Masonry Walls MAAS 42(7) 09

ORIGINAL ARTICLE

Shear resistance of masonry walls and Eurocode 6:shear versus tensile strength of masonry

Miha Tomazevic

Received: 7 April 2008 / Accepted: 17 September 2008

RILEM 2008

Abstract In the case of masonry structures sub-

jected to seismic loads, shear failure mechanism of

walls, characterised by the formation of diagonal

cracks, by far predominates the sliding shear failure

mechanism. However, as assumed by Eurocode 6,

the latter represents the critical mechanism for the

assessment of the shear resistance of structural walls.

The results of a series of laboratory tests are analysed

to show that in the case of the diagonal tension shear

failure the results of the Eurocode 6 based calcula-

tions are not in agreement with the actual resistance

of masonry walls. The results of calculations, where

the diagonal tension shear mechanism and tensile

strength of masonry are considered as the critical

parameters, are more realistic. Since the results of

seismic resistance verification, based on the Eurocode

6 assumed sliding shear mechanism, are not in favour

of structural safety, it is proposed that in addition

to sliding shear, the diagonal tension shear mecha-

nism be also considered. Besides, in order to avoid

misleading distribution of seismic actions on the

resisting shear walls, the deformability characteristics

of masonry at shear should be determined on the

basis of experiments and not by taking into account

the Eurocode 6 recommended G/E ratio.

Keywords Masonry structures Seismicresistance Shear Sliding shear mechanism Diagonal tension shear mechanism Shear strength Tensile strength Shear resistance Eurocodes

1 Introduction

Masonry is a typical composite construction material,

which is suitable to carry the compressive loads;

however its capacity to carry the tension and shear is

relatively low. As a result of non-homogeneity and

anisotropy of masonry, the relationships between the

mechanical characteristics of masonry at shear and

compression are significantly different than in the case

of the homogeneous and isotropic materials. Since the

walls and piers represent the basic structural elements

of masonry structures, shear mechanisms prevail in

the case where the masonry walls are subjected to

in-plane lateral loads. Flexural mechanisms are rarely

observed. Therefore, the parameters which define the

behaviour of masonry walls at shear are of relevant

importance for the seismic resistance verification of

buildings in seismic-prone areas.

Because of specific characteristics of each constit-

uent material, it is not easy to predict the mechanical

properties of a specific masonry construction type by

knowing only the characteristics of its constituents.

The values, which determine the strength character-

istics of masonry, do not represent the actual stresses

M. Tomazevic (&)Slovenian National Building and Civil Engineering

Institute, Dimiceva 12, 1000 Ljubljana, Slovenia

e-mail: [email protected]

Materials and Structures

DOI 10.1617/s11527-008-9430-6

in materials at failure but the average values, calcu-

lated on the basis of the gross sectional areas of

individual structural elements. For example, stresses

in material at compressive failure in the case of a solid

brick are not the same as in the case of a hollow block,

although the declared strength of both units is equal.

Although the normalized values, determined in

accordance with EN 772-1 [1] are used, significant

differences exist between the actual compressive

stresses in masonry material and the design values,

obtained on the basis of the gross sectional area of the

units. Similarly, in order to simplify the numerical

procedures, the sectional stresses and forces are used

and the gross dimensions of masonry walls are taken

into consideration in the case of the structural analysis,

assuming that masonry is elastic, homogeneous and

isotropic construction material. However, the equa-

tions of the elastic theory of structures and methods of

calculation are modified in order to take into account

the specific characteristics of masonry materials.

Correlation of experimental results with Eurocode

6 [2] recommended values of parameters, which

determine the strength and deformability characteris-

tics of masonry at compression, indicates that the

values of the compressive strength f and modulus of

elasticity E of masonry can be predicted reasonably

well on the basis of the known compressive strength

of individual units and masonry mortar. However, the

experiments indicate that the relationships are not

straightforward in the case where the walls are

subjected to lateral loads and different failure mech-

anisms are possible. In this contribution, the results

of a recent study, carried out at Slovenian National

Building and Civil Engineering Institute in Ljubljana,

Slovenia, aimed at providing the values of national

parameters regarding the shear resistance of unrein-

forced masonry walls to be recommended by

Slovenian National Annex to Eurocode 6, will be

presented and discussed.

2 Behaviour of masonry walls subjected

to in-plane acting seismic loads and testing

The behaviour of masonry walls subjected to a

combination of vertical and horizontal loads depends

on the geometry of the walls (height/length ratio),

mechanical characteristics of masonry and reinforce-

ment, if any, as well as on the boundary conditions.

Besides, the behaviour depends on the level of

precompression, i.e. the ratio between the working

stresses in the wall due to gravity loads and compres-

sive strength of masonry, as well as on the direction of

action of horizontal loads (in-plane, out-of-plane).

Consequently, various types of failure mechanism are

possible. In this contribution, however, only the shear

failure mechanism of unreinforced masonry walls

subjected to in-plane action of lateral loads will be

discussed.

If the vertical compressive stresses in the wall are

low and the quality of mortar is poor, seismic forces

may cause sliding of a part of the wall along one of the

bed-joints (Fig. 1a). Sliding shear failure of unrein-

forced walls usually takes place in the upper parts of

masonry buildings below rigid roof structures, where

the compressive stresses are low and the response

accelerations are high. However, this phenomenon is

seldom observed in the buildings bottom parts,

where, typically, diagonally oriented cracks develop

in the walls when subjected to seismic loads (Fig. 1b).

Because of the orientation of cracks, the failure of the

wall in such a case is also called diagonal tension

shear failure. Depending on the quality of masonry

units and mortar, diagonally oriented cracks may

either follow the bed- and head-joints or pass through

the units or partly follow the joints and partly pass

through the units. Typical examples of diagonal shear

cracks in the load-bearing walls caused by the

earthquakes are shown in Figs. 2 and 3.

Although the resistance to lateral loads is the key

parameter, other parameters, such as deformability,

ductility and energy dissipation capacity, strength and

stiffness degradation at repeated lateral load rever-

sals, are also important for the assessment of the

seismic resistance of the structure. Therefore, decades

ago the experimental tests for the evaluation of the

seismic resistance of masonry walls have been

Fig. 1 Shear failure mechanisms: a shear sliding on the bed-joint, b shear failure characterized by formation of diagonalcracks


designed to simulate the cyclic character of lateral

loading and actual boundary restraints (for example

[37]). Such tests made possible the evaluation of all

important parameters, influencing the seismic resis-

tance of masonry structures.

Horizontal and vertical actions, which act on

individual walls in a masonry structure during the

earthquake, change in an alternate, cyclic way. Since

the wall is restrained by horizontal elements, such as

parapets, lintels and floors, which hinder its rotation

at large lateral displacements, additional compressive

stresses develop in the wall at each cycle, which

prevent the formation of horizontal tension cracks at

the walls end sections. When tested in the labora-

tory, however, the simulation of actual restraints

would increase the costs of testing. Therefore, the

walls are tested at a controlled, usually constant level

of vertical load, as well as at controlled conditions of

boundary supports either as symmetrically fixed or as

vertical cantilevers. The specimens are constructed

on a reinforced-concrete (r.c.) foundation block,

whereas vertical and cyclic lateral load act on an

r.c. bond beam, located on the top of the walls.

