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Canadian Journal on Environmental, Construction and Civil Engineering Vol. 3, No. 3, March 2012
EXPERIMENTAL DETERMINATION OF THE MECHANICAL PROPERTIES
OF CLAY BRICK MASONRY
T.C. Nwofor
Department of Civil and Environmental Engineering
University of Port Harcourt, Rivers State, Nigeria.
P.M.B 5323, Port Harcourt
Abstract:
The structural behaviour of masonry is influenced by the mechanical properties of the
constituent materials. Therefore a full mechanical characterization is required for propernon-linear analysis of masonry structures. Hence uniaxial compressive test is carried out
on unreinforced masonry and its constituents (clay bricks and mortar). From this study,
compressive stress-strain relationships at different confining stress levels have been
defined. In this paper the experimental results obtained is used to formulate simpleanalytical models for the purpose of estimating the modulus of elasticity of unreinforced
masonry, utilizing the control points established in this work. The proposed material
model can be employed in the non-linear finite element analysis of masonry structures.
Keywords: Brick-mortar masonry, compressive stress, strain and modulus of elasticity.
1. Introduction
The properties of brickwork are influenced by variables of bricks, type of mortar,
physical properties of the sand and lime used for the mortar, state of bricks before
casting, curing workmanship and many others. Hence it can be deduced that in the
experimental determination of mechanical properties of brickwork, a large number of
variables can be considered. We should note that the analysis and design of buildings
require the material properties of masonry, for example, the modulus of elasticity of
masonry is require for the non-linear static analysis. Stress-strain curves of masonry are
required for more detailed non-linear analysis of masonry structures. Limited research
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has been carried out by researches to obtain a realistic material property for masonry [1]-
[4]. Also laboratory test have also been carried out on masonry, adopting the approach of
a homogenous continuum material made up of brick units, mortar joints and any unit-
joint interfaces [5]. The wide variation of test value of the mechanical property of
masonry and its units especially when under the influence of compressive load [6]-[9] has
not aided the formulation of realistic stress-strain curves for non-linear modeling of
masonry and infilled frame structures. Hence, in this present study, extensive
experimental testing of brick masonry prism material according to ASTM specification
[10] would be performed to obtain stress-strain curves. Also experimental relationships
would be obtained between the modulus of elasticity of masonry units of its compressive
strength. Furthermore, simple analytical equations are developed using the experimental
data to estimate the mechanical properties and plot the stress-strain curves for masonry.
However, to maintain the scope of this research, the materials used have been kept
constant. The bricks, cement, sand and lime used are described below.
2. Materials and Experimental Procedure
The bricks employed are solid burnt clay bricks of average size of 224 x 106 x 72mm.
Typical physical properties are shown in Table 1. The absorption rate of bricks immense
in water at room temperature is also shown in Figure 1.
Table 1: Physical properties of bricks
No. of
specimens
Compressive Strength
(x 106 kN/m
2 ) Std Dev
Mean Range
Crushing strength * 20 23.30 18.69-27.25 2.21
ψ 102 22.00 - 2.32
Length (mm)
Breadth (mm)
Depth (mm)
*
*
*
20
20
20
224
106
72
223.1-224.5
106.2-106.8
71.1-72.9
0.391
0.183
0.194
Water Absorption
% by wt. after 25 hrs, immersion 12.49
% by wt. after 5 hrs, boiling 12.91
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(*) Values obtained by author
(ψ ) Values obtained by British Ceramic Research Association
The mortal mixes will consist of cement, lime and sand, while ordinary Portland cement
would be used for this investigation so as to use the 28
th
day strength.
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25
immersion time (mins)
A b s o r p t i o n
( b y w e i g h t ) %
Figure 1: Absorption of Bricks
Also, graded sand classified in zone 2 was generally used for this investigation to prepare
the mortar. The particles distribution analysis is shown below for a sample of 300grams.
Sieve analysis was carried out on the river sand sample and the results shown in Table 2.
