingham .................................................................................. 29

CHAPTER 4 ........................................................................................................... 30

ANALYSIS OF WALL DATA ..................................................................................... 304.1 Interpretation of Shear Equations...............................................................30

4.2 First Hypothesis...........................................................................................30

4.2.1 Results .................................................................................................. 31

4.2.2 Conclusion ............................................................................................. 33

4.3 Second Hypothesis......................................................................................33

4.3.1 Shing et al.s New numbers of bars ..................................................... 34

4.3.2 Matsumuras New numbers of bars ..................................................35

4.3.3 Sveinssons New numbers of bars ...................................................... 36

4.3.4 Voons New numbers of bars ............................................................ 39

....................................................................................................................... 39

4.3.5 Results .................................................................................................. 40

4.3.6 Conclusion ............................................................................................. 43

4.4 Other code limitations ................................................................................43

4.4.1 Results .................................................................................................. 44

4.4.2 Conclusion ............................................................................................. 44

CHAPTER 5 ........................................................................................................... 45

CONCLUSION ........................................................................................................ 45

REFERENCES ....................................................................................................... 46

APPENDIX A .......................................................................................................... 48

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APPENDIX B .......................................................................................................... 50

RESUME DU STAGE EN FRANCAIS ......................................................................... 58

Contexte ...........................................................................................................58

Introduction.......................................................................................................58

Premire hypothse..........................................................................................59

Seconde hypothse...........................................................................................61

Dautres limitations...........................................................................................63

Conclusion.........................................................................................................64

List of tables

Table 3.1: Provisions............................................................................................22

Table 3.2: Type Dependent Nominal Strengths (fm in MPa; from NZS, 2004).....23

Table 4.1: Statistics with Switched term in the equation......................................32

Table 4.2 : Statitics with a new number of effective bars.....................................41

Table 4.3 : Statistics with CSA and NZS................................................................44

Table A-1: Original Wall Data................................................................................49

Table B-2: MSJC Provisions (0.6 factor).................................................................54



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CHAPTER 1

INTRODUCTION

1.1 Background

Design provisions for shear in masonry structures are different for every

country in that each one has its own code of requirements. In this report, we will

look specifically at a few of them, including the Canadian code (CSA S304.1-04),

the New Zealand code (NZS 4230:2004) and the United States Code (MSJC

2008). The US design standard is the Building Code Requirements and

Specifications for Masonry Structures, and it includes provisions for allowable

stress design (ASD) and for strength design (SD). There are fundamental

differences resulting in different designs with the two approaches, but

increasingly the SD method is gaining wider acceptance.

The current approach for shear design is largely based on tests with

separate treatment for different types of shear. Most of these experimental

studies have been conducted over the past 25 years. The shear stresses are

particularly present in earthquakes stresses; if not appropriately considered, their

effects on the masonry can be devastating.

In order to evaluate the accuracy of different code provisions and

equations for predicting the shear strength of masonry shear walls, Davis (2008)

performed statistical analyses isolating the effects of many wall parameters on

shear strength, including level of axial compressive stress, amount of vertical

reinforcement, masonry compressive strength, amount of shear reinforcement,

wall aspect ratio and displacement ductility. Davis gathered experimental data

from four previous studies, consisting of tests of masonry walls by Shing et al

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(1990), Sveinsson et al (1985), Voon and Ingham (2006) and Voon (2007). Fifty

six walls were tested, all of which were fully grouted, subjected to in-plane shear

loading, and failed in shear. The data set included results from clay masonry

walls and concrete masonry walls.

Based on her analyses, Davis made recommendations to improve the

current MSJC provisions. Among others, the current MSJC provisions do not take

into consideration the loss of masonry shear strength in plastic hinging regions.

She proposed an factor depending of the ductility ratio which will be added to

the 2011 MSJC. She also indicated that its appropriate and more accurate to

combine at the same time the shear contribution from the masonry and the

contribution from shear reinforcement. Indeed, the MSJC provides a conservative

equation for the contribution to nominal shear strength from horizontal shear

reinforcement. This equation (2.2; term with dv)assumes a 45 shear crack which

results in excessive amount of shear reinforcement for walls with aspect ratio

greater than 1. She advocated for using the dv/s term given by Paulay and

Priestley (1992).

1.2 Scope and Objectives

The purpose of our research is to improve the MSJC further by

reconsidering the contribution of the horizontal shear reinforcement based on a

new hypothesis. This hypothesis consists of more accurately considering the

number of reinforcing bars contributing to shear strength. In the current MSJC SD

design equation, there is a 0.5 factor which has no physical explanation. Instead,

it was derived to appropriately fit the design equation to the test results. In

other codes around the world, this factor ranges from 0.5 to 0.8. This study then

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is to re-evaluate this factor in comparison to the test data considering only those

reinforcing bars that are effective at improving shear strength.

1.3 Organization of this report

This report consists of four chapters. In first in this study, a quick

presentation and a historical of Washington State University developed in

Chapter 2.