If unreinforced masonry walls are tested, horizontal

cracks develop at the most stressed bed-joints as a

result of low axial tensile strength of masonry, so that

rocking of the wall on the support takes place. In order

to prevent the rotation, the vertical steel ties, which

take the tension forces developed on the tensioned

side of the wall, are used in the case of the so called

racking test [8]. In the case of cyclic testing, however,

this is not the practice. As a result, the phenomena,

typical for flexural mechanism can be observed in the

initial phase of testing (Fig. 4). Before the formation

of diagonal shear cracks in the central part of the wall,

the horizontal tensile cracks develop in the tensioned

part of the bed-joints at the supports and the crushing

of masonry units at the compressed corners takes

place. Although the flexural effects prevail in the

beginning of the test, and the compressive stresses at

the compressed corners are near to the compressive

strength of masonry units, this is not the flexural

failure of the wall. The resistance increases until the

diagonal cracks develop in the central part of the wall

and the wall finally fails in shear.

No such phenomena take place if the wall is tested

in situ, where the specimen is separated from the

surrounding masonry by two vertical cuts. Although

in the particular case, shown in Fig. 5, the level of

vertical stresses has been relatively low (estimated

compressive stresses ro = 0.15 MPa representedabout 7.5% of the masonrys compressive strength)

neither the horizontal cracks nor the crushing of

bricks have been observed at supports [9].

In their recommendations for the design of masonry

structures, CIB recommended three methods of testing

the masonry walls for assessing the values of para-

meters needed for the earthquake resistant design of

masonry structures (design by testing; [10]): cyclic

lateral resistance tests of symmetrically fixed or

cantilever walls at constant vertical load, as well as

diagonal compression test of the walls (Fig. 6).

3 Shear strength of masonry

Shear strength is the mechanical property of masonry,

which defines the resistance of masonry wall to

Fig. 2 Typical shear failure of brick masonry piers of a threestorey building after the earthquake

Fig. 3 Shear cracks in stone-masonry walls of a historicbuilding after the earthquake


lateral in-plane loads in the case that the wall fails in

shear. As there are several modes of such failure, the

definition of the shear strength is not straightfor-

ward. The parameter, which determines the shear

resistance of a masonry wall, depends on the physical

model describing the failure mechanism.

In the case of the sliding shear mechanism, which

is characterized by the formation of horizontal

cracks, masonry units slide upon one of the bed-

joints as soon as the shear stresses exceed the value,

called the shear strength of masonry (friction

analogy). In the case of the shear mechanism,

however, characterised by the formation of diago-

nally oriented cracks, shear cracks are caused by the

principal tensile stresses developed in the wall under

the combination of vertical and lateral load. When

the principal tensile stresses exceed the value called

the tensile or diagonal tensile strength of

masonry, diagonal cracks occur in the wall (tensile

strength hypothesis). A clear distinction should be

made between both mechanisms [11, 12], and the

resistance of a masonry wall should be checked for

both of them.

Whereas the tests for the determination of initial

shear strength of masonry are standardized, the

procedure for obtaining the tensile strength is not.

However, statistical correlation analysis, carried out

on the basis of the results of tests of a number of

masonry walls of the same type, tested by using

testing methods, recommended by CIB, has shown

that any method is suitable to determine the values of

tensile strength [13]. It is recommended that the walls

having the geometry aspect ratio h/l = 1.5 or smaller

are tested, where h is the height and l is the length of

the wall.

Fig. 4 Damage to masonry walls during laboratory testing. aHollow clay units type B2: shear cracks are passing through the

units. b Perforated clay units type B6: shear cracks pass partly

through the joints and partly through the units. In both cases,

tensile cracks and crushing of units at support have been

observed before the shear failure

Fig. 5 In-situ shear resistance test of a brick masonry wall:neither horizontal cracks nor crushing of bricks is observed at

supports (adapted from [9])


3.1 Tensile strength of masonry

Turnsek and Cacovic [14] found that it is not possible

to explain the formation of diagonally oriented cracks

in the walls by using the friction theory. Assuming

that the masonry wall behaves as an ideal elastic,

homogeneous and isotropic panel all the way up to

the failure, they called the principal tensile stress at

the attained maximum resistance of the wall the

tensile, or better the referential tensile strength of

masonry, ft. On the basis of such, purely conven-

tional definition, the equation for the calculation of

the shear resistance of masonry walls has been

proposed [14], modified by various other authors in

the following years (e.g. [15, 16]). The equations

based on the idea that the tensile strength governs the

shear resistance of masonry walls have been imple-

mented in several recommendations (e.g. [17]) and

seismic codes in former Yugoslavia [18] and other

countries.

By taking into account the assumption that

masonry wall is an elastic, homogeneous and isotropic

panel, the basic equation can be derived on the basis

of the elementary theory of elasticity. If the vertical,

N, and horizontal (shear) load, H, are acting on the

wall, the principal compressive and tensile stresses

develop in the middle section of the wall:

rP

ro2

2

bs2r

ro2

; 1

oriented in the directions of both diagonals of the

wall:

/c /t 0:5 arc tg2sro

: 2

The meaning of the symbols in Eqs. 1 and 2 is as

follows: ro = N/Awthe average compressive stressin the horizontal section of the walls due to constant

vertical load N; s = H/Awthe average shear stressin the horizontal section of the wall due to horizontal

load H; Awthe area of the horizontal cross-section

of the wall; bthe shear stress distribution factor,

which depends on the geometry of the wall and the

ratio between the vertical load N and maximum

horizontal load Hmax. In case that the aspect ratio

is equal to or greater than h/l = 1.5, the value of

b = 1.5 can be assumed. The value decreases in the

case of squat walls. Factor b is not the shear stress

distribution factor j, used in the theory of the strengthof materials.

Assuming the elastic, homogeneous and isotropic

behaviour of the wall panel all the way up to the

attained maximum value of horizontal load, Hmax, the

idealised principal tensile stress at that instant is

conventionally called the tensile or referential

tensile strength of masonry, ft:

ft rt

ro2

2

bsmax2r

ro2

; 3

where ftthe tensile strength of masonry; smaxtheaverage shear stress in the horizontal section of the

wall at the attained maximum horizontal load Hmax(at maximum lateral resistance).

A substantial number of test results of fixed-ended

and cantilever walls have been evaluated using the

Eq. 3 in the last decades. Typical values have been

recommended for the design in seismic codes. The

values of the tensile strength, recently evaluated on

the basis of cyclic lateral resistance tests of wall

specimens, made of different types of hollow clay

blocks, which have been also used for the determi-

nation of the initial shear strength of masonry at zero

compression, discussed in the following, are given

in Table 1. Surprisingly, in this series of tests the

masonry units strength did not significantly influence

the tensile strength of masonry.