The result revealed the sand sample was well graded falling into zone 2 near border of
zone 1, which is very appropriate for concrete work in accordance with BS 882, part 2
1992 [11]. The fineness modulus of the sand was found to be 3.15, which makes the sand
sample a rather coarse one.
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Canadian Journal on Environmental, Construction and Civil Engineering Vol. 3, No. 3, March 2012
Table 2: Particle size analysis on fine aggregate sampleSieve Mass on
(g)
% on sieve %
retained
%
passing
Zone 2
Limits
Max. on sieve
permitted (g)
5.00mm
2.36mm
1.18mm
600.00µm300.00µm
150.00µmTray
No.7
14
2552
100
12
54
60
6663
+
39
6
4
18
20
2221
13
2
4
22
42
6485
98
-
96
78
58
3615
2
-
90-100
75-100
55-90
35-598-30
0-10
-
-
200
100
7550
40
315
+Needed dividing as it exceeded the maximum permitted on sieve.
Zone = zone 2, near border of zone 1.
Fineness modulus (FM) 315 ÷ 100 = 3.15 (rather coarse)
A mortar mix proportioning of 1:¼:3, 1:0.5:4.5 and 1:0:6 corresponding to avolume proportioning of cement, lime, and sand respectively are generally used, while
maintaining reasonable workability for mortar is achieved by varying the water-cement
ratio ( C W ) to produce suitable workability.
2.1 Water Cement Ratio ( C W ) of Mortar
In concrete work the term water/cement ratio, if not qualified, could refer either to
effective water/cement ratio or total water/cement ratio. In this investigation, thewater/cement ratio of fresh mortar is an important factor in determining the properties of
the hardened mortar (as a joint) in brickwork. It is therefore necessary to clarify the
definition of this term as used in this work.
Assuming only fine aggregates (i.e. sand in the case of this investigation), the effective
water/cement ratio for strength is defined as:
Effective ( C W ) = total ( C W ) – as( C S ) (1)
where
total C W = total amount of water added to the dry mix
aS = 30mins absorption capacity of the sand (in the air-dry state).
S/c = sand/cement ratio by weight.
For the oven-dry sand used throughout this investigation as (in this case corresponding to
maximum absorption capacity) was found to be 0.024.
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Hence from equation 1
Eff. W/C = total W/C – 0.024s/c (2)
Table 3 gives a comparison of the effective W/C with the total W/C for two typical mixes
used.
Table 3: Comparison of the effective W/C with the total W/C
Mortar Total W/C (by wt.) Effective W/C (by wt.)
1:¼:3 1.0
0.8
0.93
0.73
1:05:45 1.0
2.6
0.88
2.48
It should be noted that the term W/C used throughout this work refers to the total
W/C as defined above.
2.2 Actual C W of Mortar Joint
Owing to absorption of water by bricks, the W/C of the mortar before placing is
different from that after placing between bricks. Therefore, while any control specimens
(such as cubes or prisms) would be useful for indicating the relative qualities of different
batches of mortar mixes, it should be appreciated that properties such as crushing
strength, Young’s modulus, Poisson’s ratio, determined from such specimens may not
bear much resemblance (except by correlation) to those of the same mortar in the
hardened state (as a joint) between the bricks.
A theoretical relation between the W/C’s of the control specimens and the mortar
joint was derived by considering the amount of water absorbed from a known weight of
fresh mortar placed between two bricks. The relationship is given by
C W a = W/C – k(C + L + S + W)/C (3)
where
C W a = actual water/cement ratio of mortar between bricks (or of mortar joint)
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C W = water/cement ratio of the fresh mortar (or control specimen)
mortaroriginalof wt.
bricksbyabsorbedwaterof wt.=K
The value of k was determined experimentally. It is assumed that loss of water to theatmosphere from the bricks- mortar couplet and from the control specimen is the same.
For 1:¼:3 mortar with W/C = 1.0
C W a = 1.0 – 5.25k (3a)
Corresponding expressions for other values of C W could be obtained similarly.
