Masonry Clay Brick Under Uni Axial Load

8/13/2019 Masonry Clay Brick Under Uni Axial Load

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Stress-Strain Characteristics of Clay Brick Masonryunder Uniaxial Compression

Hemant B. Kaushik1; Durgesh C. Rai

2; and Sudhir K. Jain, M.ASCE

3

Abstract: The uniaxial monotonic compressive stress-strain behavior and other characteristics of unreinforced masonry and its constitu-

ents, i.e., solid clay bricks and mortar, have been studied by several laboratory tests. Based on the results and observations of the

comprehensive experimental study, nonlinear stress-strain curves have been obtained for bricks, mortar, and masonry and six

control points have been identified on the stress-strain curves of masonry, which can also be used to define the performance limit

states of the masonry material or member. Usin linear reression analysis, a simple analytical model has been proposed for obtainin the

stress-strain curves for masonry that can be used in the analysis and desin procedures. The model re!uires only the compressive

strenths of bricks and mortar as input data, which can be easily obtained experimentally and alsoareenerally available in codes. "imple

relationships have been identified for obtainin the modulus of elasticity of bricks, mortar, and masonry from their correspondin

compressive strenths. #t was observed that for the stron and stiff bricks and mortar of lesser but comparable strenth and stiffness,

the stress-strain curves of masonry do not necessarily fall in between those ofbricksand mortar.

DO: $%.$%&$' (")* %+-$&$ %%/ $0/+C! Database sub"ect headin#s: Bricks1 Brick masonry1 2ortars1 )ompressive strenth1 "tress strain relations1 3eression analysis.

ntroduction

2asonry walls are used in almost all types of buildin construc-tion in many parts of the world because of low cost material, ood

sound and heat insulation properties, easy availability, and locallyavailable material and skilled labor. 2athematical modelin of

structures with masonry walls re!uires the material properties andconstitutive relationships of masonry and its constituents, i.e.,

bricks and mortar, which are not easily available because of scar-city of controlled experimental tests and sinificant variation in

material properties eoraphically.The paper is concerned with the uniaxial monotonic compres-

sive stress-strain behavior and other characteristics of local handmolded burnt clay solid bricks, mortar, and unreinforced masonry

prisms. #n the comprehensive experimental study, tests were per-formed on 4% brick specimens manufactured by four different

kilns, / mortar cube specimens of three different rades, and +4specimens of masonry prisms combination of four bricks and

three mortar types . #n addition, initial rate of absorption #3(andwater absorption 5( of bricks were determined by standard

$6h.7. "cholar, 7ept. of )ivil *nineerin, #ndian #nstitute of

Technoloy 8anpur, 8anpur %+ %$&, #ndia. *-mail0

hemantbk9 mail.com(ssociate 6rofessor, 7ept. of )ivil *nineerin, #ndian #nstituteof

Technoloy 8anpur, 8anpur %+ %$&, #ndia correspondin author .*-mail0 dcrai9iitk.ac.in

:6rofessor, 7ept. of )ivil *nineerin, #ndian #nstitute of Technoloy

8anpur, 8anpur %+ %$&, #ndia. *-mail0 sk;ain9iitk.ac.in


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: D %.f

%.Zm E

j

$4f j F $%%% F %.%%

:

(i#) *) Test setup for different specimens0 a masonry prism1 b

triaxial state of stress at interface of brick and mortar inmasonry prism1 c brick unit1 and d mortar cube

"ince masonry is an assemblae of bricks and mortar, it isenerally believed that the strenth and stiffness of masonry

would lie somewhere between that of bricks and mortar. #t may betrue in cases when one component of masonry, i.e., either bricks

or mortar, is substantially weaker and softer than the other,for example, bricks found in the southern part of #ndia are veryweak and soft as reported by 7ayaratnam $+/ and "aranapaniet al.

%% . Based on an experimental study, "aranapani et al. %%reported that soft bricks modulus of elasticity %% 26a wereresponsible for development of triaxialcompression in bricks andaxial compression with lateral tension in mortar ;oints of masonry

prism. This behavior is contradictory to the enerally acceptedbehavior of the masonry constructed with stiff bricks and softer

mortar."aranapani et al. %% conducted a series of tests on ma-

sonry prisms constructed with very soft bricks modulus of elas-ticity %% 26a and a combination of different mortar rades. #twas observed that for the soft brick-stiff mortar masonry, thecompressive strenth of masonry increases with the increase in

bond strenth, which increases with the mortar strenth alonwith other factors. *win and 8owalsky %%4 tested three un-

confined and unrouted sinle-wythe clay brick masonry prismsconstructed with sinle brick type and mortar rade and proposedfour performance limit states, which correspond to / and %G of

prism compressive strenth on the risin part of stress-strain

curve and % and %G of prism compressive strenth on the fall-in branch. #t was concluded that the stress-strain curve of ma-

sonry can be ade!uately predicted by the modified 8entA6arkmodel proposed for concrete masonry by 6riestley and *lder$+: . The modified 8entA6ark model 6riestley and *lder$+: was also ;ustified by 6aulay and 6riestley $ for use incase of unconfined masonry. The model consists of three

portions0 a parabolic risin curve, a linear fallin branch, and afinal hori- