12TH INTERNATIONAL

BRICK/BLOCK Masonry CONFERENCE

A THEORETICAl ANO EXPERIMENTAL STUOY OF INTERSECTING BONOED WAllS UNDER

VERTICAL lOADS

V. Capuzzo Neto 1; M.R.S. Corrêa2

; M.A. Ramalho2

'Graduate student, ' Senior Lecturer

USP . University of São Paulo, EESC - São Carlos School of Engineering

Av. Dr. Carlos Botleho 1465, 13560-250 São Carlos, SP, Brazil

ABSTRACT

The purpose of this work was to analyse intersecting load-bearing walls under verti­calloads. The paper deals with two aspects of the phenomenon: the integrity of the intersecting region and the passibility of transferring loads from one bearing wall to another. The study is based on a series of laboratory tests carried out on three inter­secting full-scale H-shaped bonded walls. Although only the main wall was load bea­ring, measurements were taken af ali three walls to identify the rate of transferred 10-ads among the walls. Numerical finite element simulations were made to help interpret the results and to make thearetical and experimental comparisons.

Key words: structural masonry, interaction, laboratary tests, numerical modelling, bonded beam, blocks.

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1. INTRODUCTION

The growing demand for structural masonry building design with increasingly nu­merous floors has led to the need for refined design models. Improved represen­tation of load distributions along the height of the building are also needed. Wit­hout such improvements, two serious errors may occur, i.e., designs that are unfeasible in terms of cost and/or designs that jeopardise a building's structural safety.

Few studies have focused on the behaviour of wall intersections under vertical 10-ads and the reports available on the subject are contradictory. SINHA & HENDRY (1979) consider that walls work separately, while SUTHERLAND, quoted by HENDRY (1981) and CURTIN et aI. (1984), admits the interaction of adjacent walls, i.e., the possibility of load transference from one wall to another.

Few international investigations have addressed this subject, probably because masonry buildings usually have only a few floors and thick walls to provide com­fort and protection against extreme temperatures. In such cases, taking into ac­count the isolated functioning of walls does not lead to cost-related problems, even when wall interaction is disregarded, since the minimum resistance required by codes and/or the thickness required to ensure thermal comfort are sufficient. Nonetheless, the reality of Brazil has led to increased interest in the subject and investigations are therefore needed.

In order to verify the interaction of walls and determine the load transfer ratio, full -scale specimens were tested at the laboratory of the Structural Engineering Department. The tested masonry panels were also modelled numerically by the Finite Element Method (FEM) in order to make a comparison of the theoretical and experimental results.

2. EXPERIMENTAL WORK

2.1. Blocks

The masonry panels were built of clay blocks with modular dimensions of 15 cm x 20 cm x 30 cm, using half blocks, bond beam blocks, sim pie blocks and inter­locking blocks (see figure 1). The block's mean compressive strength in relation to the net area was 22 MPa, while the characteristic strength according to the NBR 6136 (1994) code is 17,6 MPa. The coefficient of variation of strength is 12,6%. The ratio between the net area and the gross area was 50%.

Half blocks were used to determine the modulus of elasticity of the clay, since de­termining this property based on the block tests proved to be complicated by the appearance of internai and occasionally even externai cracking under low com­pression, which prevented non-linear behaviour of the block. The use of half blocks minimised this problem. A controlled hydraulic INSTRON machine was

Figure 7. C/ay blocks used in tests Figure 2. Test to determine the

modulus of elasticity.

used, which allows for load to be applied with controlled displacement speed. Shortening measures were taken for the rigid plates of the test machine using dis­placement transducers (see figure 2). The data were recorded using a SYSTEM 5000 machine. Neither electric nor mechanical strain gages were used due to the dispersed results obtained from previous tests carried out in the laboratory.

The mean modulus of elasticity in relation to the net area was 8026 MPa, with a va­riation coefficient of approximately 12,5%. The average ratio between modulus of elasticity and mean compressive strength was 322, with a variation of 8,5%. This number lies within the range of values found in the literature. DRYSDALE et aI. (1994) indicate that, in the case of clay blocks, this ratio may vary from 210 to 1670.