These relationships are plotted in Figure 2. The conditions for saturated bricks and for
bricks soaked for one minute before casting are indicated by vertical lines AB and CD
respectively obtained from measured values of k. The intersections of these lines with
the straight line represented by equation 3a give the values of actual water/cement ratio
(Wa/C) for ‘saturated’ bricks and for bricks soaked for one minute.
.
.
.
.
.
.
. . . . . . .
/ .
/ .
/ .
Figure 2: Relationship between C W a and K
The respective values being 0.94 and 0.5. The indication is therefore that for
saturated bricks, while the W/C for the control specimen is 1.0, the actual water/cement
ratio ( C W a ) of the corresponding mortar joint would be of the order of 0.94. For bricks
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soaked for one minute (or with a moisture content of about 6%) the corresponding values
are W/C = 1.0, C W a = 0.5. The deductions drawn from these results are as follows:-
i. To determine properties of mortar joint, such as tensile or shear strength, realistic
values may be directly obtained from test on brick-mortar couplets.
ii. For elastic analysis of brick-mortar couplet or brick-work as a non-homogenous
material, meaningful values of elastic modulus and Poisson ratio for the mortar
joints may be obtained from tests on mortar specimens with C W ratio value
equal to the value of the actual water/cement ratio ( C W a ) of the mortar joint.
3. Mechanical Properties of Bricks and Mortar
3.1 Compressive/Crushing Strength of Brick The maximum compressive stress of a brick-mortar prism is determined by applying a
compressive load in the direction parallel and perpendicular to the bedding planes, hence,
the fabricated bricks are built into a prism of different layers with constant mortar joint
thickness. It is important to note that while these test give reasonably good indication of
the crushing strength of brick-mortar prism for control purposes it is doubtful if they give
the compressive strength of brick work as a basic physical property. Several research
work on concrete specimens which can also be related to brickwork has shown that some
important factors influences the compressive strength of specimen such as size of
specimen, surface condition, state of stress induced in the specimen, thickness of mortar
joint and also the testing technique. Hence the most important factor arrived at, is that
the direct measure of the uniaxial compressive strength of concrete which gave a realistic
value of the value for the basic property of concrete in uniaxial compression is a case
where the height to width ratio of the prisms is greater than 2.5.
From the foregoing, compression tests were carried out on bricks with varying
height to width ratios in the compression machine. For the case of loading parallel single
bricks were tested, Figure 3a while for the case of loading perpendicular to the bedding
planes of the brick the respective H/L ratios are obtained by varying the number of bricks
in the prisms as is shown in Figure 3b.
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The crushing strength of the bricks were generally found to decrease with increase
H/L ratio to a limiting value of 23.28N/mm2. This reflects the value shown in table 3.1.
This value shows the average of the result obtain from both loading perpendicular and
parallel to the bedding plane. The variation of brick crushing strength with H/L ratios is
shown in Figure 4. Hence it can be observed that more realistic results would be
obtained by loading single bricks parallel to these bedding plane.
Table 4: Summary of crushing strength of bricks
Number oftests
H/L Crushing meanstrength (f b)
×103kN/m3
Range description
10
101010
10
0.32
0.901.512.15
2.12
38.36
25.1929.7124.15
23.16
33.92-44.33
22.59-28.0819.26-29.8222.48-25.89
18.69-27.25
Type (b) 1 brick
Type (b) 3 brickType (b) 5 brickType (b) 7 brick
Type (a) 1 brick
3.2 Crushing Strength of Mortar
Compressive strength test were carried out on 20mm mortar cubes and a graphical
representation of the results shown in Figure 3.4 for different ages of a 1:¼:3 nominal
mix of mortar by varying the water-cement ration of the mix.
() ()
Figure 3: Compressive loading on brick specimens (a) Loading parallel to
bedding planes (b) loading perpendicular to bedding plane
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0
2
4
6
8
10
12
14
16
18
20
0 5 10 15 20 25 30
Age (days)
C r u s h i n g s t r e n g t h
( x 1 0 3 k N / m 2 )
W/c = 0.8
W/c = 1.0
W/c = 1.2
Figure 4: Crushing strength of 1:¼:3 grade of mortar mix.