Chapter 3 provides a basis to understand the purpose of this research,

details of the walls and a review of the various code provisions.

Chapter 4 evaluates the contribution of the horizontal reinforcement in

terms of contributing to shear strength and proposes an improved method for

defining that contribution.

Finally, Chapter 5 presents conclusions based on the results of this study

along with possible recommendations for changes to the in-plane shear provision

in the MSJC code.

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CHAPTER 2

PRESENTATION OF WASHINGTON STATE UNIVERSITY

A quick presentation and a historical of Washington State University (WSU) will

be presented and described in this chapter.

2.1 General presentation and History

Washington state university is a public research university based in Pullman,

Washington, in the Palouse region of the Pacific Northwest. Founded in 1890,

WSU confers bachelors, masters, professional and doctoral degrees, and offers

more than 200 fields of study (veterinary medicine, agriculture, food science,

architecture, communications ). The university also has campuses acrossWashington known as WSU Spokane, WSU Tri-Cities, and WSU Vancouver, all

founded in 1989 (shown in figure II.1). WSUs athletic teams (the Cougars) are a

member of the Pacific 10 Conference, which participates in the NCAA Division I.

The schools mascot is Butch T. Cougar and the schools colors are crimson and

gray.

WSU is classified as one of 96 U.S. public and private universities with very high

research activity. U.S News and World Report consistently rank the University

among the top 60 public universities.

The current president of the university is Elson S. Floyd, Ph.D.

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Map of the locations of the campuses of Washington State University.

2.2 Quick facts

WSU enrollment: 25 352

Pullman enrollment: 17 753

WSU employees: 6 167

Out-of-state students: 12%

International students: 5%

Multicultural students (excluding international students): 15%

Masters degree programs: 73

Doctoral degree programs: 46

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Campus ofWSU


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2.3 Financial situation

Operating Budget (2007-2009): $1.7 billion

Research and development expenditures (2007): $213.3 million

Private support (2008): $143.6 million

Endowment (2008): $683.2 million

Capital Budget (2007-2009): $322.5 million

Financial Aid and Scholarships (Fiscal Year 2008): More than $207million to17,215 students

2.4 Organization chart

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CHAPTER 3

BACKGROUND AND PREVIOUS RESEARCH

3.1 MSJC Building Code

The US design standard Building Code Requirements and Specification for

Masonry Structures is written by the Masonry Standards Joint Committee (MSJC

2008). It provides two sets of provisions for shear design: Allowable Stress Design

(ASD) and Strength Design (SD). The MSJC SD provisions are the same as those

developed by the National Earthquake Hazards Reduction Program (NEHRP,

2003). The activities of NEHRP are, among others, to improved design and

construction methods and practices

We will focus on SD provisions for reinforced masonry.

3.1.1 MSJC Strength Design (SD)

MSJC provisions based on Strength Design (SD) for reinforced masonry are

given in MSJC Section 3.3.4. Past researchers have established that the shear

resistance of reinforced masonry is due to several mechanisms, including dowel

action of vertical reinforcement, tension of horizontal reinforcement, and axial

compression force. No effective theoretical models have yet been developed to

predict the shear strength of a wall panel. So, practically, a semi-empirical model

is used: the nominal shear strength, Vn, is given as the sum of the nominal shear

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strength provided by the masonry, Vm, and the nominal shear strength provided

by the shear reinforcement, Vs.

Vn = Vm + Vs (3.1)

vyv

umn

vu

un df

s

A.P.'A

dV

M..V

++

= 5025075104 (3.2)

The first term in this equation represents the strength contribution from

the masonry, and the second term represents the shear strength contribution

from the applied axial compressive load. The third term represents the nominal

shear strength provided by the shear reinforcement, Vs.

The wall height-to-length aspect ratio (h/Lw) has an influence on the shear

strength.

Assuming a 45 crack caused by an applied force V, walls behavior under

loading is different in function of the aspect ratio. This is accounted for in the

design equation.2 as follows:

Figure 3.1: Aspect ratio

16

Lw

h

V


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= (3.3)

We have to distinguish two heights: the physical height of the wall and the

effective height of the wall. This consideration depends on the bending of the

wall, which can be in single bending or in double bending. In this latter case, the

in-plane force applied to the wall is prevented from rotation by vertical actuators

(lab test equipment) and the effective height of the wall is equal to the half of the

physical height.

Figure 3.2: Single and double bending

The MSJC limits the nominal shear strength as follows:

For (3.4)

For (3.5)

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Single bending Double bending


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For The maximum value of Vn is linearly interpolated:

Figure 3.3: Interpolation of the limitation of Vn

Therefore, based on the interpolation for walls with aspect ratio between 0.25

and 1.0:

(3.6)

The MSJC SD provisions do not make any difference between in-plane and

out-of-plane shear.