2.2. Mortar

The volume proportion of 1: 0,5: 4,5 (cement: lime: sand) was used to prepare the mortar, in line with the BS 5628 (1978) and NBR 8798 (1985) codes. The ma­teriais used for this mixture were naturally siliceous sand, Portland CP 11 F 32 ce­ment and hydrated lime. The mean compressive strength, tested on cylindrical specimens (5 em x 10 em) was 9,49 MPa with variation coefficient of 7%. The mean modulus of elasticity obtained was 10900 MPa.

2.3. Grout and reinforcement

The mass proportion of grout used was 1: 0,05: 2,20; 2,40 (cement: lime: sand: gravei) with a 0,72 water/cement (w/c) ratio. The tests to determine axial eom­pressive strength were based on the NBR 5739 (1994) code, with a mean strength of 22,6 MPa and a mean slump of 20 em achieved after 28 days. The materiais used in the mixture were gravei, naturally siliceous sand, Portland CP 11 F 32 ce­ment and hydrated lime. This grout was used to fill the bloeks for beam bonding.

Two 8-mm CA-50A bars were used along the entire length of the bond beams so­lely for constructive purposes. For this reason, a better eharacterisation of the bars was not a coneern .

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2.4. Masonry specimens

Two block prisms were used as masonry specimens and two samples of each type we­re prepared for each panel to determine compressive strength, with each prism. A hy­draulic INSTRON machine was used for these tests, with the prisms coated with sulp­hur. These tests were carried out together with the masonry panel tests. The panels were divided into two series (1 and 2), due the differences in their construction, which are described under item 2.5.1 . The mean compressive strength of the prisms of the no. 1 series was 12,6 MPa while that of the no. 2 series was 9,0 MPa. The efficiencies of the mean compressive strength of the block for series 1 and 2 were, respectively, 0,57 and 0,41 . It can be observed that the efficiency of the prisms of two of the no. 2 series blocks was 30% smaller than the efficiency obtained for the no. 1 series. A possible explanation for this is that the compressive strength of the blocks used in the no. 2 series is less than the average compressive strength of the total set of blocks, sin­ce the compressive strength of the mortar and the grout showed no appreciable va­riation (variation coefficients of less than 10%) and the same labour was used .

2.5. Masonry panels

2.5.1. Description of the structure

Two series of panels were tested . Series 1 consisted of three H-shaped panels with a bond beam in the top row. The vertical joint and the bed joint, both 1-cm thick, were filled with mortar. The no. 2 series, very similar to the no. 1 series, also con­sisted of three H-shaped panels, the only difference being the presence of a bond beam in the middle row. The dimensions of the panels of both series were the sa­me, as shown in figure 3. Figure 4 illustrates ali the panels of both series. It should be pointed out that the H-shape was used to reduce the effects of eccentricity.

Figure 3. Masonry panels

Without bond beam in the intermediate course - Series 7

With bond beam in the intermediate course Series 2

Figure 4. View af the built pane/s.

2.5.2 Instrumentation of the structure

A diagram illustrating the instrumentation used to measure the structure is shown in figure 5. The points on the opposite face (not shown in the diagram) are arran­ged in the same manner. The points from 1 to 12 (except for point 7) are trans­ducers with a 1 O-mm course and a 57-em base, whose purpose is to measure the shortening of the upper or lower parts of each wall . Point 7 and points 13 to 20 are transducers with a 20-mm course and a 60-cm base, which serve the same purpose. Points 21,22 and 23 are transducers with a 50-mm course placed per­pendicularly to the walls to measure the displacements in that direction.

Figure 5. Measurements af the pane/s.

(3) ®

®

I r- I I

,R? I I

I I

I I

I I

I I

2.5.3 Test procedure

I

0 0

@)

• Visible face

~ I

(}) I I ® 1 I I 1

i I

1 1 ~ 14

I I

• Opposite face

The test procedure used was based on the NBR 8949 (1985) code - Structural ma­sonry walls - Compressive strength testo Load increments of 40 kN (Iess than 10% of the expected failure load) were used, with loading divided into three stages:

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• In the first stage, three load increments were applied, followed by unloading to zero;

• In the second stage, after reaching 120 kN (Ioading of the first stage), two 10-ad increments were applied up to 200 kN (Iess than 50% of the expected fai­lure load) was reached, followed by unloading down to zero.