3.3 Modulus of Elasticity and Poissons Ratio for Brick
The static method was used to obtain elastic properties of brick. In order to
produce uniaxial compression in the middle portion, single bricks were loaded in
compression in a direction perpendicular to the bedding planes. Longitudinal
compressive strain yε and the corresponding lateral tensile strain ( )
xε were measured
in the middle region by using suitable electrical strain gauges. By measuring the
compression load and the strains ε y and ε x as shown on table 5, the stress-strain curves
y
y
ε α
and x
y
ε α
can be obtained. Young’s modulus (E) and Poissons ratio (v) were
obtained from the slopes of the linear portions of the stress-strain curves as follows.
x
y E
ε
α = (4)
x
y
y
y
y
xv
ε α
ε
α
ε ε == (5)
Table 5 shows values of Modulus of elasticity (E) and Poissons ratio (v) thus
obtained. E1 and V1 denote values obtained from strain measurements on face 1, E2 and
V2 correspond to values for face 2. Two sizes of bricks were tested. Type (a) is the
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normal single brick, and type (b) is the single brick made to produce a square section
(72mm x 72mm) perpendicular to the loading direction.The values shown in Table 5
were obtained from test on twenty (20) specimen of bricks and the stress-strain curves
were obtained from an average of about six sets of readings obtained by loading and
unloading the specimen six times.
Table 5: Summary of test result for brick units
Description No. of
specimens
(x 103kN /
m2) Fb
(x 10 kN/m2) V1 V2 Failure
strainE1 E2 Av.E
10 23.10 8.83 8.14 8.49 0.09 0.08 0.0045
10 23.18 8.76 8.89 8.83 .06 .08 0.0048
The stress-strain curve as a result of the two cases of loading for bricks is shown
in Figure.5. The average value for crushing strength Fb and failure strain is also shown inTable 6. The variation of modulus of elasticity Eb with the crushing strength Fb is shown
in Figure 6 and it is seen with the best line of fit drawn, that the average relationship in
equation (6) can be obtained between Eb and Fb with a coefficient of correlation Cr = 0.60
=b
E 348.51Fb (6)
Type (a)
2 1
Normal bricks
2 1
Type b
Brick with squarecross-section
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. . . . . . . . .
(εεεε)
( σ σσ σ )
Figure.5: Stress-strain curves for brick
.
.
( )
( )
Figure 6: Variation of modulus of elasticity with crushing
strength of bricks (40No. bricks)
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3.4 Modulus of Elasticity and Poissons Ratio for Mortar
It was seen earlier that due to the absorption of water by the bricks from the fresh mortar,
the value of the actual water/cement ratio of the mortar joint is smaller than its original
value. In order to obtain realistic values of the Modulus of elasticity and Poisson ratio for
the mortar joint, a 50mm x 50mm x 125mm mortar Prisms with a particular water/cement
cured for 21 days, were tested. Both longitudinal strain yε and lateral strain ( )
xε were
measured by electrical resistance strain gauges, and stress-strain curves can be plotted for
εy and εx. Modulus (E) and Poissons ratio (v) were calculated by using Equations 4 and 5.
Table 6: Summary of average of test result conducted on different mix proportions
of mortar prisms
Mortargrade
No. ofspecimen
Average f rx 10
3kN/m
2
Er x 10
6kN/m
2
V Failurestrain
1:¼:3
1:0.5:4.51:0:6
4
44
22.03
13.104.2
3.90
3.450.75
0.18
0.180.17
0.019
0.02200.0090
The compressive stress-strain curves for the mortar mix for the adopted grades of
mortar is shown in Figure 7 while the variation of the modulus of elasticity of mortar (Er)
with the corresponding compressive strength (f r) is shown in Figure 8.
. . . . . .
(εεεε)
( σ )
( σ )
( σ )
( σ )
/
..
Figure 7: Stress-strain curve for different grade of mortar prisms
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.
.
( )
( )
/
. .