Fig. 6 Schematicpresentation of different

types of tests suitable for

evaluation of parameters of

seismic resistance of

masonry walls. a cyclic testof a fixed-ended wall, bcyclic or racking test of a

cantilever wall, c diagonalcompression test (after [10])


3.2 Shear strength according to Eurocode 6

According to Eurocode 6, the shear strength of

masonry is defined as a sum of the initial shear

strength (shear strength at zero compressive stress)

and a contribution due to the design compressive

stress perpendicular to shear at the level under

consideration. Characteristic initial shear strength at

zero compression, fvko, is determined by testing

specimens made of three masonry units according

to standard EN 1052-3 ([20], Figs. 7 and 8). As can

be seen in Fig. 7, the standard does not define the

geometry aspect ratio of the specimen. The scheme,

shown in Fig. 7, is presented for the case of testing

the specimens made of bricks, whereas the specimens

made of hollow blocks with different geometrical

proportions have been actually tested (Fig. 8). During

the test, it should be ensured that pure shear stresses

develop in the connecting planes between the units

and mortar. Six specimens of each type are tested. As

the characteristic, the lesser value of the minimal

obtained or 80% of the mean value is considered.

Characteristic shear strength of masonry, fvk, made

of any mortar, at the condition that all, bed- and head-

joints are fully filled with mortar, is determined by:

fvk fvko 0:4rd: 4Equation is modified in the case where the vertical

joints are not filled with mortar:

fvk 0:5fvko 0:4rd; 4awhere rd is the design compressive stress in the wallssection. Since the value depends on the stress state

in the particular wall under consideration, the shear

strength, as defined by the Eurocode, cannot be

considered as the mechanical characteristic of

masonry. The shear strength represents the average

shear stress in the horizontal section of a wall

subjected to specific axial load at sliding shear failure.

The coefficient defining the contribution of the shear

strength due to compressive stresses in the wall, 0.4, is

taken as a constant for all types of masonry, although

the procedure for the determination of the internal

Table 1 Mean, ft, andcharacteristic values of

tensile strength of hollow

clay unit masonry, ftk,obtained by lateral

resistance tests of walls

(adapted from [19])

Units Normalized compressive

strength of unit fb (MPa)Mean compressive

strength of mortar

fm (MPa)

Tensile strength of masonry

ft (MPa) ftk (MPa)

B1 20.7 4.7 0.23 0.19

B2 13.0 5.0 0.24 0.20

B3 14.6 5.4 0.20 0.17

B4 12.2 5.0 0.26 0.22

B6 30.3 2.8 0.23 0.19

Fig. 7 Schematic presentation of initial shear strength testaccording to EN 1502-3

Fig. 8 Initial shear strength test according to EN 1502-3 in thelaboratory


friction angle is specified by standard EN 1502-3.

According to Eurocode 6, in no case the characteristic

shear strength should be greater than either 0.065fb(6.5% of the units compressive strength) or the limit

value fvlt, which should be determined by the National

Annex.

In the case that the experimental values of fvko are

not available, recommended values of the initial shear

strength can be taken into consideration. As can be

seen in Table 2, the Eurocode 6 recommended values

depend only on the units materials and mortar

strength class, but not on the strength of the units.

Recently, the characteristic initial shear strength

has been determined by testing a series of masonry

specimens prepared with six different hollow clay

unit types and two mortar classes. Altogether 72

specimens have been tested. The shape of the units is

shown in Figs. 9 and 10, whereas their dimensions

and physical properties are given in Table 3. The

actual test layout and typical specimens after the test

can be seen in Figs. 8 and 11, respectively. Factory

made, pre-batched mortar of strength classes M5 and

M10 (brand name Omalt MzZ type M5 and M10,

produced by Cinkarna Celje, Ltd.) has been used to

prepare the specimens. The values of initial shear

strength obtained by testing are given in Table 4.

Shear failure along the mortar joints occurred in all

cases. As can be seen, failure is the result of the

exhausted bond between mortar and units where, as a

rule, the mortar delaminated from the units (see

Fig. 11). In no case the failure occurred through the

units. In the particular case studied, EN 1502-3 tests

indicated that the initial shear strength values do not

depend on the strength of the mortar. Also, no direct

correlation could be observed between the initial

shear strength and geometry (volume of holes) or

compressive strength of the unit. The values obtained

by testing the specimens made with units B5 are

significantly higher than those obtained by testing

other types of units. Since the differences could not

be explained by comparing neither the mechanical

and geometrical characteristics of the units (see

Table 3) nor the failure modes, the values have not

been considered in the calculation of the average

values of the initial shear strength of the tested series

of specimens.

Table 2 Characteristic initial shear strength of masonry fvko (EN 1996-1-1:2005)

Material fvko (MPa)

General purpose

mortar of the strength

class given

Thin layer mortar

(bed joint C0.5 mm

and B3 mm)

Lightweight

mortar

Clay M10M20 0.30 0.30 0.15

M2.5M9 0.20

Calcium silicate M10M20 0.20 0.40 0.15

M2.5M9 0.15

Concrete M10M20 0.20 0.30 0.15

Autoclaved aerated concrete M2.5M9 0.15

Manufactured and dimensioned natural stone M1M2 0.10

Fig. 9 Hollow clay units B1, B2 and B3, used for construction of walls for cyclic seismic resistance tests and initial shear strengthtests according to EN 1502-3


The tests did not confirm the recommendations of

Eurocode 6 that the initial shear strength depends on

the mortars strength class (Table 2). As can be seen

in Table 4, the experimental characteristic values

are close to those recommended only for the case

where the specimens have been prepared with the

mortar of declared strength class M5 (actually

17.9 MPa).

3.3 Correlation between the shear and tensile

strength

If the shear strength and tensile strength were the

parameters which determine the same property, i.e.

the shear resistance of a masonry wall, there should

be a correlation between them. At least there should

be a correlation between the initial shear strength at

zero vertical stress, fvko, and the tensile strength of

masonry, ftk, since these parameters obviously repre-

sent the characteristics of masonry materials. If this

were the case, then the average shear stress in the

section at shear failure could have been the common

denominator. Assuming that smax in Eq. 3 actuallyrepresents an equivalent of the shear strength fvk,

determined by Eq. 4:

smax fvk; 5which would be the case if the wall is under

compression along the whole length of the walls

horizontal section, and by introducing this

Fig. 10 Hollow clay units B4, B5 and B6, used for construction of walls for cyclic seismic resistance tests and initial shear strengthtests according to EN 1502-3

Table 3 Dimensions andcompressive strength of

hollow clay masonry units,

used for the construction of

walls for lateral resistance

tests and initial shear

strength tests of masonry

(adapted from [19])

a Normalized mean values

Units Length

(mm)

Width

(mm)

Height

(mm)

Volume

of holes

(%)

Thickness

of shells

(mm)

Thickness

of webs

(mm)

Compressive

strengtha

(MPa)

B1 188 288 189 58 9.8 6.5 20.7

B2 238 282 234 55 10.8 6.7 13.0

B3 189 292 188 53 11.4 7.2 14.6

B4 331 292 189 54 11.7 7.4 12.2

B5 244 297 236 51 11.8 6.8 11.5

B6 254 122 121 25 21.6 7.3 30.3

Fig. 11 Typical view on failure planes after the completed initial shear strength tests of specimens made of units B3, B5 and B6


assumption into Eq. 4, the equivalent tensile strength,

f 0tk, can be expressed as:

f 0tk

rd2

2

bfvk2r

rd2

: 6

Taking into consideration the Eurocodes 6 recom-

mended value of fvko from Table 2 (fvko = 0.2 MPa)

and a series of values of design compressive stresses

rd, expressed in terms of the ratio between the designstress and characteristic compressive strength of

masonry, equivalent characteristic tensile strength

of masonry, f 0tk, can be calculated. However, as can beseen in Table 5, such values are unacceptably high and

are much higher than the values, obtained by testing

the considered types of masonry walls (see Table 1).