• In the last stage, after reaching 200 kN, incrementai loads were applied until failure of the panel occurred.

At each increment, the load levei acted on the wall for 5 minutes or more. The loads, the shortenings and the sags were, thus, recorded at the end of this period. Figure 6 shows the diagram that illustrates panel loading while figure 7 gives an overall view of the testo

Figure 6. Diagram af panellaad. Figure 7. Overall view af the testo

3725cm 455an 3725cm

Steel beam 1 I ~ II I I

"" I I

I I

§ I I

I I I ~ I I

I I I I I

I I I I I

91 em , 119 em

Fronl-view Side-view

3. NUMERICAL ANAL YSIS

3.1. Modelling with finite elements

The walls were discretized to model with finite elements, simulating the blocks, the mortar joints and the bond beams, using the modulus of elasticity of the block and mortar obtained experimentally. The modulus of elasticity of the bond beam was estimated by the expression given by the NBR 6.118 (1978) code. The finite element software program used was ANSYS 5.5, and only a linear analysis of the problem was made.

The nodes translations at the bottoms of the panels were restricted in the x, yand z directions. Nodes coupling was done at the intersections of the walls, i.e., the

same translations and rotation were imposed on the nodes of this region that had the same co-ordinates. As for the results, the displacements obtained referred to the middle plane of the element. The stresses were those located either at the top, the bottom or the middle plane of the element.

Loads were applied only in the area between the flanges in the form of a load dis­tributed by unit of length. In the numerical modelling, the loading used had a 10-ad of 280 kN, which corresponds to 60% of the theoretical failure load (460 kN).

This value was adopted because it is a stage of the test which serves for future comparison with the experimental results, and because it was believed that the masonry would still show a linear behaviour. HENDRY et aI. (1981) indicate that masonry can be considered linear material up to 75% of the failure load. Table 1 presents the values used in modelling both the series 1 and the series 2 panels. The numerical results of series 1 and 2 were almost the same, for which reason only the results of the series 1 panels are shown.

Toble 1. Volues used in the modelling.

E_, , 802,6 kN /cm' Egtout 3000 kN/cm'

v_, 0,25 V groul 0,20

E"""" 1090 kN/cm' Element thickness 7cm

V rnort., 0,20 Loading' 3,07 kN/cm

Note: 'related to the net area, ' only main wa ll

3.2. Vertical displacements

Figure 8 presents the results obtained from the numerical modelling of vertical displacements for a 280 kN load. The figure shows that the displacements of the points of the main wall in the upper region (close to where the load was applied) are far greater than the flange displacements. On the other hand, the main wall and flange displacements in the lower region even out.

The results obtained from the series 1 and 2 models are shown in the graph of figure 9, with the vertical displacement values of the main wall (or web) and the flanges along the height of the panel. These displacements refer to the same ver­tical line along which the measurement points of the test were located (see fi­gure 5). An observation of figure 9 shows that, in the no. 2 series, due to the presence of the bond beam at half height, the main wall and flange displace­ments are slightly smaller than those obtained for the no. 1 series. It can be ob­served that initially the displacements in the main wall are greater than in the flange, and that the difference between them gradually reduces until, in the 10-wer half of the panel, the displacements become almost the same. The same be­haviour can be observed in the two series except for the region of the interme­diate bond beam.

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Figure 8. Vertical displacements (y direction).

Ois.JllIcemenly (em)

• . O,D613J 1::1 . 0,05452 0 , 0,04110 0, 0,04089

DO : ~ :~~~~ . 0.02044

CJ . 0 ,0 1363 CJ . 0,00682 . 0

3.3. Normal vertical stress

Figure 9. Vertical displacements along the height of the panel.

240

Ê 200 !:!. ~ 160

~ ~ 120 :5 Õ 80

~ .~ 40 J:

Vertical displacements (F=280kN)

O~--~---r---.----~--~--~---.

