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INFLUENCE DF M,\TERIAL I'ROl'ERTIES DN TIIE BEIlAVIDUR DF BRICK M.\SDNRY SIlEAR VALLS

The

ADRIAN W. PAGE Senior Lecturer

Department of Civil Engineering and Surveying University of Newcastle, N.S.W., 2308, Australia

ABSTRACT

The influence of masonry bond and compressive strength on the performance of brick masonry shear walls is studied using an iterative, incrementaI finite element computer programo For a given set of strength parameters, a series of racking tests on shear walls is simulated, with varying ratios of vertical load to racking load being applied. A failure criterion in terms of the average normal stress (an ) and shear stress (T) on the bed joint is then derived for each set of tests, and the criteria compared for a range of bond and compressi ve strengths. It is shown that strength variations significantly influence the resulting failure criterion, and that a representative criterion should include the influence of these effects, as well as the influence on local stress distributions of such things as wall geometry and boundary conditions.

INTRODUCTION

Design rules for predicting the strength of masonry shear walls are usually expressed in terms of the average shear and normal stresses on the bed joint, regardless of wall geometry and boundary condi tions. These results are typically a conservative lower bound on test results obtained by pooling the resul ts of many shear wall tests of varying geometry, masonry strength and testing procedure.

This investigation studies the influence of masonry strength properties (shear and tensile bond strength and compressive strength), on the behaviour of a shear wall with fixed geometry and boundary conditions using a previously developed finite element modelo The model incorporates material propertiesfor the masonry which include appropriate elastic properties, inelastic stress-strain relations, and a failure surface. For a gi ven set of parameters, a complete ' racking test can therefore be simulated. A total of 98 analyses \lere performed for a range of strength properties and ratios of racking load to wall precompression . In each case, equivalent average shear and normal bed joint stresses (T and Gn)

529

\,ere calculated, and comparisons made to determine the relat i ve importance of each material strength parameter.

DESIGN OF MASONRY SHEAR WALLS

Walls subjected to vertical compression and racking loads usually fail by tensile cracking at the heel of the wall, by crushing at the toe in the zone of biaxial compressive stress, or by diagonal cracking induced by a biaxial tension- compression stress state (see Figure 1). The mode of failure will be influenced by many factors such as the wall geometry, the ratio of the racking to compressive load, the boundary conditions of the wall, and the masonry strength properties. The influence of these factors on shear wall failure has been previously discussed (1, 2).

Rockinll

Force

Vertical Load

~ .. l:I:I:1

, ....

" , Diollonol Tension • Foilur. ~ , , .

, , Tension Failur.

-- .. ~ Bioxiol Compression Foilur.

Figure 1. Modes of Failure for a Shear Wall

In design, the shear capacity of a wall subjected to a racking load is usually determined by evaluating a nominal shear capacity expressed in the form of a Coulomb-type failure criterion (see Figure 2):

T = TO + J.L an (1)

where T average shear stress at failure TO initial shear bond strength a average normal n stress at the bed joint

J.L coefficient of friction

The stresses T and a are average values obtained by di viding the n racking and vertical forces by the bed joint area. The failure criterion therefore does not allow for variations in stress distribution within the panel caused by the variables mentioned above. The values for J.L and TO

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used in design codes are based typically on a conservative lower bound fit to the pooled results of a large number of shear tests, with no consideration gi ven to wall geometry, boundary condi tions or masonry strength. The procedure, although convenient, is not therefore completely representative of shear wall behaviour.

When the vertical load from above is high in relation to the racking force, a crushing failure may occur in the region of the toe of the wall. In this case, equation (1) does not apply, and a check of the compressive capacity of the masonry is required. Ideally, the biaxial compressive strength should be checked. However, in most cases, a conservative estimate of compressive strength will be obtained by using the uniaxial value (3). This compression failure corresponds to the second part of the curve shown in Figure 2. For moderate values of applied vertical compression, a crushing failure may also be preceded by some diagonal tension cracking.

The purpose of this study is to investigate the sensitivity of the criterion shown in Figure 2 to variations in masonry bond and compressive strength.

l-OI OI

~ u; :; ., ~ (J)

OI

'" ~ li > <t

"shear· failure. 'compression" foilure.

Averoge Normol Stress ()n

Figure 2. Failure Criterion for Masonry Shear Walls

ANALYTICAL MO DEL

Material Model:

The analytical model used for the study was developed from a large number of biaxial tests on half scale, solid clay brick masonry panels. The panels were tested under biaxial compression and tension-compression, with the principal stresses being applied at varying angles to the jointing planes. These stresses were transformed normal and parallel to the bed joint, as a formulation in terms of the normal and parallel stresses and shear stress on the bed joints was found to be the most suitable for the finite element model (4, 5). The brick\wrk was found to have non-linear

531

deformation characteristics, with both inelastic behaviour and failure critically influenced by the orientation of the jointing planes.