Although the theoretical relationship between the

quantities seems correct, there is actually no correla-

tion between the initial shear strength and tensile

strength of masonry. The quantities have different

physical meanings and define two different failure

mechanisms. Whereas the shear strength, fv (Eq. 4), is

defined on the basis of the assumption that the shear

failure of the wall takes place because of sliding of the

units along the bed-joint, and is therefore depending

on the design compressive stresses in each particular

wall under consideration, the tensile strength, ft(Eq. 3), is considered as one of the mechanical

characteristics of masonry, not depending on the

stress state in the wall panel. Therefore, the

transformation from the Eurocodes shear strength

to tensile strength is even not possible.

4 Shear resistance of unreinforced masonry walls

According to Eurocode 6, the design shear resistance

of the wall is calculated by simply multiplying the

characteristic shear strength of masonry by the area

of the cross-section of the wall, which carries the

shear. Characteristic shear strength is reduced by

the partial safety factor for masonry, cM, so that thedesign shear resistance of an unreinforced masonry

wall, Rds,w, is calculated by:

Rds;w fvkcMtlc; 7

where tthe thickness of the wall, and lcthe length

of the compressed part of the wall, ignoring any part

of the wall that is in tension, and calculated assuming

a linear stress distribution of the compressive

stresses, and taking into account any openings, chases

or recesses.

It can be shown that in the case where the

eccentricity of axial load exceeds 1/6 of the walls

length, the length of the compressed part of the wall is

expressed by:

lc 3 l2 e

; 8

where e = Hah/N is the eccentricity of the verticalload, ah is the arm of the horizontal load, whichdepends on restraints, i.e. boundary conditions at the

bottom and the top of the wall (a = 1.0 in the case ofa cantilever and a = 0.5 in the case of a fixed endedwall).

Obviously, when using Eq. 7, the seismic shear

should be already distributed onto the walls: to

Table 4 Characteristic, fvko, and mean values of initial shearstrength of masonry, fvo, obtained by testing specimensaccording to EN 1502-3 (values in MPa)

Units Compressive

strength of unitsaStrength class of mortar

5 MPab 10 MPac

fvko fvo fvko fvo

B1 20.7 0.17 0.23 0.19 0.27

B2 13.0 0.19 0.26 0.21 0.26

B3 14.6 0.16 0.20 0.16 0.20

B4 12.2 0.26 0.31 0.22 0.38

B5 11.5 0.50 0.60 0.55 0.66

B6 30.3 0.28 0.34 0.28 0.33

Averaged 0.21 0.27 0.21 0.29

a Normalized mean valuebActual mean value of compressive strength is fm = 17.9 MPac Actual mean value of compressive strength is fm = 23.2 MPad The values obtained for units B5 are not considered

Table 5 Correlation between the characteristic initial shearstrength, fvko, and corresponding characteristic tensile strengthof masonry, f 0tk, at different levels of design compressivestresses, rd, in the walls (values in MPa)

rd 0.1 fka 0.2 fk

a 0.3 fka 0.4 fk

a 0.5 fka

fvko f0tk f

0tk f

0tk f

0tk f

0tk

0.20 0.400 0.530 0.665 0.803 0.941

0.30 0.541 0.663 0.794 0.929 1.066

a fk = 5.0 MPa


calculate the length of the compressed part of the

wall, the design vertical and design seismic loads

should be known. Therefore, Eq. 7 is only useful in

the case of traditional safety verification procedures,

where for each structural element and for the

structure as a whole, the design resistance capacity

is compared with the design action effects. In the case

of the non-linear push-over procedures, iterations

would be required due to the changes in lateral load

distribution in the non-linear range.

By taking into consideration the same structural

safety requirements and reducing the characteristic

value of the tensile strength by partial safety factor

for masonry, cM, the shear resistance of an unrein-forced masonry wall in the case of the diagonal

tension shear failure can be expressed by:

Rds;w Aw ftkcM1

b

cMftk

rd 1r

: 9

A series of unreinforced masonry walls, built of

different types of hollow clay units, have been recently

tested under a combination of constant vertical and

cyclic lateral load [19]. The same units as used for the

initial shear strength tests (see Table 3), have been

used for the construction of walls. Disposition of tests

is shown in Fig. 12, whereas the dimensions of the

walls and vertical load, V, acting on the walls during

the lateral resistance tests and respective compressive

stress, ro, in the horizontal section of the walls aregiven in Table 6. In the same table, the main

experimental results, such as the maximum horizontal

load, measured during the tests, Hmax,exp, and

respective average values of the shear stresses in the

walls sections, smax, are summarized. All walls failedin shear, characterized by the formation of diagonal

cracks, with the initial tension cracks and crushing of

units occurring at the support (Fig. 4).

Test results have been used to compare the shear

resistance of the walls, calculated by assuming that

either the sliding shear (Eq. 7) or diagonal tension

shear (Eq. 9) mechanisms govern the failure mode. In

the first case, the shear strength of masonry has been

determined by Eq. 4. Instead of design, mean values

of the shear strength, calculated on the basis of the

mean values of the initial shear strength, given in

Table 4 (mortar class M5), and actual compressive

stresses in the walls during the tests have been

considered in the calculations. In the second case,

mean values of the tensile strength, given in Table 1,

and actual compressive stresses in the walls have

been considered in assessing the shear resistance of

the walls. No reduction with partial safety factor for

masonry, cM, has been considered. In other words, ithas been assumed that cM = 1.0.

Actual ratio between the vertical and lateral load at

failure, observed during the tests, has been taken into

account when determining the compressed part of the

walls length. The walls have been tested as vertical

cantilevers, so that, obviously, the bottom most

section should have been considered. However, as

the calculated compressed length at the foundation

was unrealistically short (in two cases, the walls

should have overturned during the test, although no

such phenomenon has been observed), the section at

the mid-height of the walls has been also considered.

Compressive stresses in the compressed section, used

to determine the shear strength, have been calculated

by taking into account the compressed length of the

wall. The results, obtained by considering the com-

pressed length of the walls at both, support and mid-

height sections, are summarized in Table 7. It can be

seen that in all cases the shear strength of the walls,

relevant for the support section, fvk, exceeds the

allowable limit value, i.e. 0.065fb. Therefore, in the

calculation of the shear resistance at support, the limit

value of the shear strength has been taken into

account.

