Structural Analysis of Historical Constructions - Modena, Lourenço & Roca (eds) © 2005 Taylor & Francis Group, London, ISBN 04 15363799

In-plane shear and tensile strength tests of small brickwork specimens

L. Malyszko Faculty of Technical Sciences, University ofWarmia and Mazury in O/sztyn, Po/and

ABSTRACT: Under monotonic force control several strength tests were performed on coupon-size masonry panels (dimensions mostly 520 x 520 x 120 mm) in order to get information on the in-plane response ofbrick­work walls. Ali specimens were made up ofpolish standard clay bricks (250 x 120 x 65mm) and a 1:0.5:4.5 portland cement-lime mortar. The response to direct shear was investigated by means ofboth the standard triplet test and the test with the predetermined single plane of the shear failure. In the latter test there is not need to measure the strength at a number of the precompression leveis in order to predict the initial shear strength. Tests with the single shear plane normal to the bed joints were also performed. The diagonal compression test has been chosen to simulate in-plane shear phenomenon related to the diagonal cracking. The test was carried out on ten masonry panels capturing the failure modes and the splitting strength. Additionally, the various strength characteristics of bricks and mortar were investigated. The strength cri teria related are also discussed. For the experimental data the simplest form of the cri teria are presented in the shear-precompression stress state. The three basic failure modes are distinguished: shear slip along the bed joints, diagonal tension cracking and shear compression fai lure. Some remarks on taking advantage of the strength parameters from triplet and diagonal compression tests are also given.

TNTRODUCTION

A large number of buildings are constructed with masonry walls that significantly affect the distribu­tion of lateral loads to various parts of the building if the tensile and shear strengths of masonry are suf­ficient. Unfortunately, the combination of relatively low tensile and shear strength and brittle behavior results in masonry being susceptible to cracking. In addition to the potential for developing horizontal cracks corresponding to the shear slip along the bed joints, various forms of diagonal cracking can occur. These important in-plane failure modes are the crucial effects in the infill panels and the shear wall designo In loadbearing masonry buildings, shear walls carry vertical loads and resist the lateral in-plane loads due to wind or earthquakes. This combined loading creates a biaxial tension-compression stress state in the wall leading to cracking when the tensile or shear strength of masonry is exceeded. Therefore, although unre­inforced masonry is primary designed to withstand compression, it is important that these types offailure can be properly predicled for a complete description of the material behavior.

In lhe present experimental work, which was per­formed on coupon-size masonry panels under mono­tonic force control, severa I tests have been carried out on lhe same masonry panels in order to get information

291

on the in-plane response of brickwork walls under lateral loads.

In order to predict properly the masonry shear capacity, it is necessary to first identify the most anti c­ipated failure mechanism and next to formulale the strength criteria applicable to the specified mecha­nism. In the paper the simple forms of the failure criterion are proposed that are taking advantage ofthe strenglh parameters obtained. The strength cri teria can be represented by three independent analytical expres­sions, each being the condition of limit equilibrium of masonry applicable to specified failure mechanism. The failure surfaces in the shear-precompression stress space are similar to those known from the appropriate literature.

The paper sums up experimental and theoretical research performed at the University in Olsztyn on solid clay brick masonry. The results have been parlly published by Malyszko (2002, 2003).

2 MATERIALS CHARACTERIZATION

Masonry mechanical properties depend on the charac­teristics of the constituent elements (bricks and mor­tar), as well as on the workrnanship and the interaction within the assemblage. Thus, an extensive program of tests, ranging from the units to the small assemblages

Table I. Synthesis of the additional programo

Mean Number strength

Material Type oftest of tests [N/mm2 ]

Brick Standard 6 27. 1 250 x 120 x compression 65mm3 Flexural tension 6 3.86

(modulus of rupture)

Splitting tension 6 2.84 Direct tension 12 0.60 One-plane shear 10 3.21 Dual-plane shear 10 0.85

Mortar Compression 6 8.50 Flexural tension 6 2.2 1

Triplet Sliding along 3 x 4 0.53 mortar bed joints 0.54

Masonry Standard 5 14.31 compression

Horizontal 5 14.09 compression

scale, was additionally performed. However, accurate prediction of assemblages behaviors using properties of the constituent materiaIs is rather hard to do due to the interactions between the individual materiaIs being too complex to be accurately modeled using a few basic material properties. Table I gives the scheme of the whole additional program with mean strengths obtained.