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Front view

Side view

In-plane

load

Out-of-plane load


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Figure 3.4: In-plane and out-of-plane load

3.1.2 MSJC 2011

Based on Daviss (2008) research, the MSJC modified the design equation for Vn

as follows:

vy

v

umn

vu

u

ndf

s

A0.50.25P'A

dV

M1.754.0V

++

=

The limitations on maximum values of Vn were kept the same as before.

Alpha is given in Figure 3.5

0.00

0.50

1.00

1.50

0.0 2.0 4.0 6.0

Coefficient

Ductility Ratio ()

Figure 3.5: Ductility Reduction Factor

3.1.3 Horizontal Reinforcement Ratio

Davis (2008) represented the amount of hoizontal reinforcement present in

a wall as a horizontal reinforcing ratio .

For this study, we will change the number of effective bars. Consequently, it will

change the horizontal reinforcement ratio. So, we need to recalculate the

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(3.7)


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horizontal reinforcement ratio after having changed rebars. To do it, we will use

equation 3.8. This equation assumes a even spacing between bars:

With:

: Cross-sectional area of one rebar (in)

: Cross-sectional area of all the rebars (in)

: Spacing between the rebars (in)

This equation is verified if you consider the spacing between bars to be the

average of the spacing.

Therefore, Vs becomes:

To understand the performance of the equations prediction, all terms have

to be understood. is assuming a 45 crack, is the yield strength of the

horizontal reinforcement, and is the reinforcement factors to define the

amount of reinforcement. The 0.5 factor has no physical explanation. It is placed

to better match the code prediction of strength with the experimental results. As

a comparison, the Canadian code required a 0.6 factor, and the New Zealand

code 0.8. The value of this coefficient will be studied in the next chapter.

It is not possible to reinforce indefinitely a wall. In fact, there are two kinds

of failure: brittle and ductile. A heavy reinforced wall will carry more stresses but

his failure will be brittle, unfixable and especially unpredictable. Conversely, a

less reinforced wall will have a ductile failure, fixable (insofar as possible), and

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(3.8)

(3.9)


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progressive which allowed people to evacuate the building. A ductile wall is safer

and is required for design.

This new hypothesis is based on the number of really efficient horizontal bars.Considering bars who are efficient in carrying shear loads, we can calculate a

new nominal shear strength and perform a statistical anaylis to try to move the

theoritical results closer to practicals.

Statistical analysis of each sequence of walls was performed isolating the effect

of Vs.

3.1.4 MSJC Notation

: Ductility reduction factor

Ah: cross-sectional area of shear reinforcement (1 rebar) (square

inches)

Ah total : total cross-sectional area of shear reinforcement (all rebars)

(square inches)

An: net cross sectional area of a member (square inches)

dv the actual depth of a member in direction of shear considered (inches)

fm: specified compressive strength of masonry (psi)

fyh: specified yield strength of steel for reinforcement or anchors (psi)

h: physical height of the specimen (inch)

he: effective height of the wall (be aware of double bending) (inches)

Lw: length of the wall (inches)

Mu: factored moment (lbs.inch)

Pu: factored axial load (lbs)

S: spacing between horizontal reinforcement bars (inches)

n: axial stress of the wall (psi)

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Vn : nominal shear strength (shear capacity of the wall) with Vu


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Table 3 .2: Type Dependent Nominal Strengths (fm in MPa; from NZS,

2004)

We will assume in this research that the test walls are a Type A of masonry.

Therefore, the limitation is:

In SI Units (3.11)

So, in US Customary Units:

(3.12)

Compared to MSJC Limitations, it does not take into consideration the aspect ratio

of the specimen.

3.2.2 New Zealand Standard Notation

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fm: specified compressive strength of masonry (psi)

: Total shear stress corresponding to Vn (psi)

: Nominal shear strength of section (lbs)

: Distance from extreme compression fiber to centroid of longitudinal

tension reinforcement, equal to 0.8Lw for walls (figure 0000) (inches)

: Effective web width (inches)

: Basic type-dependent shear strength of masonry (psi)

: Maximum permitted type-dependent total shear stress (psi)

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Figure 3.5: Effective Areas for shear

3.2.3 Canadian Standards Association S304.1-04

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The Canadian Standards Association Design of Masonry Structures (CSA

S304.1, 2004) provides recommendations in Section 7.10. Like the MSJC and NZS

codes, unreinforced masonry and reinforced masonry are specified separately,

but our focus is only on reinforced masonry shear walls.

For these walls:

In SI Units (3.13)

So, in US Customary Units,

Compared to the MSJC Limitations, the limitation in the Canadian provisions is

greater.

3.2.4 Canadian Standards Notation

Canadians are using different units in their formulas (besides, its in SI

units) but I switched the Canadian notations by the MSJC reference to make it

easier.