The calculated values of the shear resistance of the

tested walls are compared with the experimentally

obtained maximal values of horizontal load in

Table 8. It should be noted that the diagonal tensionFig. 12 Disposition of cyclic lateral resistance test of acantilever wall


shear failure, characterised by the formation of

diagonal cracks, has been observed in the case of

all tests. Therefore, good agreement between the

experimental results and calculations, based on the

diagonal tension shear failure mechanism, is obvious.

It should be noticed, however, that, in the particular

case studied, the calculated resistance is slightly

overestimated in the case of the low precompression.

However, no correlation between the experimental

values and calculations can be observed in the case

where the shear resistance of the walls has been

calculated on the basis of the sliding shear

mechanism and using methods, required by Eurocode

6. In the case where the requirements of Eurocode 6

have been strictly respected, i.e. where the support

sections and the values of the shear strength limited

by the units strength have been taken into account,

any agreement can be considered as a mere coinci-

dence. In the case where the mid-height section has

been considered as critical, the calculations by 1.6

2.3-times overestimate the experimentally obtained

values.

The meaning of the symbols in Table 8 is as

follows:

Table 6 Characteristics of tested walls and results of lateral resistance tests (adapted from [19])

Units Wall Dimensions of

walls l/h/t (cm)

Aw (m2) fk (MPa) V (kN) ro (MPa) ro/fk Hmax,exp (kN) smax (MPa)

B1 B1/1 100/143/28 0.281 4.78 550.8 1.92 0.40 140.6 0.49

B1/2 274.8 0.96 0.20 92.0 0.32

B2 B2/1 102/151/28 0.287 4.82 490.2 1.71 0.35 133.7 0.47

B2/2 268.0 0.94 0.20 90.9 0.32

B2/3 388.2 1.37 0.28 118.0 0.41

B3 B3/1 101/142/29 0.294 4.48 509.2 1.67 0.37 128.7 0.44

B3/2 259.2 0.89 0.20 84.2 0.29

B4 B4/1 99/142/29 0.287 4.73 464.7 1.62 0.34 141.7 0.51

B4/2 261.7 1.00 0.21 93.9 0.34

B6 B6/1 107/147/25 0.270 5.47 524.2 1.96 0.36 131.0 0.49

B6/2 273.9 1.01 0.18 91.6 0.34

Table 7 Mean values of the tensile strength of masonry, ft,length of the compressed section, lc, and corresponding meanvalues of the shear strength of the tested walls, fv, evaluated bytaking into account the compressed length of the wall at the

supporta and middle of the heightb

Wall ft(MPa)

lca

(cm)

fva

(MPa)

lcb

(cm)

fvb

(MPa)

0.065fb(MPa)

B1/1 0.23 41.0 2.11 95.6 1.04 1.35

B1/2 6.8 5.89 78.5 0.72 1.35

B2/1 0.24 29.0 2.66 91.0 1.03 0.85

B2/2 -1.0 75.6 0.77 0.85

B2/3 14.9 4.01 83.5 0.93 0.85

B3/1 0.20 43.6 1.74 97.4 0.89 0.95

B3/2 13.0 2.95 82.1 0.63 0.95

B4/1 0.26 14.2 4.69 79.0 1.10 0.79

B4/2 -8.7 67.5 0.88 0.79

B6/1 0.23 50.3 2.00 105.3 1.13 1.97

B6/2 13.2 3.62 86.7 0.84 1.97

a Bottom section, b Mid-height section

Table 8 Comparison of experimentally obtained and calcu-lated values of the shear resistance of the tested walls

Wall Hmax,exp (kN) Rs,w-ft (kN) Rs,w-fva (kN) Rs,w-fv

b (kN)

B1/1 140.6 134.1 157.7c 282.6

B1/2 92.0 99.9 26.3c 161.8

B2/1 133.7 130.1 69.2c 216.2c

B2/2 90.9 101.1 162.4

B2/3 118.0 118.1 35.5c 199.3c

B3/1 128.7 119.3 120.2c 252.0

B3/2 84.2 90.9 35.8c 151.3

B4/1 141.7 128. 5 32.2c 179.5c

B4/2 93.9 105.1 153.5c

B6/1 131.0 127.2 250.1c 300.8

B6/2 91.6 95.9 65.6c 183.6

a Bottom sectionb Mid-height sectionc fv = 0.065fb (see Table 7)


Hmax,expthe experimentally obtained maximal

value of lateral load, representing the shear

resistance of the tested wall,

Rs,w-ftthe shear resistance of the wall, calcu-

lated by taking into account the diagonal tension

shear failure mechanism and mean values of the

tensile strength,

Rs,w-fvthe shear resistance of the wall, calculated

by taking into account the sliding shear failure

mechanism and mean values of the shear strength.

5 Shear modulus of masonry

Mechanical characteristics of masonry at shear have

predominant effect on the resistance and deformabi-

lity of load-resisting elements of masonry structures.

Eurocode 6 recommends that the shear modulus, G,

of masonry be evaluated on the basis of the known

modulus of elasticity, E, of masonry as follows:

G 0:4E; 10where the modulus of elasticity E is determined by

either testing the walls according to EN 1502-1 [21]

or using equations, based on the known compressive

strength of units and mortar. However, the experi-

ments indicate that, because of inelastic, non-

homogeneous and anisotropic characteristics of

masonry, the actual relationships are quite different.

The tests to determine the shear modulus G of

masonry are not standardized. However, modulus G

can be evaluated on the basis of lateral displacements,

measured during the lateral resistance tests of wall

specimens. In this, purely conventional procedure,

the definition of the lateral stiffness of the wall, K,

which is defined as the lateral load, H, causing unit

displacement of the wall, is used:

K H=d: 11In the case of the wall, fixed at both ends and

subjected to horizontal load, H, acting at the top, the

displacement, d, at the top is due partly to bending

and partly to shear:

d Hh3

12EIw jHh

GAw; 12

where Iw =tl3

12the moment of inertia of the walls

horizontal cross-section; j = 1.2the shear coeffi-cient for rectangular section.

On the experimentally obtained resistance curve,

the equivalent elastic stiffness of the wall (called

also initial, or effective stiffness), K, is defined

by the slope of a secant, connecting the origin with

the point on the curve where the first cracks occur in

the wall. If the modulus of elasticity of masonry E

had been determined by compression tests according

to EN 1502-1, shear modulus G can be evaluated by

simply introducing Eq. 11 into Eq. 12 and rearrang-

ing Eq 12:

G KAw

1:2h a0 KE hl 2

; 13

where a0 is the coefficient of boundary restraints(a0 = 0.83 for a fixed-ended and a = 3.33 for acantilever wall). It has to be noted, that such

definition of the shear modulus G is purely conven-

tional. As the experiments indicate, the value slightly

depends on the level of compressive stresses in the

walls section. Conventionally, shear modulus G is

determined at the precompression level between 0.20

and 0.33 of the masonrys compressive strength.