The main mechanical properties of the bricks have been determined by axial compressive and tensi le tests. Knowledge of the tensile strength of bricks was expected to be important for the development of a proper understanding of fa ilure mechanisms in the diagonal compression test. When the fai lure plane passes through the bricks, as can be expected for dia­gonal cracking and for tension parallel to the bed joints, the in-plane tensile strength should be affected by the tensile strength of the brick. Therefore, apart from the modulus of rupture test, direct tension and splitting tests were also preformed to obtain a com­para tive measure of tensile strength. In the splitting test, the nearly constant tension developed over the centra l part of the brick height between the line loads is closer to a direct tension than to a flexural tension condition. However, the calculated average strengths tend to be much higher (almost five-times) than the direct tension results but with much less variability. The flexural tensile strength ofbricks, also denoted as modulus of rupture, is 36% higher than the splitting tensile strength.

Although a certain amount of testing of shear in masonry units may be essential fo r verification of strength criteria and fa ilure mechanism, there has been

a) b)

Figure I. Set-up of shear tests on single brick specimens: a) two planes ofshear fai lure, b) single plane ofshear fail ure, I - brick, 2 - shear planes.

little attempt to standardize procedures. Results in Table 1 are given according to the experimental set-up from Figure I. Mean values indicate much higher shear strengths in the single plane tests than those obtained in the dual-plane tests. This is because of different fa ilure mechanisms. In the dual-plane shear test, the fa ilure mechanism is strongly influenced by flexural tensile stresses .

3 STRENGTH OF PANELS IN DIRECT SHEAR

3. 1 Triplet tests

Triplet tests are commonly used as a standard test to obtain experimental data relating to masonry joint shear strength . Here, triplet shear samples were used according to Polish standard, which is quite similar to Eurocode 6 (1996). In order to investigate the local interaction between mortar and bricks, three series of sliding tests were preformed on four triplets (12 specimens in total). Interpolating the experimental points obtained at three leveis of confining compres­sive stress - 0.2,0.6 and 1.0 N/mm2 , it was possible to detect the parameters describing the strength for shear slip along mortar bed joints. According to Eurocode 6 and Polish standard the Coulomb equation represent­ing the dry frict ion mechanism during joint slidi ng is:

fI' = f vo + lia c = 0.53 + 0.54 a c (I)

The tests were performed by keeping constant the con­fining compressive load normal to the bed joints and by increasing monotonically the in-plane loads paral­lei to the joints in order to evaluate the mortar-brick friction coefficient !1- and the shear strength for null compressionj~o . Assuming that under pure shear the limiting strength is defined either by the diagonal ten­sile strength ofthe mortar (equals to 0.46 N/mm2, that is 21 % ofthe flexural tensile strength) or by the direct tensile strength of the brick (0.60 N/mm2), it can be seen that the cohesion value Uvo = 0.53 N/mm2

) is in good agreement with this assumption.

292

Figure 2. Shear strength test with the predetermined single plane of a failure: a) for loading tangential to the bed joints (Cz), b) for loading normal to the bedjoints (Cx).

3.2 Tests with the predetermined single plane 01 shear lailure

Apart from triplet test, the other test has been used to obtain the initial shear strength related the adhe­sion and shear-friction resistance between the mortar and the units. Although the triplet test is assumed to be performed without a flexural tension due to the precompression, the failure mechanism is yet influ­enced by flexural tensile stresses, especially at the low precompression leveI. Besides, in the triplet test there is need to measure the strength at a number of the precompression levei in order to obtain the initial shear strength, i.e. the strength for null precompres­sion. Alternatively, the response to direct shear may be Investlgated by means of the test with the prede­termined single plane of the shear failure, similar to that from Figure I b. [n the test there is not need to measure the strength at a number of the precompres­sion leveis in order to predict the initial shear strength. However, that strength is the only value obtained. The test may be performed both for tangential and normal to the bed joints loading, Figures 2a and 2b, respec­tlvely. Sh~ar strength may be calculated as a ratio Ps / A, where A IS the average area of the cross section along the failure plane and Ps is a shear force caused by the applied load P. The specimens with the dimen­sions 520 x 520 x 120 mm were used, although the test may be performed on a triplet if a suitable loading

Table 2. Tests with predetermined single plane of shear failure .