Finite Element Model:

An iterative, non-linear finite element model incorporating the material model described above has been developed with a view to analysing shear wall structures and framed structures wi th masonry infill (6). Eight noded isoparametric elements are used with the integrations being carried out using 4 point Gauss quadrature. The loads are applied incrementally, with 2 sets of iterations being performed at each increment of load. Dne allows for material non-lineari ty, the other accounts for progressi ve local failure (either cracking or crushing of the masonry). At a given load leveI, iteration continues until the unbalanced nodal forces associated with material non-linearity are less than a prescribed tolerance limit. The stresses are then checked at each Gauss point for violation of the failure criterion. lf failure is indicated, the stiffness coefficients are reduced to a value appropriate to the mode of failure and the problem re- solved. Dnce convergence has been achieved, a further increment of load is applied and the process repeated. Loading continues until the solution fails to converge. A complete test can thus be simulated.

Racking tests on steel frames with masonry infill were used as a means of verifying the effectiveness of the finite element model. Good agreement was achieved between theory and experiment for a range of frame stiffnesses and wall geometries, both with regard to masonry infill behaviour up to and including failure, and the performance of the surrounding frame (7). The model can therefore be confidently used to simulate the behaviour of shear walls, since the masonry is stressed in a similar manner.

INFLUENCE DF MATERIAL PRDPERTIES DN TllE BEIIAVIDUR DF SIIEAR h1ALLS

Parametric Study:

The above analytical model was used to carry out a parametric study of the influence of masonry strength properties on the behaviour of shear walls. A typical racking test was simulated for a shear wall with an aspect ratio (base length/height) equal to 1.5. The wall was subjected to a uniform vertical compression and a racking force. A typical finite element subdivision is shown in Figure 3. Due to the nature of the material model, a reasonably coarse element subdivision could be used with each element encompassing several bricks and joints. When failure occurs at a Gauss point within an element, the effects of this local failure are smeared across the relevant quadrant of that elemento

--

532

"'" "~~'" ~""

~ ~ ~ ~ ~ ~ ~ ~ 7W~'WP'''''W,",,,,,,,,,,,,,--,,,,~,,,,,,,,,,

• 1500

1.6

~

J

·0 o o

• Holf Scole Oimension.

Figure 3. Typical Finite Element Subdivision

The wall was analysed for a range of bond and compressive strengths as summarized in Table 1. In the model, the strengths were varied by adjustment of the relevant portion of the three dimensional failure surface. The defonnation characteristics were left unchanged for alI cases. Previous analyses had shown that the overall behaviour was insensitive to this parameter, with progressive cracking being the principal source of non-linear behaviour (7). During each simulated test, the racking and vertical loads were increased proportionally to maintain a constant load ratio.

In each case, failure of the wall was deemed to have occurred when ei ther suff icient cracking had taken place to allow a collapse mechanism to form (usually when the cracking extended from the top to the bottom of the wall) , or when local crushing of the masonry was evident, usually in the toe region. Failure also usually coincided with a marked change in the slope of the racking load- deflection curve which was plotted for the loaded top corner of the wall in each case. For a gi ven set of strength parameters, once a series of tests with varying racking loadjvertical load ratios had been simulated, a curve of the tonn shown in Figure 2 was then obtained by determining the average shear and normal stresses at failure for each case. A total of 98 analyses were performed using this procedure.

til

*

MODEL NO.

1 2 3 4 5 6 7

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TAI3LE 1 Summary of Parametric Study

SIlEAR AND TENSILE 130ND STRENGTH

* Original 2 x Original

0.5 x Original Original Original

2 x Original 0.5 x Original

COMPRESSIVE STRENGTH

* Original OriginaI Original

2 x Original 0.5 x Original 2 x Original

0.5 x Original

The original 3-D failure surface is given in Ref. (5) Some significant values from this surface are: Shear bond strength = 0.30 MPa Tensile bond strength 0.40 MPa Uniaxial compressive strength = 7.6 MPa (load normal to bed joint)

RESULTS

The failure criteria for each set of material parameters derived using the above procedure are shown in Figures 4, 5, 6 and 7. In each case, smooth curves have been drawn through the data which exhibited some scatter due to the incrementaI nature of the loading. In the plots, distinction has been made between walIs which failed in a cracking mode (i.e., a "shear failure"), and those which failed by local crushing (a "compression failure").

It is apparent that in alI cases, variations in bond strength andjor compressive strength significantly influenced the resulting failure criterion. Variations in bond strength affected not only the first section of the curve (corresponding to the Coulomb criterion), but al so the transition section which involved both cracking and crushing of the masonry. Variations in compressive strength drastically varied the second part of the criterion, but did not influence the initial portion of the curve, except to terminate the linear section once compress ion fail ure governed.

In most practical applicat ions, the compressi ve stress from above (a ) is usualIy less than 2 MPa. The behaviour in this region for the 7

n cases studied is shown in Figure 8. For purposes of comparison, the provisions of the new Draft Australian Masonry Code (8) are shown . It can be seen that even in this region, a criterion of the form of equation (1) is not always valid, particularly for masonry with a low compressive strength.

o n. ::E

I-

o n. ::E

I-

534

1·5

1,0

C Croc king Foilu," e,.- -- .... , • Crushino Failure ., '. , \

" . ...-.-. , C' / " ~ . ~

" ai .~ ............ , c....... '-' .... , .... " //" '...... ., .......... 2. Bond Slrenglh

D D. ""'. '. ...., / / --.---. ""';--, ....