Experimentally obtained values of the shear

modulus G and resulting ratio between the shear

modulus G and modulus of elasticity E are given in

Table 9. As can be seen, the actual values are within

the range of 613% of the value of modulus of

elasticity E. In no case the values close to 40% of

E, as recommended by Eurocode 6, have been

observed. It can be therefore concluded, that the use

of Eurocode 6 recommended G/E ratio results into

unrealistic distribution of seismic loads onto the

shear walls. In order to avoid inadequate distribu-

tion, it is recommended that instead of Eurocode 6

proposed value G = 0.4E, either the values obtained

Table 9 Correlation between the experimentally obtained andEurocode 6 recommended values of the shear modulus of

masonry G

Unit Experimental Eurocode 6

E (MPa) G (MPa) G/E G = 0.4Ea (MPa)

B1 6,826 551 0.08 2,388

B2 7,402 561 0.08 1,757

B3 5,436 565 0.10 1,950

B4 6,883 573 0.08 1,680

B6 4,724 603 0.13 2,669

a E = 1,000 Kfba fm

b; see Table 1 for fb and fm


by testing or the value G = 0.10E be considered in

the calculations.

6 Verification of the seismic resistance

of unreinforced masonry structures

Various methods have been developed for the

seismic resistance verification of masonry structures.

In Slovenia, for example, a simplified non-linear,

push-over type method for the seismic resistance

verification of unreinforced masonry buildings named

POR has been proposed after the earthquake of Friuli

in 1976 [22, 23]. The original method has been

improved and other methods of the same push-over

type have been developed, like method SAM [12]. In

all cases, the lateral resistance of individual shear

walls is checked for different possible failure mech-

anisms, like the diagonal tension shear and flexural

failure. The critical mechanism, yielding the lowest

value of the lateral resistance of the wall, is taken into

account in further analysis. Resistance curve of the

critical storey is calculated on the basis of the

idealised resistance curves of all resisting walls in

the storey. The seismic resistance of the building is

verified by comparing the calculated maximum

resistance and ductility of the structure with the

design seismic loads and ductility demand, required

by the structural behaviour factor, taken into consid-

eration for the determination of the design seismic

loads. The results of such calculations have been

verified by experiments and correlations with earth-

quake damage observations.

According to the principles of Eurocodes, the

following general relationship shall be satisfied for all

structural elements and the structure as a whole:

Ed Rd; 14where Ed is the design action effect and Rd is the

design resistance capacity of a structural element

under consideration. When considering a limit state

of transformation of the structure into a mechanism, it

should be verified that a mechanism does not occur

unless the actions exceed their design values. In

the case of the simplified non-linear methods, the

requirement is verified for the structure as whole.

In the case where the elastic structural models are

used for the distribution of design action effects on

individual elements, the resistance of the structure is

verified by comparing the design resistance of each

individual structural element with the corresponding

design seismic action effect. In the following, the results

of the seismic resistance verification of a typical three-

storey confined masonry building, shown in Fig. 13,

Fig. 13 Floor plan ofmasonry building, used for

seismic resistance analysis


carried out by using this principle, will be discussed.

In the analysis, a simple elastic structural model has

been used for the distribution of the design seismic

shear on individual shear walls. Storey mechanism of

the seismic behaviour, i.e. the pier action of shear

walls, fixed at both ends, has been assumed and the

lateral stiffnesses of the walls have been calculated

accordingly.

The dimensions of structural walls, considered in the

calculation (see Fig. 13), are given in Table 10. The

values of the design compressive stresses in the walls

section, rd, have been taken from the actual analysis ofthe building under consideration. The values of the

lateral stiffnesses of the walls, K, calculated by

rearranging Eq. 13, are also given in Table 10:

K GAw1:2h 1 a0 GE hl

2h i : 15

Since the shear resistance, calculated on the basis of

Eq. 7, depends on the compressed length of the walls

section, i.e. the lateral/vertical load ratio, the influence

of G/E ratio on the distribution of the design base shear

on the walls, and, hence, on the calculated shear

resistance values, has been also analysed. Therefore,

the lateral stiffness of the i-th wall, Ki, has been

calculated by considering either the experimentally

obtained values of modules E and G (Ki,test), or the

Eurocode 6 recommended G/E ratio (Ki,EC6). It can be

seen that, although quantitative values of individual

stiffnesses differ significantly, the differences in

distribution factors Ki/RKi are not so great.Mechanical characteristics of masonry, taken into

account in the calculations of the shear resistance and

lateral stiffness of the walls, are given in Table 11.

Walls type B1 have been considered. To determine

the design values, partial material safety factor for

masonry cM = 1.5 has been taken into account.In the case where the design shear resistance has

been calculated on the basis of the sliding shear failure

mechanism (Rds,w-fv), the characteristic values of

Table 10 Dimensions of walls, design compressive stresses and calculated values of lateral stiffnesses

Wall no. l (m) t (m) h (m) rd (MPa) Ki,test (kN/m) (Ki/RKi)test (%) Ki,EC6 (kN/m) (Ki/RKi)EC6 (%)

1 3.65 0.30 2.62 0.38 198.53 5.59 973.95 5.26

2 1.45 0.30 1.50 0.69 142.71 4.02 782.10 4.23

3 1.28 0.30 1.50 0.34 128.36 3.61 741.67 4.01

4 1.28 0.30 1.50 0.34 128.36 3.61 741.67 4.01

5 1.45 0.30 1.50 0.69 142.71 4.02 782.10 4.23

6 3.65 0.30 2.62 0.38 198.53 5.59 973.95 5.26

7 4.43 0.25 2.62 0.48 198.64 5.59 938.86 5.07

8 1.35 0.20 2.13 0.47 67.91 1.91 460.70 2.49

9 2.53 0.25 2.13 0.34 142.82 4.02 729.96 3.94

10 1.22 0.25 2.13 0.36 79.18 2.23 573.28 3.10

11 9.43 0.25 2.62 0.43 415.30 11.69 1836.50 9.92

12 2.58 0.25 2.13 0.40 145.39 4.09 738.94 3.99

13 1.58 0.25 2.13 0.38 95.52 2.69 591.67 3.20

14 1.25 0.25 2.62 0.29 70.89 2.00 583.50 3.15

15 2.25 0.25 2.62 0.33 107.54 3.03 619.54 3.35

16 4.43 0.25 2.62 0.48 198.64 5.59 938.86 5.07

17 3.65 0.30 2.62 0.38 198.53 5.59 973.95 5.26

18 1.45 0.30 1.50 0.69 142.71 4.02 782.10 4.23

19 2.15 0.30 1.50 0.28 203.88 5.74 993.96 5.37

20 2.15 0.30 1.50 0.28 203.88 5.74 993.96 5.37

21 1.45 0.30 1.50 0.69 142.71 4.02 782.10 4.23

22 3.65 0.30 2.62 0.38 198.53 5.59 973.95 5.26

Note: Ki,test, values of E and G obtained by testing: E = 6,826 MPa, G = 551 MPa; Ki,EC6, values of E and G calculated according toEurocode 6: E = 5,971 MPa, G = 0.4E = 2,388 MPa


mechanical properties of masonry have been calcu-

lated on the basis of the known strength characteristics

of masonry units and mortar using equations given in

Eurocode 6. For the distribution of design seismic

loads, lateral stiffnesses Ki,test and Ki,EC6 have been

taken into account. In the case where the design shear

resistance of individual walls has been calculated on

the basis of diagonal tension shear failure mechanism

(Rds,w-ft), experimentally obtained characteristic val-

ues of mechanical properties of masonry have been

considered. For the distribution of design seismic

loads, lateral stiffnesses of individual walls Ki,test have

been taken into account.