Cx (vertica l) and Cz (horizontal) shear strengths

Cz P MAX Cx No. PMAX [kN] [N/mm2] [kN] [N/mm2]

I 55 0.83 68.5 1.00 2 50 0.75 73.0 1.07 3 38 0.57 68.5 1.00 4 40 0.60 90.5 1.32 5 47 0.70 90.3 1.32 Mean value 0.69 1.14 Standard deviation 0.11 0.17 Coefficient of variation 0.15 0.14

rig is made. Ten specimens were used in total. The maximum values of applied load P and the ca1culated strengths are given in Table 2. . [t is expected that both the shear strength for tangen­

tlal and normal loading are related to the initial shear strength from the triplet test and to the shear strength of brick, respectively. However, the shear strength for tangential loading (Cz = 0.69 N/mm2) is higher then that obtained from the triplet test (fvo = 0.53 N/mm2).

On the other hand, assuming that under direct shear for loading normal to the bed joints the limiting strength is defined by the shear strength of bricks in three courses, i.e. is equal to 1.2 N/mm2 = 3.21 x 3 x 65/520, it can be seen that the obtained strength value (Cx = 1.14 N/mm2) is in good agreement with this assumption.

4 DIAGONAL COMPRESSION TEST

4.1 Test method

The RlLEM standard LUMB6 (1991) describes test method to determine the capacity of masonry under conditions that can produce diagonal cracking. The diagonal compression test, shown in Figure 3 for the brickwork panels made of solid clay bricks, is based on subjecting a square section of wall to diagonal compression through steel or polymer concrete shoes (loading plates) on two diagonally opposite corners ofthe specimen. The loading shoes should be dimen­sioned such that the sides of the vee are one tenth of the height of the specimen (i.e. the length of the side). The specimen should conta in sufficient units (a minimum of four units wide) to be reasonably repre­sentative of finished masonry. This test can be carried out with standard equipment. The strength parameter Spt is calculated from the equation:

S pt = 0.707 PI An (2)

293

where P = the load value at failure; Ali = the net area ofthe specimen = (l + h)/2 t n; t = the wall thickness and I and h the face dimension; n = the fraction ofthe gross area of the specimen that is solid.

This corresponds to the principal tensi le stress in the centre of the panel assuming isotropic elastic properties.

Similarly, ASTM (1988) describes test method based on a 4 fi ( 1.2 m) square section ofwall allowing axial load normal to the bed joints to be also applied. The shear capacity if significantly affected by the leveI ofaxial compression, which has the effect of delay­ing tensile cracking and enhancing the shear-friction component ofthe shear strength.

Due to some difficulty of relating the strengths and behaviors from diagonal tests to diagonal crack­ing in walls, there are other tests, Iike racking tests or splitting tension test of disks and square masonry assemblages. In the racking tests, lager specimens have been used consisting ofpanels several bricks in length by several courses in height. The results of these tests depend rather critically on the form of the specimen and method ofloading. They are also re latively expen­sive to carry out and requi re a special loading rig. The spli tting tension tests of disks or square masonry assemblages have been used to study the parameters affecting in-plane tensile strength.

4.2 Results

The diagonal compression tests were carried out on ten 520 x 520 x 120 mm masonry specimens (labeled as PI-PIO), made from polish standard clay bricks and a 1:0,5 :4,5 portland cement-Iime morta r. Tests were per­formed under monotonic force control. Both vertical and horizontal displacements were measured on the two ma in faces of specimens (Fig. 3). The results are given in Table 3. The average value ofthe failure load, calculated on the 8 samples according to the equa­tion (2), is equal to 93,500 N and results in the average value of diagonal tensile strength equal to 1.0 I N/mm2 .

The considerable higher values ofthe fai lure load were

p

Jc:=:::::J[

11

11

11

-

Figure 3. Experimental set-up for the diagonal compres­sion test

obtained in two tests (P2 and P4). This is because of different fai lure mo de relating to a formulation ofthe diagonal compression strut between the loading shoes on opposite ends of the diagonal. These values were rejected and not taken into consideration, since they are likely connected to the improper test arrangements. As one can see in Figure 4, where the representative force-strain diagrams are presented fo r specimen P6 (sphtting failure) and P4 (compression strut), the ver­tical and horizontal strains (SI and S 2 respectively) are smaller at the same load leveI if a compression strut is likely to form (Fig. 4b).