Figure 8: Variation of modulus of elasticity to compressive strength for mortar
The relationship between the stress and strain was linear while observing the
initial portion of the stress-strain curve up to about 35 percent of the mortar strength and
then is followed by a non-linear curve extending beyond the strain limits. The stress
reading beyond the strain limits of the mortar prisms with of grade 1:0:6 was difficult to
read because of the relatively low strength of these samples with a mean value of the
failure strain equal to 0.0090. An observation of Figure 8 shows that an average
relationship can be obtained in equation 7 by drawing a line of best fit.
Er = 231.11Fr (7)
A good correlation coefficient of 0.9 was obtained between the values of the
experiment test results. Also it would appear that more realistic values for E for the
mortar joint in a brickwork may be obtained by substituting the compressive strength
value (Fr) obtained from the test cubes of mortar with water/cement ratio value equal to
the value of the actual water/cement ratio ( C W a ) for the mortar joint given by the
expression in equation (3). An average value of 0.177 for poisons ratio (v) can also be
deduced from Table 6.
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4. Mechanical Properties for Brickwork
Elastic modulus and poisons ratio values for brickwork were obtained from compression
test on brick-mortar prisms by maintaining a length-height ratio of about 2. The
longitudinal and lateral strains would be obtained for cases of loading parallel and
perpendicular to the bedding plane as to obtain the modulus of elasticity in the two
orthogonal directions. The longitudinal and lateral strains will be measured by use of
electrical resistance strain gauges, and similarly the modulus of elasticity (E) and the
poisons ratio (v) values would be obtained through equation 4 and 5. Table 7 shows
summary of values obtained from the test carried out on a number of brick-mortar prisms
specimens. Values are obtained for compressive strength, failure strains, modulus of
elasticity and the poission’s ratio of masonry.
Table 7: Summary of test results on brick-mortar prisms
Description
of loading
Mortar
mix
Number
of
specimen
Compressive
strength
(×103kN/m
2)
Fm
Max.
strain
Modulus of
elasticity
(×106kN/m
2)
E
Poisson’s
ratio V
Perpendicularto bedding
plane
1:¼:31:0:4.5
1:0:6
88
8
13.4611.54
10.58
0.00190.0020
0.0047
8.417.21
6.61
0.290.33
0.36
Parallel to
beddingplane
1:¼:3
1:0:4.51:0:6
8
88
8.5
7.25.1
0.0057
0.00920.0086
5.32
4.673.21
0.18
0.210.28
Note * Vyx = xy x
yV
E
E
a
(b)
Figure 9: Set up for loading of brick-mortar prisms (a) perpendicularto bedding plane (b) parallel to bedding plane.
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The stress-strain curves are plotted using the average of values obtained from test
on 8 specimens of masonry prisms made with a specific mortar mix. The height of the
prisms was 400mm maintaining 10mm mortar joint thickness. A general setup for
loading in the two major directions is shown is Figure 8. The stress-strain curves for the
masonry prisms with mortar mix of 1:¼:3 is shown in Figure 10. Similar stress-strain
curves of masonry prisms made with other grades of mortar mix can also be obtained.
We should note here that in most cases, failure was as a result of vertical splitting cracks
along the depth of the prisms, when loading is perpendicular to the bedding plane while a
relatively diagonal splitting failure is notice when loading is parallel to the bedding plane.
It was generally noticed that the strength properties of masonry reduced as weaker mortar
is used. The stress-strain curve was seen to be linear to an extent after which a non-
linearity pattern is noticed. The variation of modulus of elasticity Em with compressive
strength f m is shown in Figure 11. An average relationship can be obtained for Em and f m
for perpendicular and parallel loading in Figure 8 and 9 respectively, with a coefficient of
correlation of 0.9 between the experimental value obtained from test on the masonry.
Em1 = 634.66Fm1 (8)
Em2 = 640.00Fm2 (9)
It would also be observed that the worst performance was seen in the prisms with weak
mortar joint as the compressive strength (Fm) was low with a corresponding high valuefor strain.
. . . . . .