The analysis has been carried out for the x-direction

of the building. According to the requirements of

Eurocode 6, the walls perpendicular to the direction of

seismic action have not been considered. Design

seismic loads have been determined in accordance

with the requirements of Eurocode 8 [24], following

the response spectrum approach, where the design

spectral value is calculated by:

SdT cISag2:5

q; 16

and the design base shear by:

FBd SdTW ; 17where Sd(T)the design spectrum value; in the

specific case considered, Sd(T) = 0.225 g; cItheimportance factor; cI = 1.0 for residential buildings;agthe design ground acceleration; in the specific

case considered, ag = 0.15 g; Sthe soil type coef-

ficient; in the specific case considered, S = 1.2 for soil

type B; 2.5the spectral amplification factor assumed

to be constant in the range of typical natural periods of

vibration, T, of masonry buildings; qthe structural

behavior factor; q = 2.0 for confined masonry struc-

tures; FBdthe design base shear, and Wthe weight

of the building above the analysed section.

Assuming that the weight of the building above the

analysed section is W = 12.85 MN (the value has been

taken from actual seismic analysis of the building

under consideration), the design seismic base shear

attains the value of FBd = 2.89 MN. The design

seismic base shear has been distributed on the struc-

tural shear walls in proportion with their stiffnesses:

FBd;i KiPKi

FBd: 18

In the case where the design shear resistance of the

walls has been calculated on the basis of the sliding

shear failure mechanism (Rds,w-fv), the compressed

part of the walls length and the resulting shear

strength values have been determined on the basis of

the calculated relationship between the corresponding

part of the design base shear FBd,i and design vertical

load Vd,i = rd,iAw,i, acting on the i-th wall. In thecase where the eccentricity of vertical load would

theoretically cause the overturning of the wall

(compressed part of the walls length resulted neg-

ative), the wall has not been considered as lateral load

resisting element. The design seismic shear was

redistributed to remaining walls and the calculation

repeated.

The results of calculations are given in Table 12. It

can be seen that, although the distribution factors

Ki/RKi did not differ significantly, the differencesbetween the experimentally obtained and Eurocode 6

recommended G/E ratios influenced the lateral/verti-

cal load ratio, and, consequently, the design shear

resistance of the walls, calculated in accordance with

Eurocode 6. Consequently, the verification of the

shear resistance of individual walls according to rule

(14) may lead to different conclusions, depending on

the data used for the calculation of the lateral stiffness

of the walls.

Although not all walls in the story comply with the

requirement (14), a conclusion can be made that the

Table 11 Mechanicalcharacteristics of masonry,

used in the calculations of

seismic resistance (walls

type B1, fb = 20.7 MPa,fm = 4.7 MPa)

Quantity Test (MPa) Recommended by Eurocode 6

Equation Value

Compressive strength fk 4.78 fk = K fba fm

b 5.97 MPa

Modulus of elasticity E 6,826 1,000 fk 5,971 MPa

Shear strength fvk fvk = 0.20 ? 0.4 rd Calculated for each wall

Tensile strength ftk 0.19

Shear modulus G 551 G = 0.4E 2,388 MPa


seismic resistance of the building under consider-

ation, assessed as proposed by Eurocode 6, is

adequate. Namely, the sum of the design shear

resistances of all walls in the storey, which can be

used as an indicator of the seismic resistance of the

building, is greater than the design base shear. This,

however, is not the case if the design resistance of the

walls is determined by taking into account the

diagonal tension shear failure mechanism (Rds,w-ft).

In the latter case, the sum of the design resistances of

all walls in the storey does not attain the required

value of the design base shear. By comparing the

values, given in Table 12, it can be seen that for all

walls in the storey, except where the overturning is

theoretically expected, the resistance of the walls to

diagonal tension is smaller than the resistance to

sliding shear. Generally speaking, the differences are

not as great as those obtained by correlating the

calculations with the results of tests of individual

walls (Table 8). However, they are significant. In the

particular case studied, the ratio between the sliding

shear and diagonal tension shear based calculated

lateral resistances of individual walls exceeds 1.5.

Moreover, if calculated in accordance with Euro-

code 6, the shear resistance of the same wall in

different seismic situations does not remain the same.

Namely, if the design seismic shear, acting on the

wall, changes, the lateral/vertical load ratio, hence the

compressed part of the walls length, and, conse-

quently, the design shear resistance also change. To

assess the possible differences, the seismic resistance

of the same building has been verified for varying

seismic loads. The results of this analysis are

presented in Table 13, where again the sum of

resistances of all walls in the storey is considered

as an indicator of the seismic resistance of the

building under consideration. As can be seen, signif-

icantly different values are obtained for the same

Table 12 Design seismicshear acting on individual

walls, FBdi, and designshear resistance of

structural walls, calculated

on the basis of the sliding

shear, Rds,wi-fv, and diagonaltension shear failure

mechanism, Rds,wi-ft

Wall no. Sliding shear mechanismEurocode 6 Diagonal tension failure

Distribution by Ki-test Distribution by Ki-EC6 Distribution by Ki-test

FBdi (kN) Rds,wi-fv (kN) FBdi (kN) Rds,wi-fv (kN) FBdi (kN) Rds,wi-ft (kN)

1 168.8 257.5 190.1 247.2 161.6 166.8

2 121.3 128.4 152.7 114.4 116.2 84.2

3 109.1 11.0 104.5 55.9

4 109.1 11.0 104.5 55.9

5 121.3 128.4 152.7 114.4 116.2 84.2

6 168.8 257.5 190.1 247.2 161.6 166.8

7 168.9 288.5 183.2 288.5 161.7 183.8

8 57.7 46.4 55.3 44.7

9 121.4 120.2 142.5 103.2 116.3 92.7

10 64.5 45.3

11 353.1 586.6 358.4 586.6 338.1 376.6

12 123.6 142.6 144.2 128.3 118.4 100.0

13 81.2 55.6 77.8 59.8

14 57.7 42.9

15 91.4 90.4 120.9 60.2 87.6 80.7

16 168.9 288.5 183.2 288.5 161.7 183.8

17 168.8 261.9 190.1 247.2 161.6 166.8

18 121.3 128.4 152.7 114.4 116.2 84.2

19 173.3 81.7 194.0 52.5 166.0 87.4

20 173.3 81.7 194.0 52.5 166.0 87.4

21 121.3 128.4 152.7 114.4 116.2 84.2

22 168.8 257.5 190.1 247.2 161.6 166.8

R (kN) 2891.5 3352.4 2891.5 3006.7 2891.5 2500.3


structure in different seismic situations in the case

where the shear resistance of the walls is assessed

according to Eurocode 6. The seismic resistance of

the building does not depend on seismic loads if the

diagonal tension shear mechanism is assumed to be

critical.