Table 3. Resu lts of diagonal compression test

Diagonal tensi le strength Spl [N/mm2 ] and fai lure load P [N]; I x h = 520 x 520 mm

Specimen P [N] Spl

PI 100,000 1.09 P2 150,000* 1.63* P3 108,000 1.1 7 P4 170,000* 1.85* P5 98,000 1.06 P6 100,000 1.09 P7 80,000 0.87 P 8 96,000 1.04 P9 93,000 1.0 I PIO 71,000 0.77 Mean value 93,500 1.0 I Sample standard dev iation 12 0.02 Coefficient of variation 13%

* Formulation of the compression strut; values of both specimens were rejected.

z o .. ... ... o r-.

a)

b)

-300 -200

Specimcn P6

-lOO

Strain [/lm/ml

SpecimenP4

o

I tEV1 1 -150 -100 -50 O 50 100

Strain [/lm/m]

100

~ ~

Figure 4. Force-strain diagrams: a) for lhe case of combi­nation of shear slip along bed joints and diagonal tension fai lure, b) for the case of compression strut fai1ure.

294

4.3 Failure modes

The diagonal compression tests tend to produce three basic failure modes (Fig. 5). In general, the stress field tends to force the cracks to follow the line of action of the compression load. The splitting tension stress results in diagonal tension at 90° to the line load. Typ­ical failures are shown in Figure 5b and 6a. In this case, the tension crack may have a rougher surface as the weakest path along combinations of head and bed joints and through units is followed to some extent. However, depending on the path of least resistance, the combination of diagonal splitting and step-pattern sliding along the mortar joints may occur (Fig. 5c and 6b, c). For practical purpose this is the more important

a) b) c) d)

++++ Figure 5. Typical crack pattem of masonry panels: a) the­oretical splitting failure, b) diagonal tension, c) combina­tion of shear slip along bed joints and diagonal tension , d) compression strut.

Figure 6. Experimental failure modes of masonry panels: a) diagonal tension, b) and c) combination ofshear slip along bed joints and diagonal tension, d) compression strut.

case related to diagonal tension in the wall, because the shear mode offailure will be either shear slip along a bed joints or a stepped diagonal crack by breaking the bricks or the bond along a combination of head and bed joints. This type of failure may be captured in the diagonal compression test. In some cases, the loading shoes on opposite ends of diagonal can transfer com­pression load through a fairly large compression stmt formed after the appearance of diagonal cracks (Fig. 5d and 6d). This compression stmt can carry higher loads than those required to produce diagonal cracking, as it happened in the case of specimens P2 and P4.

The diagonal compression test belongs to the indi­rect test methods and is easy to perforrn and yields reliable results. Although not difficult to carry out in standard testing machine, it seems that the application ofthis form oftest has not been fully explored.

5 DIRECT TENSILE STRENGTH OF PANELS

The tensile behavior of masonry can be also inves­tigated by direct methods. They are characterized by applying directly the tensile force to the specimen. The main drawbacks of direct tests are their sensitivity with respect to eccentric application oftensile force and to shrinkage. For direct tensile loading perpendicular to the bedjoints, the masonry strength is generally under influence of the relatively low tensile bond strength between the bed joint and the unit. In the paper the tests were performed for direct tensile loading par­alieI to the bed joints. The specimens (dimensions 520 x 215 x 120mm) were regained from the tests with predetermined single plane of shear failure (see section 3.2). In the case of direct tensile loading paral­leI to the bed joints, two different types of failure are possible, depending on the relative strength of joints and units (Fig. 7). In the first type of failure cracks zigzag through head and bed joints, in the second one cracks mn almost vertically through the units and head joints. The failure load and the calculated strengths are given in Table 4. The tensile strength were calculated as a ratio of the failure load and the area A, where A = 215 x 120 mm2

.

Observations of the behavior of masonry in tension have been recorded in the literature (see Schubert 1997 for example). The simple formulae have been deduced

Figure 7. Failures modes for masonry under axial loads along the bed joints.

295

Table 4. Results of determination of direct tensile strength.

Direct tensi le strength [N /mm2) and failure load

Specimen Load [N) Strength

I 43,000 1.67 2 34,500 1.34 3 52,500 2.03 4 38,000 1.47 5 37,500 1.45 6 46,500 1.80 Mean value 42,000 1.63 Standard deviation 6,700 Coefficient of variation 15 .9%

to determine the masonry tensile strength as the low­est value of two possible forms of failure: fai lure of the unit due to tension and shear slip along the bed joints. However, in this case none of these formulae can be applied, since they are deduced by equilibriurn, assuming that there is a uniform distribution of ten­sile stress and shear stress. The test without a vertical precompression is rather sensitive to applied load and stress peaks are likely to occur.