3.3 Data tests

Davis (2008) collected available results from laboratory tests of masonry

walls. Much of the data were already collected by Voon (2007). She gathered 56

walls; all were fully grouted, subjected to in-plane loads and failed in shear. The

walls were tested by four researchers: Shing et al (1990 University of Colorado),

Matsumura (1987 University of Kanagawa-Japan), Sveinsson et al (1985

University of Berkeley-California) and Voon & Ingham (2006 University of

Auckland-NZS). In fact, the researchers tested others walls, but we will consider

only those that failed in shear. The data set include clay and concrete walls.

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(3.14)


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3.3.1 Shing et al.

Shing et al. (1990) tested 22 masonry walls with an aspect ratio keptconstant equal to 1 (72 in. by 72 in.). They were loaded in single bending (see

Figure 2.2). Only ten of these walls failed in shear. So, our analysis will just take

data from these 10 walls. Among these, eight specimens were assembled with

nominal 6 in. x 8 in. x 16 in. concrete blocks. The last two were made with clay

units (4 in. x 6 in. x 16 in.). Some of these walls were subjected to high axial

stress which induced severe toe crushing and thereby, reduced flexural ductility.

The horizontal reinforcing ratios ranged from 0.00122 to 0.00222. Data from thewall tests by Shing are given in Appendix A.

Figure 3.6: Shing et al. - Test Apparatus and Setup

3.3.2 Matsumura

Matsumura (1987) tested 80 masonry walls. Only 18 of them failed in

shear and were fully grouted. Fourteen were made of concrete blocks (15.4 in. x

7.48 in. x 7.48 in. and 15.4 in. x 7.48 in. x 5.91 in.) and four were made of clay

blocks (11.4 in. x 3.5 in. x 7.48 in.). They were subjected to double bending. As

expected in this study, they failed in shear, accompanied by X-shaped shear

cracks and the crush of compressive corners of walls. Report to figure 2.7 to see

the details of the experiment. Aspect ratios ranged from 0.57 to 1.14, and the

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horizontal reinforcing ratio varied from 0 to 0.0067. Data from the wall tests by

Matsumura are given in Appendix A.

Figure 3.7: Matsumura Test Apparatus and Setup

3.3.3 Sveinsson et al.

Sveinsson et al. tested 10 concrete walls and 10 clay walls in 1985. There

were loaded in double bending, which makes the effective wall height, he, equal

to half of the real height. All these walls are identical in dimensions and had an

aspect ratio equal of 0.58 with flanges. The horizontal reinforcing ratio varied

from 0.0008 to 0.0063. Horizontal reinforcing bars contribute three times more

than vertical reinforcing bars to the shear strength. The loading for failure was 3

sinusoidal cycles of loading with amplitude gradually increased. See Appendix A

for more data on these specimens.

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Figure 3.8: Sveinsson Test Apparatus and Setup

3.3.4 Voon and Ingham

For his thesis of PhD in 2003, Voon, advised by Ingham, constructed seven

walls, all in concrete blocks fully grouted and subjected to single bending. The

aspect ratios for the walls ranged from 0.6 to 2.0, and the horizontal reinforcing

ratio varied from 0.0005 to 0.00062. The walls had low axial compressive stress

levels. See Figure 3.9 and Appendix A for more details.

Figure 3.9: Voon - Test Apparatus and Setup

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CHAPTER 4

ANALYSIS OF WALL DATA

4.1 Interpretation of Shear Equations

As explained earlier, the purpose of this research is to reevaluate the

current MSJC design provisions for possible improvements. The evaluation

consisted of determining the specific predicted wall strength for in-plane shear,

Vn, and to then compared the strength to the test data. Statistical comparisons

were performed to achieve this comparison and to enable conclusions to be

drawn in regard to two hypotheses. These comparisons provide a measure of the

effective of the different design provisions considered in this study.

4.2 First Hypothesis

The first hypothesis is more correctly consider the wall aspect ratio in

terms of influencing shear strength. The current equation for the shear strength,

Vn, is modified as follows:

The original equation (3.9) is given as:

As noted before, this equation assumes a 45 shear crack (not real but

conservative), with a horizontal projection of Lw. However, if we consider a wall

whose aspect ratio is lesser than 1, that is the wall is wider than it is tall, the

representation of the horizontal projection of the assumed 45 crack with L w is

incorrect. This case could consider that there are bars in the footing.

So, to consider the reality for walls with aspect ratio lesser than 1, we will

performed statistical analysis switching Lw by h in the equation (3.9) for this

kind of walls.

This situation is illustrated in Figure 4.1.

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(3.9)


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Figure 4.1: The impact of using the incorrect horizontalprojection

4.2.1 Results

To see the performance of this first hypothesis, we will use a reference

(MSJC) and make a statistical analysis using mean, standard deviation, coefficient

of variation on the ratio .

Secondly, as said in the introduction, we are interested in improving the

0.5 factor which is in the equation to fit reality and theory. To do that, we are

going to change this factor by 0.6, 0.7 and 0.8 and look at the effect on the

statistics.

STATISTICSMean

Vtest/Vn

Standa

rd

Deviati

on

Coeff.