-0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07

Displacement (em)

The distribution of normal vertical stresses (sy) in the panels are shown in figure 10. The values refer to a 280 kN load, and the stresses relate to the net area. This figure clearly shows that bending in the flange occurred at the point where the internai face was more strongly compressed than the externai one; tension can even be seen in the upper region (the last 2 rows) of the externai face. Also in the main wall, as expected, there was a natural concentration of compressive stresses in the region where the load was applied

Figure 11 illustrates the distribution of normal vertical stress in the main wall (web) and flanges along the height of the pane!. The values correspond to the sa­me vertical line of the points instrumented in the testo The flange stresses were measured on their externai faces in order to observe the most significant diffe­rences in stress. This figure shows a minor tension in the upper region of the flan­ge and the high compression stresses in the ma in wall . These high compression

Figure 10. Vertical normal stress.

1 z/ ........... :t

s,,,,. ,, (Io:Klem2)

- ~ :~!~ : 0 , 0,)681 O O'W,)8

~: ~~!: CJ ~:~ DO.oG91 _ O,U20

Figure 11. Oistribution Df vertical normal stress along the height of the panel.

Ê ~ .. a . '" o :g, .;; :J:

240

200

160

120

80

40

Normal vertical stress (F=280kN)

0.00 ·0.05 -0.10 -0 .15 -0.20 -0.25 -0.30 ·0 .35 -0.40 -0.45

Stress (kN/cm2)

stresses correspond to that of an isolated wall with the same length as the main wall, which is equivalent to a stress in a net area of 0,44 kN/cm2 for a 280 kN 10-ad. Thus, it is to be expected that rupture of the panel occur in this upper region with a failure load equivalent to that of the isolated wall. This result is in agree­ment with the test results obtained by SINHA & HENDRY (1979), which showed no gain in strength in the walls with flanges in comparison to the isolated walls due to a failure located in the main wall.

As interaction between the walls appears, so do the differences of the stress de­crease along the height of the pane!. Figures 10 and 11 clearly show uniform stress in the lower half of the panel, which means that it functions as a single group of walls . This behaviour is confirmed by the stress in the net area of the 10-wer region, obtained by numerical modelling (approximately 0,16 kN/cm2 - 1,6 MPa), which is very close to the stress calculated by the process of isolated groups of walls (0,167 kN/cm2 - 1 ,67MPa), consisting of the uniform distribution of the load throughout the entire area of the H-shaped pane!.

3.4. Shear stress

Figures 12 (flanges) and 13 (main wall) show the shear stress, which is also rela­ted to the net area and to a vertical 280 kN load, similarly to the previous ones. These figures reveal that the shear stress, as expected, concentrates in the region of the intersection. Again, the greatest stresses occur in the region of the bond beam in the top row. Both figures 12 and 13 also indicate that the stresses in 10-wer region of the panel are practically inexistent, indicating that ali the loads transferred from the main wall to the flanges concentrate in the upper half of the

Figure 12. Shear stress in the flanges.

Stress xy (kN/cIIl2)

• . 0,17968 0 .0,13915 0 . 0,09982 0. 0,05990 0 . 0,01991 0°,01991 O 0,05990

O 0,09982 0,13915

• 0,11968

Figure 13. Shear stress in the main wall.

y

z~ Stress ry

(kN/cm2)

• . 0,35835 c::::J . 0,21811 0. 0,19908 0 .0,11945 0 .0,03982

O ~:~~~:~ O 0,19908 O 0,21811 • 0,35835

150 1

7502

F/2 F/2

-0.02 0.00

Shear stress

..... flange_series2

-+- main_series2

......... main_series 1

-+-flange_series1

0.04 0.06 0.08 0.10

Stress (kN/cm 2)

Figure 74. Detail af intersectian. Figure 75. Shear stress in measured regian.

panel. The shear stress in the flanges is 50% less than in the main wall because the resistant area in the flange is twice the size of the resistant area in the main wall (see figure 14).

Figure 15 shows the behaviour of the shear stress in the instrumented region and compares the results of the two series. The maximum stress occurs in the upper region and tends to reduce to zero in the lower region, with a disturbance appe­aring only in the region near the base of the panel. The behaviour of the two se­ries is practically the same, the only difference being the region located dose to the bond beam in the intermediate row in the no. 2 series.

4. EXPERIMENTAL ANALYSIS

4.1. Strength

According to the numerical analysis discussed in the previous item, the behaviour of the two series is practically the same. Therefore, an analysis is made considering the panels of the two series as a single set. Table 2 gives the failure load values, the stresses calculated considering the main wall separately and the entire group. The mean values, standard deviations and variation coefficients are also shown.

