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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: miha.tomazevic@zag.si
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
Materials and Structures
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
Materials and Structures
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])
Materials and Structures
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])
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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)
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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
Materials and Structures
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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Materials and Structures
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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