Of

variatio

n

Minimu

m

Value

Maximu

m

Value

5th

Percent

ile

MSJC (0.5) 1,157 0,177 15,33% 0,770 1,547 0,908

31

Lw

Lw

Projection

Incorrect

h

4

5


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0.5 Switched w/

lim1,153 0,236 20.5% 0,770 1,547 0,901

0.6 Switched w/

lim1,145 0,175 15,30% 0,758 1,547 0,901

0.7 Switched w/

lim1,137 0,178 15,69% 0,747 1,547 0,894

0.8 Switched w/

lim1,130 0,183 16,17% 0,736 1,547 0,870

Table 4.1: Statistics with Switched term in the equation

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Figure 4.2: Effectiveness of Switched hypothesis

4.2.2 Conclusion

The results of this hypothesis do not seem to be significant. Indeed, the

statistical analysis does not give really better results than the reference.

However, using the 0.8 coefficient improves noticeably the fit between V test and

Vn.

4.3 Second Hypothesis

This second hypothesis evaluated in this study is that, in a wall subjected

to shear loads, the horizontal reinforcement bars placed in this wall are not all

fully effective in terms of contributing to shear strength. Bars in the middle of this

wall will be more effective at carrying loads than bars near the top and the

bottom of the wall. As an explanation for this behavior, consider a 45 shear

crack existing in the wall and see Figure 4.3. The issue is lack of sufficient

anchorage exists in bars that are crossed by the crack near the ends of the bars.

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Figure 4.3: Location of cracking and bars

The effectiveness of each bar is based on the location of cracking in the bar. A

bar in which the crack is within an estimated 10% of the end of the bar

should be considered ineffective.

This is important because, in the equation (3.9),

s

Ah =

h

Ahtotaldefines the number of horizontal reinforcing bars that contribute

to shear strength (assuming a 45 degree crack and that s is the average

spacing of the bars).

4.3.1 Shing et al.s New numbers of bars

Figure 4.4: Shings Walls

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So, applying this hypothesis to Shings walls, it is determined that the top

bar is not effective, yielding 4 bars contributing to the shear strength.

4.3.2 Matsumuras New numbers of bars

In a similar manner, the hypothesis was applied to Matsumuras walls,

yielding the total number of bars contributing to shear strength as given in the

following figures.

35

Wall 11 : 3 effective Walls 12-13: 3

Wall 14 : 3 effective Wall 15 : No bar


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4.3.3 Sveinssons New numbers of bars

In Sveinssons tests, it can be noticed that, because the bars are placed

mainly in the middle of the wall, there is no significant difference in the number

of effective bars from the total bars.

36

Walls 29-30 :3 Wall 31 : 3 Wall 32 : 3 bars

Figure 4.5: Matsumuras walls

Walls 16-17-18-19-20-21-22-23-

24: 3 effective bars

Wall 25 : No bar

Walls 26-27-28 : 3 effective


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37

Wall 34-37-38 : 2Wall 33 : 2 bars Wall 35 : 4 Dur-O-

Wall 36 : 4 DOW +2 Wall 39 : 2 bars Wall 40 : 5 bars


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38

Wall 41 : 2 Wall 42 : 5 Wall 43 : 2

Wall 44 : 5 Wall 45 : 2 Wall 46 : 5

Wall 47 : 4 Wall 48 : 6 Wall 49 : 4

Figure 4.6: Sveinssons


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4.3.4 Voons New numbers of bars

Considering the second hypothesis, Voons walls have been evaluated to

determine the effectiveness of bars. For most of them, top and bottom bars are

not effective. See Figure 4.7 below for details.

39

Wall 50 : 3 bars Wall 51 : 0 bar Wall 52 : 1 bar

Wall 53 : 3 bars Wall 54 : 3 bars


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4.3.5 Results

Statistics

Mean

Vtest/

Vn

Standar

d

Deviatio

n

Coeff. Of

variatio

n

Minimu

m Value

Maximu

m Value

5th

Percenti

le

MSJC 1,157 0,177 15,33% 0,770 1,547 0,908

0.5

Changed

w/lim

1,171 0,169 14,40% 0,797 1,547 0,929

0,6

Changed

w/lim

1,163 0,168 14,48% 0,790 1,547 0,914

0.7

Changed

w/lim

1,156 0,169 14,61% 0,783 1,547 0,906

0.8

Changed

w/lim

1,150 0,170 14,81% 0,776 1,547 0,901

40

Wall 55 : 5Wall 56 : 3 bars

Figure 4.7: Voons walls


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Table 4.2 : Statitics with a new number of effective bars

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42


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Figure 4.8: Effectiveness of the coefficient with a newnumber of bars

4.3.6 Conclusion

We can see that the change in the determination of effective bars does not

have a significant impact on the final statistics. Nevertheless, I would say that the

coefficient 0.8 is the best. Our conclusions are not so significant because the

contribution of Vs on Vnmax (without limitation) is not that important (between 18%

and 26% depending on what factor we use). Therefore, if Vs changes by 20% (for

example), the impact on Vnmax is between 3.6% and 5.2%.