Table 2. Failure laad and stress values.

Test F,." ,,, (kN) Isolated stress (Mpa) Group stress (Mpa)

1.1 490 7,70 2,92

1.2 480 7,54 2,86

1.3 560 8,80 3,34

2.1 440 6,90 2,64

2.2 440 6,90 2,64

2.3 390 6,12 2,34

Mean: 467 7,32 2,78

Varo Coef. 12,4% 12,4% 12,4%

The mean failure load of 467 kN was very close to the expected theoretical load of 460 kN, with a variation coefficient of 12,4% that was perfectly acceptable in view of the small number of tests that were carried out. This result is in agree­ment with that obtained by SINHA &: HENDRY (1979), in which the failure load of an H-shaped panel is the same as that of an isolated wall of the same length. As can be seen, the values of the no. 1 series are higher than those of the no. 2 series; however, this was expected since the prism tests of two of the no. 1 se­ries blocks showed a higher compressive strength than those of the no. 2 series. Considering the two series separately, series 1 shows an average load of 510 kN (11 % higher than the theoretical value) while the mean load for series 2 is 423 KN (9% below the theoretical value). The mean strength obtained for the panel of the no. 1 series is 20% higher than that found for the no. 2 series, and the mean strength for the two-block prisms is 30% higher, indicating that these re­sults are coherent.

The first cracks always appeared in the panel's upper region close to the in­tersection and were usually tilted, with a tendency to approach the interfaces, indicating that they were caused by shear stress. The numerical simulation described under item 3.4 revealed that the greatest shear stresses occurred in this area, indicating agreement between the experimental and numerical re­sults.

4.2. Strain properties

It was decided to relate the strains and displacements to group stress (load spre­ad throughout the entire H-shaped panel) beca use the numerical simulation re­vealed that, beginning from the lower half of the panel, the stresses were uni­form, and also due to the preliminary tests, which showed that the readings of the displacement transducers in the lower region of the panel were close, confir­ming this uniformity. Transference of the load from the ma in wall to the flanges occurred in the upper region.

The modulus of elasticity of the masonry panels of the two series was initially de­termined considering only the average readings taken in the lower region (flan­ges and main wall), based on the group stress, as mentioned earlier. The regions in the diagram showing stress vs. strain, which clearly show a loss of linearity, we­re disregarded. The average modulus of elasticity was 10732 MPa, with a 5,5%va­riation coefficient. The ratio between the modulus of elasticity of the masonry and the compressive strength of the 2-block prism was 850 for the no. 1 series and 1200 for the no. 2 series. These values are close to the value long recommended by the ACI 530-92 (1995) code, which is 1000. Figure 16 presents a typical dia­gram of stress vs. strain, which clearly shows the linearity of this phenomenon. Fi­gure 17 provides a general view of the stress vs. strain behaviour at ali the mea­sured points. The numbering of the instrumented points is the same as that used under item 2.5.3.

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As can be seen in figure 17, the no.l series shows a linear behaviour with an ave­rage loss of linearity of 68% of the rupture value in some load stages before the actual failure. The loss of linearity in the no. 2 series occurred at a stage closer to the failure load, i.e., at an average of 82% of this load. However, the mean load at which the theoreticalloss of linearity occurs is the same for the two series (347 kN).

The loss of linearity is associated to cracking. In some cases (tests 1.1, 1.3, 2.2 e 2.3), visible cracking in the panel faces appeared only in the stage subsequent to the loss of linearity, indicating internai cracking. In the no. 2.1 test, however, the first apparent crack occurred in the previous stage, but to a degree that was in­sufficient to cause loss of linearity. It should be pointed out that this non-linear phase begins on average with a load of 75% of the failure load, which is the sa­me value indicated by HENDRY et aI. (1981). For vertical loading in a service si­tuation (approximately 20% of the failure load) the behaviour of the masonry can be considered linear.

The loss of linearity of the masonry panel is also associated to the separation that occurs in the upper region due to cracks appearing in the intersecting region . This

Figure 16. Diagram af typical stress vs. strain.