6 ANALYSIS OF RESULTS

Depending on the in-plane lateral and axial loads, as well on the form ofwall construction, the shear fai lure mode may be characterized by three basic mecha­nisms: shear slip along the bed joints, diagonal tension cracking and shear compression failure. In unrein­forced masonry, the f irst failure mode results from lateral shear forces exceeding the adhesion and shear­friction resistance between the mortar and the units or the floor. The diagonal tension cracking occurs either as a diagonal splitting or as step-pattern sliding along the mortar joints, depending on the characteris­tics of the constituent materiais (mortars and bricks). Both of these two modes may be captured in diagonal compression tests. The third fa ilure mode is attributed to predominance of the axial load leading to vertical cracking failure or to the more localized biaxial com­pression failure . Therefore, in order to predict properly the masonry shear capacity, it is necessary to first iden­tify the most anticipated fai lure mechanism, based on the knowledge of the involved materiais. To this end, the fai lure cri teria are needed. For practical purposes however, it is necessary that the calculation of the shear strength of a wall should not be unduly com­plicated and that related test methods should be such that they can be carried out economically and without the need for highly specialized equipment. The failure criterion commonly adopted in codes of practice for combined compression and shear re lates the strength

1" .fc 0.25

~

" ] 0.2

'" ~ 0. 15 ~ ;: 0.1

'" tl 0.05

o 0. 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I Precompression

Figure 8. The comparison of the strength cri teria for the experimental data: I - the Coulomb criterion, 2 - the principal tensile stress criterion, 3 - the compressive stress criterion.

to the compression by a Coulomb type equation (Equation 1). This relationship is in accordance with experimental resu lts at least up to a certain value ofthe compressive stress. The Coulomb criterion is related to the shear slip along the bedjoints fai lure mode. An alternative criterion may be based on the assumption that failure will be related to the attainment of a lim­iting value of the principal tensile stress (see Hendry 1997). Application of this criterion depends on being able to determine the principal tensi le stress at fai lure. Assuming that the principal tensile stress at failure is constant and equal to the diagonal tensile strength, the criterion may be written in the simplest form as:

I =S ~l + (J" C v pl S

pl

(3)

where Iv = shear strength of masonry (shear strength at fai lure), ac = precompression normal to the bedjoints. By using the diagonal tensile strength SPI> this cri te­rion is related to the shear failure mo de defined by diagonal cracking.

The third fai lure mode may be related to the princi­pal compressive stress criterion for the case of biaxial compression state (see Malyszko 2002). This criterion may be written in the simplest form as:

(4)

where!c = the compressive strength of masonry for axialloading normal to the bedjoints; nc = ratio ofthe compressive strengths for parallel and normalloadings to the bed joints, respectively.

The comparison of the strength cri teria for the experimental parameters obtained is shown in Figure 8. The plot is formatted in the dimensionless axes ac(fc andfvlf, .. The lines are drawn according to the follow­ing criteria: line 1 - Coulomb friction (Equation I),

296

line 2 - the principal tensile stress (Equation 3) and line 3 - the principIe compressive stress (Equation 4). The dash line denotes the shear failure criterion adopted from the pape r Malyszko (2002). This criterion is not discussed here. The area between the lines and lhe hori­zontal axis describes the loading conditions for which the shear strength of the wall is not exceeded. The area is similar to that developed by Mann & Muller (1985) based on consideration of the equilibrium and strength of a unit within a wall. From the comparison ofthe principal tensile strength criterion (line 2) to the Coulomb criterion (line I) for the experimental param­eters i.e. for the cohesion value/.,o = 0.53 N/mm2 and the friction coefficient J.L = 0.54 and the diagonal ten­sile strength SPI = 1.01 N/mm2 (Tables I and 3) it is seen the shear slip along the bed joints should be expected in the wall for the precompression stress bel­low about 2.5 N/mm2 . Above this value, which may be outside the range ofthe practical design, there is failure of the bricks as well of the bed joints, so, the diago­nal cracking mechanism is likely to occur. This case is beyond the validity of Equation I and the assess­ment of the shear strength should be done based on Equation 3.