Besides, if we consider that more than 30(on 56) Vnmax values encounter

the MSJC Limitation, the final modification o, Vs negligible on Vn . To illustrate this,

in the statistical analysis, a change of 30% on Vs leads to a modification of less

than 2% on Vn.

4.4 Other code limitations

As we saw, the MSJC limitations on Vn,max prevent an evaluation of the two

hypothesis. We will see if, using other limitations like the New Zealand and

Canadian limitations, we can improve our model. For this, we just took the

original factor 0.5.

As we saw in Chapter 2, New Zealand and Canadian limitations do not take

the aspect ratio in consideration and are, in general slightly lesser than MSJClimitation.

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4.4.1 Results

Statistic

s

Mean

Vtest/Vn

Standar

d

Deviatio

n

Coeff. Of

variation

Minimu

m Value

Maximu

m Value

5th

Percentile

MSJC 1,157 0,177 15,33% 0,770 1,547 0,908

NZS

Switched1,244 0,177 14,22% 0,715 1,737 0,934

CSA

Switched1,355 0,304 22,41% 0,715 1,954 0,952

NZS with

change1,263 0,226 17,87% 0,797 1,737 0,937

CSA with

change1,372 0,289 21,08% 0,797 1,954 0,959

Table 4.3 : Statistics with CSA and NZS

4.4.2 Conclusion

The change of limitation does not seem to have a good result on our Vs. Its

the exact opposite. Indeed, 34 walls fell upon NZS limitation and 40 upon CSA

limitation.

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CHAPTER 5

CONCLUSION

So, the result of this research is that the conclusions are not significant.

We lack data for having significant results in our switched hypothesis and the

MSJC limitations are so predominant that it dilutes any change on Vs.

Nevertheless, based on our 56 walls, our statistical analysis shows that a 0.8

factor, associated to a news number of efficient bars are a little bit better than

the reference we took.

During this semester, I learned how the work in a laboratory is and how a

university in the United States of America operates. I improve my knowledge of

the works world and the way of life of the American people. I improve also my

English by working everyday with American people.

In this internship, I have had the opportunity to see a different mode of work and

teach. Indeed, I followed some class in this university; and I have realized that

the way to approach the class was very different. The American educationsystem is different on a lot of point in comparison to France. I think that it is

45


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really an opportunity to me and my career that live such experience. And it is for

this I want to go back to the United States of America for my masters degree.

This research and the work at the WSU have really enriched me. I encountered afew difficulties during my internship here. The most important has been to

understand all the physical meaning of my work and to analyze the data after the

experiment done. But I learned to organize my work and my schedule. I also

learned how a scientific research article is done.

To conclude, this internship has given me the desire to work with people who

have a culture, traditions, a language, a way of life and points-of-view different

because it enriches me professionally and personally.

REFERENCES

- Courtney Lynn Davis (2008), Evaluation of Design Provisions for In-

plane Shear in Masonry Walls

- Canadian Standards Association (2004). S304.1-04 Design of Masonry

Structures. Mississauga, Ontario, Canada, pp. 34-55.

- New Zealand Standard 4230:2004, Design of reinforced Concrete Masonry

Structures, Standards Association of New Zealand, Wellington.

- TMS 402-08/ACI 530-08/ASCE 6-08. (2002), Building Code Requirements and

Specification for Masonry Structures, Masonry Standards Joint Committee

- Matsumura, A. (1987), Shear Strength of reinforced Hollow Unit Masonry

Walls, Proceedings of the 4th North American Masonry Conference, Paper No.50,

Los Angeles, CA, pp.50-150-16

46


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- Paulay, Thomas, and M. J. Priestley. Seismic Design of Reinforced Concrete and

Masonry Buildings. New York: Wiley-Interscience, 1992.

- Shing, P. B.,Schuller, M., and Hoskere,V. S. (1990a),In-plane Resistance ofReinforced Masonry Shear Walls, ASCE Journal of Structural Engineering,

Vol.116, No.3, pp.619-640

- Shing, P. B.,Schuller, M., and Hoskere,V. S. (1990b),Strength and Ductility of

Reinforced Masonry Shear Walls, Proceedings of the 5th North American Masonry

Conference, University of Illinois, Urbana-Champaign, pp.309-320

- Voon, K. C., In-plane Seismic Design of Concrete Masonry Structures, Thesis

(PhD-Civil and Environmental Engineering)-University of Auckland, 2007

- Sveinsson, B.I., Mayes, R.L., and McNiven, H.D. (1985), Cyclic Loading of

Masonry Single Piers, Volume 4, Report No.UCB.EERC-85/15, Earthquake

Engineering Research centre, University of California, Berkeley

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APPENDIX A

48

*Specimenswithgra

ysh

ading

werecons

tructedwit h

Clay

MasonryU

nits


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Table A-1: Original Wall Data