(εεεε)
( )
Figure 10: Stress-strain curve for brickwork
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A study of the stress-strain curve, especially for the case of parallel loading shows that
certain salient points are easily observed on the stress-strain prisms pattern. The strain
values used to determine these points of interest varying with the grade of mortar used in
the prisms, as great difficulty is observed with deriving strain values when a weak grade
of mortar is used, especially after the near linear range; due to brick-mortar bond failure
and inivitable sudden collapse of the test specimens.
( )
( )
..
/
(a)
( )
(
)
/
.
(b)
Figure 11: Variation of modulus of elasticity for brickwork with corresponding
compressive strength (a) case of perpendicular loading (b) case of parallel loading
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Hence the following salient points are easily observed from this work and compares
favourably with [11].
(a) point 0.40Fm corresponding to the limit of the region at which the stress-strain
curve is near linear as much as possible, after which regional cracks starts
developing suggesting non-linearity.
(b) Point 0.75Fm corresponding to the particular stress at which vertical splitting
cracks are seen, but the masonry specimen still remains relatively stable.
(c) 0.95Fm corresponds to the stress level at which the splitting cracks have reached a
very advanced level and failure is ready to occur.
(d) Fm is the ultimate stress level in which the masonry is in a collapse state with a
corresponding rapid increase in strain reaching an observable failure strain in the
masonry.
5. Analytical Model for prediction of Stress-strain Curves of Masonry
Acknowledging that there exist a reasonable mathematical relationship between
the compressive strength of masonry and the modulus of elasticity of masonry, hence
analytically modeling to obtain f m is necessary as it is not always very feasible to conduct
test on masonry prisms. On the other hand, the compressive strength of bricks and
mortar (Fb and Fr) can readily to obtained through tests. The compressive strengths of
bricks, mortar and masonry can be properly related as proposed by Eurocode [12] by
equation 10
β α r bm f Kf f = (10)
where k, α and β are all constants for effective relationship. Observing experimental
stress-strain curves, f m depends on the brick strength more than the mortar strength, hence
α must be higher than β. Conducting an unconstrained regression analysis of equation 10
using the data obtained from our experimental study the values of 0.61, 0.51 and 0.36
have been obtained for k, α and β respectively using the least – square fit method and the
following equation proposed.
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Fm = 0.6136.051.0
r b f f (11)
The effectiveness of this relationship can be tested by the parameter λ, which represents
the standard error of estimate. A value of λ in equation 12 close to minimum reflects
low scatter of the actual data from the value obtained by the regression analysis [13].
( )
3
2
−
−= ∑
n
f f Riiλ (12)
where f i and^
Ri f = ith experimentally obtained and regression estimated prism strength,
respectively.
n = total number of data points.
From the experimental data a value of and 0.46 x 10
3
kN/m
2
is obtained for λ.
6. Conclusion
From the foregoing the basic mechanical properties of masonry has been obtained by
tests carried out on specimens. These mechanical properties are basic input parameters
for the numerical modeling of masonry and infilled frame structure, noting that masonry
is a composite material made up of brick units binded by mortar. Thus non-linear stress-
strain curves have been obtain for masonry with salient points identified on the stress-
strain curves with stress level of 0.40Fm corresponding to the limit of the near linear
region. Also simple analytical model has been proposed for prediction of the modulus of
elasticity of masonry, to aid the numerical analysis of masonry structures. Finally,
compressive test result obtained from test on brick units and mortar is enough to predict
the elastic properly of masonry, as simple relationships have been obtained for obtaining
the modulus of elasticity of bricks, mortar and masonry from their corresponding
compressive strengths.
References
1. Atkinson, R. H.; Noland, J. L.; Abrams, D.P. and McNary S., “ A deformation
failure theory for stack-bond brick masonry prisms in compression,’’ Proc. 3rd
NAMC, Arlington, pp. 1-18, 1985.
2 Lourenço, P.B., “Computational strategies for masonry structure,’’ PhD-Thesis,
Delft University of Technology, 1996, Delft University Press: Delft.
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Canadian Journal on Environmental, Construction and Civil Engineering Vol. 3, No. 3, March 2012
3. Augenti, N., ‘’ Il Calcolo Sismico Degli Edifici In Muratura’’, UTET: Turin (in
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