ICal

.................... ~lglnOI C I ....... ,

I ....... ,C 0'5. B~n d Slrenglh a

0·5

0·0 2·0 4'0 6'0

O"n - M Po

Figure 4. Influence of Variation of Bond Strength on the Failure Criterion

1·5 ., ..... __ ._.. • C Crotklng Foilur.

,.,' ...... • Cru shing Foilur. -. ..::.......... ... ~ ..... ,'. "-.~., ~ ,2 • Comp. Slrenglh

8-~ Originol. "

~ " ,; .~'~

? "'a...... . ' ,~ ...... ' 0',...... • r ... ~~. Campo Slrenglh ., . . "

1'0

0'5

•

0·0 2'0 4'0. 6·0

O"n - MPo

Figure 5. Influence of Variation of Compressive Strength on the Failure Criterion

•

-

o a.. ~

1·0

535

o Crockinv Foilur •

Foilure • • Cru.hlnv ~" 'i' -.--............ . , ... .. o. • ..... //...- -.......... ... ...

l/ ~ ............ /' 00 .... ~. Comp . 8 Bond SIr.nvlh

,0;1 ....

/

0'/0 0.5. Comp 8 ·~O"VlnOI"·"""""·"""". -. . Bond SIren91h ...

o/~ - ..... ..... '- . o .... " a' ...... ..,. •

2·0 4'0

r5"n - MPo

6 ' 0

Figure 6. Influence of Variation of Bond and Compressive Strength on the Failure Criterion

• o Crackin9 Foilure

1· 0

Foilure ................. ~. / '. ~

o \ .............. 0/ ~ ..........

/ ... ......... ....... .~. Band 8 Camp o SIrenvlh

C '~.............. / ...... , ................ 2 • Band SIrenvlh ...... • Ori9inal Comp, SIren9th .... .......... • ......

• Cru.hing

0·0 2·0 4·0 6·0 B ' O

Irn - MPo

Figure 7. Influence of Variation of Bond and Compressive Strength on the Failure Criterion

o a.. ~

r

536

1·5

1·0

0·5

__ ~".-J.!.0r~ -

0·0 0·5 1·0

~n - MPa

1·5

·6

2

eO I .. \Il\~i~' -­

-- .~~ ~

2·0

Figure 8. Comparison of Failure Criteria Within the Practical Range

CONCLUSIONS

A study of the influence of material properties on the behaviour of masonry shear walls has been described. It has been shown that variations in the bond and compressive strength characteristics of the masonrl can drastically influence a failure criterion expressed in terms o the average shear and normal stresses on the bed joint. To be fully representative, a shear wall failure criterion should include the infl uence of both these strength parameters, as well as the effects on stress distributions of such things as wall geometry and boundary cond i tions. In the practical stress range, the use of a Coulomb type criterion to predict shear failure of a wall (in reality a diagonal tension failure), does not appear unreasonable provided provision is also made for the possibility of premature compressive failure.

ACKNOIiLEOGEMENTS

The finite element program used for this investigation was developed at t he University of Newcastle by Dl'. M. Ohanasekar. The assistance of Mr. G. McKenzie with the computing is gratefully acknowledged. This work was supported by the Australian Research Grants Scheme.

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REFERENCES

Page, A. W., Samarasinghe, W. and Hendry, A. W. , "The Failure of Masonry Shear Walls", International Journal of Masonry Construction, Vol. 1, No. 2, 1980, pp. 52-57.

Samarasinghe, W., Page, A.W. and Hendry, A.W., "Behaviour of Brick Masonry Shear Walls 11 , The Structural Engineer, VoI. 59B, No. 3, September, 1981, pp. 42-48.

Page, A.W., "The Biaxial Compressive Strength of Brick Masonry", Proc. Instn. Ci v . Engrs., Part 2, 71, September, 1981, pp. 893-906.

Dhanasekar, M., Kleeman, P.W. and Page, A.W., "Biaxial Stress- Strain Relationships for Brick Masonry", J. Struct. Div., A.S.C.E., No. ST5, 111, May, 1981, pp.1085-1100.

Dhanasekar, M., Page, A.W. and Kleeman, P.W., "The Failure of Brick Masonry Under Biaxial Stresses", Proc. Instn. Civ. Engrs., Part 2, 79, June, 1985, pp. 293-313.

Page, A.W., Kleeman, P.W. alld Dhanasekar, M., "An In-Plane Finite Element Model for Brick Masonry", New Analysis Techlliques for Structural Masonry, S.C. Anand (Editor), A.S.C.E. Special Publication, New York, 1985.

Dhanasekar, M. alld Page, A. W. , "The Influence of Brick Masonry Infill Properties on the Behaviour of Infilled Frames", Proc. Instn. Civ. Engrs., Part 2, 81, December, 1986, pp. 593-605.

Draft Australian Stalldard SAA Masonry Code, Masonry Structures, 1987.

Commi ttee BD / 4 -