49

*Specimenswithgra

yshading

werecons

tructedwithClay

MasonryU

nits


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APPENDIX B

50


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51


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ble B-1: MSJC Provisions and MSJC , NZS and CSA Limits (0.5 factor)

52


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53


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Table B-2: MSJC Provisions (0.6 factor)

54


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55


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T able B-3: MSJC Provisions (0.7 factor)

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57


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Table B-4: MSJC Provisions (0.8 factor)

RESUME DU STAGE EN FRANCAIS

Contexte

Jai effectu mon stage lve-ingnieur dans un laboratoire de recherche

de luniversit de Washington State, plus prcisment dans le dpartement de

lingnierie civil. Ce stage a t supervis par le Dr. David Mc Lean, qui est un

professeur-chercheur de luniversit.

Pendant ce stage, jai suivi une classe de conception des structures en

bton arm que mon tuteur donnait. Cela tait dans le but de me permettre de

mieux comprendre le domaine dans lequel je travaillais. En effet, le sujet de mon

stage concernait le renforcement en acier de murs en bton.

Introduction

Les normes de conception dans les structures de maonnerie sont

diffrentes dans tous les pays. Aux Etats-Unis, cest le MSJC 2008(Masonry

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Standards Joint Committee) qui fait rfrence quand le CSA S304.1-04 et le NZS

4230 :2004 sont les rfrences, respectivement au Canada et en Nouvelle-

Zlande.

Les approches actuelles pour les efforts de cisaillement sont largement

fondes sur des tests car il nexiste aucune thorie fiable pour en prdire les

effets. Les recherches des 25 dernires annes ont permis dtablir un modle

semi-empirique afin de concevoir les structures devant rsister des contraintes

de cisaillement. Ces contraintes de cisaillement sont particulirement prsentes

lors de sismes et, mal considres, les effets peuvent tre dvastateurs.

Dans le but dvaluer la prcision de diffrentes normes internationalespour prdire les efforts de cisaillement, Davis (2008) a compar statistiquement

les diffrentes recommandations en isolant diffrents paramtres. Pour cela, elle

a runi des donnes exprimentales concernant 56 murs, entirement couls,

soumis des contraintes de cisaillement et qui ont succombs en cisaillement.

Elle a pu ainsi faire des recommandations pour amliorer les normes du MSJC.

En me basant sur son analyse, le sujet de ma recherche tait galement

de faire des recommandations sous de nouvelles hypothses. Ces hypothses

consistent en une rvaluation du renforcement horizontal des murs.

Renforcement horizontal en acier qui est la principale contribution la rsistance

au cisaillement du mur. Pour cela, jai men une analyse statistique sur les

donnes de Davis en considrant un autre niveau de renforcement.

Premire hypothse

La premire hypothse pour mieux considrer le renforcement horizontal

des murs en bton arm consiste mieux considrer le rapport daspect du mur

(rapport de la hauteur sur la largeur du mur). Les phnomnes ne sont pas les

mmes si le mur est 2 fois plus haut que large ou linverse. La thorie du

cisaillement estime que le crack caus par les forces est inclin de 45. Il sagit

dun thorie conservatrice mais pas relle avec une projection horizontale de la

longueur du mur. Ainsi, si on regarde un mur de rapport daspect infrieur 1,

c'est--dire que le mur est plus large que haut, le crack irait dans les fondations

du mur. La figure 1 rsume lenjeu :

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Figure 1: Projection du crack de 45

Par consquent, pour les murs dans ce cas, nous avons considr la

hauteur au lieu de la projection horizontale de la largeur et voir si les statistiques

donnent des rsultats plus proches des tests.

De plus, pour avoir plus quun rsultat et parce que nous ne pouvons

modifier le renforcement qu la baisse, nous avons modifi le coefficient

arbitraire (0.5) de lquation ci-dessous. Ce coefficient na aucune explication

physique (contrairement au reste de la formule) et est diffrent dans dautres

codes comme le NZS o il vaut 0.8. Dans le but de tester diffrents coefficients,

nous avons test la premire hypothse avec un coefficient de 0.5, 0.6, 0.7 et

0.8.

60

Lw

Lw

Projection

Incorrect

h

4

5


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Statistiques

Moyenn

e

Vtest/Vn

Ecart

Type

Coeff.d

e

variatio

n

Minimu

m

Maximu

m

5me

Centile

MSJC (0.5) 1,157 0,177 15,33% 0,770 1,547 0,908

0.5 w/ lim 1,153 0,236 20.5% 0,770 1,547 0,901

0.6 w/ lim 1,145 0,175 15,30% 0,758 1,547 0,901

0.7 w/ lim 1,137 0,178 15,69% 0,747 1,547 0,894

0.8 w/ lim 1,130 0,183 16,17% 0,736 1,547 0,870

On observe donc une amlioration de la prcision de la formule avec la

nouvelle hypothse de 2.3% de moyenne pour le coefficient 0.8. Par contre,

lcart type qui mesure la dispersion de la srie autour de la moyenne augmente

lgrement (+3.4% dans le cas 0.8), ce qui est lgrement contre-productif. Les

rsultats ne sont donc pas trs signifiants.