·2.50

f -2.00

~ ili -1.50 ~

! · 1.00

Diagram of stress vs. strain - Test 1-2

y = 9952.4x + 0.2179

R ' = 0 .9931

" o i5 -0.50

-+- LOl.fver average

0 .00

O.OOE+OO -1 .00E-04 -200E-04

Slrain

Figure 17. Typical behaviaur af the tests.

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0 .00

Group stress (MPa)

Test 1-2

2.ooE-04 o.ooE+oo -2.ooE-04 -4.ooE-04 -6 .ooE-04 Slrain

-3.00E-04

-+-Point01 ____ Point 02

Point03 ~Point04 __ Point05 ~Point06

-+-Point07 -Point08 _ Point09 -+- Point10

Point 11 Point 12

--M- Point 13 Point 14

__ Point15 Point16

_Point 17 -+- Point18 -+- Point19

Point20

Figure 78. 8ehaviour of the upper region.

Test 1-1 (Upper region)

Group stress (MPa) -3.00

-+- Point01

-2.50 --=~~--"F'-,tI-'--- ("----7<:=#-~.-.-_______ Pcinl 02

Point 03

-2.00 ------F"'-"i~.._..I,__.i.-_v'__~____;;;>__"':..,..._""-------"* POlnt 04

-.-PointOS -1.50 t"V""'----------~ Paint 06

-1 .00 ___ ----I-_-.r~~~~----------f--Pomt07 - Point08

-0 .50 ----+----1t 114Ui"------------__ Pcinl 19

Paint 20 0.00

2.E-04 O.E+OO -2 .E-04 -4.E-04 -6 .E-04 -B.E-04

Strain

phenomenon was more clearly visible in the nO.1 series tests because there was a larger interval between the loss of linearity and the rupture. Figure 18 presents a graph corresponding to the readings of the points located in the upper region. Points 1, 2, 3 and 8 are related to the nO.1 flange, points 6 and 7 refer the nO.2 flange and points 4, 5,19 and 20 are positioned in the main wall . This graph cle­arly illustrates the moment at which the masonry ceases to behave as a linear ma­terial (see points 06 and 19, for a 1,6 MPa stress). Figure 18 also shows that, whi­le the readings of points 6 and 7 (no. 2 flange) decreased, even reaching a state of stretching, the readings of points 19 and 20 (main wall) showed increased va­riation rates. This effect occurred predominantly in one flange. This stretching in­dicates that the flange in the upper region no longer absorbed any portion of the load. Thus, the main wall began to absorb the entire additional portion of load, causing the readings to show increased rates. This analysis confirmed the separa­tion of the nO.2 flange from the main wall.

5. COMPARISON BETWEEN NUMERICAl AND EXPERIMENTAL RESUlTS

The main parameter for comparison between numerical analysis and experimen­tai results is vertical displacement, which was measured in our test. Vertical dis­placements were determined using the finite element ANSYS 5.5 software pro­gram at the same measured points, and these displacements were compared with respective average values obtained in the testo Table 3 presents those results . It should be pointed out that the numerical analysis values for both the nO.1 and nO.2 series were practically the same. The values of the nO.1 series were therefo­re chosen for comparison . These values indicate a good correlation between the behaviour of the panel in the numerical e experimental analyses. The vertical dis­placements in the flanges and main wall of the numerical analysis are the same in the panel's lower region and our test results confirmed this behaviour, Le., the average ratio between the displacements in the flanges and in the main wall was 0,975 . As for the upper region, the numerically obtained vertical displacements in the flanges were approximately 62,2% of the displacements in main wall, whi­le the ratio of those displacements obtained in the test was 48,7%.

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Table 3. Numerical and experimental vertical displacements.