[t is interesting to note that the ratio of /.'0/ SPI> i.e. the ratio of the initial shear strength from the triplet test to the diagonal tensile strength , may determine the shear failure mode. By comparing Equation I to 3 following inequality may be establish:

~> 1+4,L,2

S PI - 41' (5)

for which the diagonal cracking mechanism should be expected. [fthis inequality does not hold the shear fail­ure mode depends on the precompression leveI. Both the shear slip along the bed joints and the diagonal tension cracking are then Iikely to occur. The justifi­cation of these remarks, however, is not entirely clear since it would not appear possible to compare results from full scale tests on shear walls or panels for which small specimen strengths from triplets and diagonal compression tests are also available.

7 CONCLUSIONS

With the use of shear walls or infill walls built within a structural frame, in-plane shear and tensile strengths may be often ofprime importance in loadbearing struc­tures. Strength tests ofmasonry assemblages are used as the basis for assigning failure load and, in some cases, as a quality control measures or as a control of strengthening efficiency. Many test methods have been proposed for determining the shear strength of brick­work, including the effect of precompression. Most

of these are joint tests on small specimens, the sim­plest being the triplet type consisting of three bricks. [n applying the Coulomb type equation, problems arise from difficulty in defining the limit ofpractical design compressive stress. AIso, it could be said that con­trol test is on a joint which is not representative of conditions in a wall. Beyond the validity of Coulomb criterion, it seems that the application of the diago­nal compression test has not been fully explored. This test is not difficult to carry out in standard testing machine and uses larger masonry assemblages. The use ofthe diagonal compression test requires at present some further verification against shear wall test results.

Some problems may arise in devising a test which will reliably measure the initial shear strength - the parameter /.'0' New type of test is being currently investigated at the University in Olsztyn on the same masonry panels like in the diagonal compression test in order to predict this parameter (Fig. 2). In this test, it is not necessary to evaluate the strength with null compression by measuring the strength at a number of precompression leveIs. There is also not need to find then the va lue by extrapolating the best fit line to these results to null compression . However, the initial strength is the only value obtained. The test may be per­formed both for tangential and normal to the bed joints loading. As it is expected, the shear strength for tan­gentia I loading is related to the initial shear strength from the triplet test. However, for the experimental brickwork specimens its value is 25% higher than that obtained from the triplet test. For loading normal to the bed joints the Iimiting strength is defined by the strength of brick in direct shear.

The estimation of shear strength is clearly empiri­cally based and approximate. Shear resistance is cal­culated on the mean shear strength in the wall , whereas the stresses are not uniform and the strength is to some extent dependent on the length ofthe wall. Neverthe­less, both the strength cri teria and tests related would appear to be sufficiently well validated for practical purposes.

ACKNOWLEDGEMENTS

The author wishes to express his gratitude for the sup­port of the Scientific Committee of the University in Olsztyn, under university grant reference 0602-0214.

REFERENCES

ASTM E 519-81. 1988. Standard Test Method for Diagonal Tension (Shear) in Masonry Assemblages. Philadelphia.

EN 1996-1-1 , EC 6: Design ofmasomy strucllIres. Part l-I: General Rules for reinforced and unreinforced masonry.

297

Hendry, A. W. 1997. Shear Strength Cri teria and Related Tests for Brick Masonry. Advances in Slruc/ural Engineering Vol. 1 No. 2: 135- 141.

Malyszko, L. 2002. Failure Criteria for Masonry as Anisotropic Material. In Proc. of the 4th Intern. Conf. "AMeM": 11 1- 115. Cracow, Poland, 5-8 June.

Malyszko, L. 2003. In-plane Tensile Strength of Masonry Panels Subjected to Diagonal Compression Tests. In Proc. ofthe Loca l Sem. of IASS PC: 63-66. Warsaw-Rzeszów Dec. 5: Micro-Publisher 180 WN.ISBN-83-908867-7-4.

RILEM LUMB6. 199 1. Diagonal tensile strength tests of small wall specimens.

Mann, W. & Muller, H. 1985. Schubtragfahigkeit von gemauerten Wanden und Voraussetzungen for das Entfallen des Windnachweises. Mauerwerk-Kalender. Berlin: Ernst & Sohn Verlag.

Schubert, P. 1997. Biegezugfestigkeit von Mauerwerk. Untersuchungsergebnisse an kleinen Wandprufkorpern. Mauerwerk-Kalender: 6 11 -628. Berlin: Ernst & Sohn Verlag.

298