Seconde hypothse

La seconde hypothse value dans ce rapport concerne toujours le

renforcement horizontal mais il sagit ici de dterminer le nombre exact de

barres horizontales en acier qui sont rellement efficaces pour la rsistance du

mur. En considrant encore un crack de 45%, la location de la charge et celles

des barres, nous avons donc dtermin pour chaque mur un nouveau nombre de

barres. Pour cela, nous avons estim quune barre dont le crack a lieu moins de

10% de lextrmit de la barre sera inefficace par manque dancrage dans le

bton cet endroit. La figure 2 rsume la situation.

Avec la mme ide que pour la premire hypothse, les coefficients 0.6,

0.7, 0.8 ont t tests statistiquement

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Figure 2 : Lieu du crack et barres

Statistiqu

es

Moyen

ne

Vtest/

Vn

Ecart

Type

Coeff.

de

variatio

n

Minimu

m

Maximu

m

5th

Centile

MSJC 1,157 0,177 15,33% 0,770 1,547 0,908

0.5 w/lim 1,171 0,169 14,40% 0,797 1,547 0,929

0,6 w/lim 1,163 0,168 14,48% 0,790 1,547 0,914

0.7 w/lim 1,156 0,169 14,61% 0,783 1,547 0,906

0.8 w/lim 1,150 0,170 14,81% 0,776 1,547 0,901

De faon similaire, le changement du nombre de bars constitutif de la seconde

hypothse na pas des rsultats trs significatifs. Avec le mme coefficient 0.8,

nous avons pu augmenter la moyenne de 0.6% dans le mme temps que lcart

type (0.4%) et que le coefficient de variation (-3.4%). Cela reste nanmoins

insuffisant pour tre sr de lefficacit de la seconde hypothse.

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Dautres limitations

Comme nous lavons vu dans les conclusions ci-dessus, les rsultats ne

sont pas trs significatifs et ne permettent pas de tirer des conclusions claires et

nettes. Cependant, comme le montre lannexe B, de nombreuses quations, lors

des calculs, sont limites par les limitations du MSJC. Dans le but damliorer les

rsultats, une analyse statistique considrant les limites des codes canadiens et

no-zlandais a galement t effectue avec lutilisation du coefficient dorigine

(0.5).

.

Statistiq

ues

Moyenn

e

Vtest/Vn

Ecart

type

Coeff.

de

variatio

n

Minimu

m

Maximu

m

5th

Centile

MSJC 1,157 0,177 15,33% 0,770 1,547 0,908

NZS 1re

Hypoths

e

1,244 0,177 14,22% 0,715 1,737 0,934

CSA 1re

Hypoths

e

1,355 0,304 22,41% 0,715 1,954 0,952

NZS 2nd

Hypoths

e

1,263 0,226 17,87% 0,797 1,737 0,937

CSA 2nd

Hypoths

e

1,372 0,289 21,08% 0,797 1,954 0,959

Dans ce dernier cas, les rsultats sont assez mdiocres. Aucune

amlioration nest observe. Cependant, nous pouvons en dduire que les

limitations du MSJC sont plus performantes mme si elles affectent plus de murs.

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Au final, quel que soit lhypothse, les rsultats ne sont pas trs

concluants. Je ne peux donc faire aucune recommandation formelle quant

lamlioration du MSJC.

Conclusion

Durant ce stage lve-ingnieur, jai effectu de nombreuses analyses

statistiques en utilisant principalement le logiciel Excel. Les rsultats finaux ne se

sont pas rvls tre la hauteur de mon attente mais ils mont permis

dadopter une mthodologie stricte et rigoureuse. Mon travail reste nanmoins

une base pour de futures recherches plus avances ncessitant des donnes et

des connaissances plus importantes. En effet, lchantillon de mon tude

statistique tait assez limit (56 murs). Limportant, pour mon tuteur, tait de

tester deux nouvelles hypothses et confirmer le potentiel de celles-ci ; ce qui est

chose faite maintenant.

Afin de pouvoir tre efficace dans mon travail, jai d complter ma

formation EPF en lisant de nombreuses thses et publications. Jai ainsi pu tre

trs autonome dans mon travail et cette autonomie sest rvle prcieuse

lorsque mon tuteur sabsentait pour un voyage daffaire.

Ce stage ma permis de voir un mode de travail et denseignement

diffrent, qui mont apport un point de vue supplmentaire sur la manire

daborder et de raliser mon travail. Cela a t une exprience enrichissant aussi

bien professionnellement que personnellement. Cest pour cela que je dsire y

retourner en 5m anne pour un masters degree.

louis research report -rendu

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