Lower region Upper region

Flange Main Flange / Flange Main Flange / 6 (mm) 6(mm) Main 6 (mm) 6 (mm) Main

Mean 01 lhe lesls ·0,086 ·0,090 0,975 ·0,066 -0,135 0,487

Coei. Varo -1,6% -11,9% 13,9% -20,2% -7,9% 19,60

ANSYS -0,119 -0,119 1,000 -0,096 -0,154 0,622

Mean/ ANSYS 72,6% 75,5% 97,5% 68,6% 87,8% 78,3%

The vertical displacement values were not closer only because of the difference bet­ween the modulus of elasticity of the numerical analysis and that of the experimental one. The tests came up with an average modulus of elasticity of 10732 MPa for the masonry (in relation to the net area), while the values used in the numerical analysis were the modulus of elasticity for the block and mortar. The procedure proposed by PANDE et aI. (1989) could be used to estimate the mean equivalent value for the mo­dulus of elasticity of the masonry, which results in 8244 MPa (in relation to the net area). This value is equivalent to 77% of the estimated modulus of elasticity based on the test results. Table 4 presents the values of the vertical displacements obtained nu­merically, corrected for the modulus of elasticity obtained in the experimental analy­sis, i.e., applying a factor of 0,77. Table 4 shows that the correction of the modulus of elasticity led to an excellent correlation of the values of the numerical and experimen­tai vertical displacements, indicating the possible need for improved procedures to de­termine the modulus of elasticity of blocks and mortar for use in numerical models.

Table 4. Experimental and corrected numerical vertical displacements.

Lower region Upper region

Flange Main Flange / Flange Main Flange / 6 (mm) 6 (mm) Main 6 (mm) 6 (mm) Main

Mean 01 lhe tests -0,086 -0,090 0,975 -0,066 ·0,135 0,487

ANSYS -0,092 -0,092 1,000 -0,074 -0,119 0,622

Mean/ ANSYS 94,1% 97,8% 97,5% 88,8% 113,8% 78,3%

With regard to normal vertical stresses, the tests demonstrated the uniformity of stresses in the lower region of the panel, which was also observed in the numeri­cal analysis. Greater strains were also observed in the upper region of the main wall, indicating that the stresses here were greater than those in the flanges. Crac­king was also located in the region with the greatest shear stress, i.e., the region close to the main wall/flange intersection. The tests also revealed the linear beha­viour of the masonry up to 75% of the failure load, confirming the findings of HENDRY et aI. (1981) and indicating that, in th is case, linear analysis is satisfactory.

6. CONClUSIONS

The failure load found for the tested panels refers to the strength of the main wall considered to be isolated, which showed a strong concentration of stress in the

upper region. This wall must first carry the entire applied load before any loads are transferred to the flanges. This finding is in agreement with that of SINHA & HENDRY (1979), who carried out similar tests to investigate the effects of stiffness.

The behaviour of the panels both with and without a bond beam in the interme­diate row was practically the same, which indicates that, in cases such as this, in­termediate bond beams exert little influence on the distribution of vertical loads. Homogenous vertical displacements in the lower region of the panel from the ini­tialload stages to about 75% of the failure load were observed in the tests. This uni­formity confirms the interaction in the pane!. It is worth pointing out that masonry in a service situation works with approximately 20% of the failure stress. Therefore, to determine the actions in service it is advisable to consider the interaction.

An analysis of the diagrams showing stress vs. strain of the panels clearly shows a li­nearity of up to 75% of the failure load, which confirms the findings of HENDRY et aI. (1981). In the upper regions of the panel one can observe that the ma in wall ca­rries a heavier load than do the flanges, since the strains obtained for the main wall are consistently greater than those in the flanges. In the lower region, the strains in ali the walls of the panel are practically the same, indicating uniform stress.

Although the numerical analysis was carried out only in a linear regime, a good correlation was found with the behaviour of the panel, indicating the regions with normal stresses and those with concentrated shear stresses. The numerical analy­sis was carried out using the values of the modulus of elasticity of the block and mortar separately, generating an equivalent modulus of elasticity for the masonry that was smaller than the one observed experimentally. This finding indicates the need to improve the procedures to correlate the modulus of elasticity of blocks and mortar determined experimentally and the values for use in numerical mo­delling. This need will be the subject of investigations in future work. It should be pointed out that the correction of the modulus of elasticity used in the numerical analysis, based on the homogenisation theory, led to an excellent correlation of the values of vertical displacement along the height of pane!.

7. ACKNOWlEDGEMENTS

The authors gratefully acknowledge the support of the Brazilian research funding institutions CNPq - National Council for Scientific and Technological Develop­ment, for the scholarship awarded, and FAPESP - São Paulo State Research Sup­port Foundation, for its support of the experimental work. Special thanks are al­so due to Cerâmica Selecta for the donation of the blocks and access to its technical reports .

8. REFERENCES

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