Although the sum of resistances of all walls does

not represent the actual resistance of the structure

(the latter can only be assessed by a push-over

analysis), indication is given that the Eurocode 6

based shear resistance verification does not provide

realistic assessment of the seismic resistance of

unreinforced and confined masonry structures. For

example, the design shear resistance of the same

confined masonry building, located on the same soil

type B (S = 1.2), and calculated for the design

base shear at ag = 0.1 g (FBd,0.1 g = 1,928 kN)

would almost satisfy the required design base shear

for ag = 0.2 g (Rds-fv,0.1 g = 3677 kN & FBd,0.2 g =3,856 kN). However, if the seismic resistance of

the same building is assessed for the design base

shear at ag = 0.2 g, the calculated resistance value

amounts to only 70% of the design resistance

calculated for the design base shear at ag = 0.1 g

(Rds-fv,0.2 g = 2,572 kN \ Rds-fv,0.1 g = 3,677 kN).For comparison, the resistance of the same build-

ing, assessed by means of a push-over analysis for

the x-direction of seismic action amounts to Rds-

ft = 2,490 kN. The fact that the value in this partic-

ular case is the same as the sum of resistances of

walls, calculated on the basis of diagonal tension

shear failure mechanism, RRds,wi-ft = 2,500 kN (see

Tables 12 and 13), is a mere coincidence. Namely,

because of ductility limitations, not all walls fully

contribute to the lateral resistance of the building.

Consequently, the value of the calculated lateral

resistance of the building does not attain the sum of

resistances of individual walls. However, the walls

perpendicular to seismic action, which are taken into

consideration in the case where the non-linear, push-

over methods are applied, also provide a contribution

to the lateral resistance of the structure. In the case of

regular unreinforced and confined masonry structures,

as is the case of the analysed building, the contribution

of perpendicular walls represents up to 25% of the

total resistance. According to Eurocodes, such walls

are not considered as lateral load resisting elements.

7 Conclusions

Because of the non-elastic, unisotropic and non-

homogeneous character, the dependence of strength

and deformability characteristics of masonry on

mechanical characteristics of constituent materials

is not straightforward. Therefore, the determination

of mechanical characteristics of masonry by adequate

testing methods is an important part of the verifica-

tion of the load bearing capacity and stability of

masonry structures. By implementation of Eurocodes

and accompanying product standards, a significant

part of testing procedures and calculation methods

has been already defined, however not always in the

most adequate way.

The results of experimental investigations of

seismic behaviour of a series of masonry walls, built

in pre-batched mortars with different types of

masonry units, available on the market, have been

used to point out the possible differences between the

experimentally obtained and calculated, Eurocode 6

based values of the shear resistance of masonry walls.

It has been shown that the calculations of the shear

resistance of masonry walls by using equations,

developed on the basis of the sliding shear mecha-

nism, do not provide accurate information regarding

the seismic resistance of unreinforced and confined

masonry structures. Despite the fact that the input

parameters have been determined by standardized

testing procedures.

On the other hand, it has been shown that the

results of calculations, based on the assumption that

Table 13 Correlation between the design shear resistance ofbuilding, represented as a sum of resistances of individual

walls calculated on the basis of the sliding shear, RRds,wi-fv, anddiagonal tension shear failure mechanism, RRds,wi-ft, anddesign seismic base shear FBd

ag (g) FBd (kN) RRds,wi-fv (kN) RRds,wi-ft (kN)

Distribution by

Ki-test Ki-EC6

0.10 1,928 3,788 3,677 2,500

0.15 2,892 3,352 3,007 2,500

0.175 3,372 3,191 3,026 2,500

0.20 3,856 2,670 2,572 2,500

0.225 4,337 2,433 2,111 2,500

0.25 4,819 428 1,135 2,500


the diagonal tension shear failure mechanism is

critical for the shear resistance of walls, are in good

agreement with experimental results. Well known

equations, developed decades ago, have been used in

the analysis.

The definition of the shear resistance of unrein-

forced and confined masonry walls as given by

Eurocode 6 is only acceptable in the case where the

sliding shear failure of walls takes place. Friction

analogy is not acceptable and parameters, like char-

acteristic initial shear strength at zero compressive

stress, fvko, can neither be used nor experimentally

determined in the case of the mechanism, character-

ised by the formation of diagonally oriented cracks in

the walls. In addition, characteristic initial shear

strength, as defined by Eurocode 6, has no meaning in

the case of the seismic resistance analysis of the

cultural heritage stone masonry buildings.

Similar non-compliances have been also found as

regards the values of the shear modulus of masonry

G. It has been found that the values, proposed by

Eurocode 6, are excessively high. In order to avoid

inadequate distribution of design seismic shear onto

the resisting walls in the storey, it is recommended

that instead of Eurocode 6 proposed value G = 0.4E,

either the values obtained by testing or the value

G = 0.10E be considered in the calculations.

The setting of limiting values in National Annexes,

i.e. either 0.065fb or fvlt, as proposed by Eurocode 6,

will not solve the problem. Since the parameters,

which define different possible failure mechanisms,

have different physical character, the correlation

between them is not possible. No generally valid

value can be proposed even if detailed parametric

analyses had been previously carried out.

The methods and equations for seismic resistance

verification of masonry buildings shall not be limited

with the requirements and recommendations, given in

Eurocode 6. Specifically in the case of unreinforced

and confined masonry, where the shear behavior is

predominant and, consequently, shear resistance of

walls is the governing parameter of the seismic

resistance of the whole structure. The models and

equations, developed on the basis of other possible, in

most cases critical failure modes, such as diagonal

tension shear failure, should be also used for seismic

resistance verification. Otherwise, the results of

seismic resistance analyses will be misleading. The

use of simplified non-linear, push-over type methods,

verified in the past by laboratory testing and analysis

of earthquake damage to masonry buildings, should

be encouraged.

It can be concluded that, regarding the calculation

of the shear resistance of masonry walls, Eurocode 6

should be amended by allowing that, as an alternative

to the existing sliding shear mechanism, different

other possible failure mechanisms be also verified in

the case of masonry walls subjected to in-plane

lateral loads. The critical, i.e. minimal calculated

value of the lateral resistance of the wall should be

considered in seismic resistance verification.

Acknowledgement The study has been based on the resultsof the recent experimental research, carried out within the

framework of the research program P2-0274, financed by the

Slovenian Research Agency in the years 20032008.

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Shear resistance of masonry walls and Eurocode 6: shear versus tensile strength of masonryAbstractIntroductionBehaviour of masonry walls subjected to in-plane acting seismic loads and testingShear strength of masonryTensile strength of masonryShear strength according to Eurocode 6Correlation between the shear and tensile strength

Shear resistance of unreinforced masonry wallsShear modulus of masonryVerification of the seismic resistance of unreinforced masonry structuresConclusionsAcknowledgementReferences

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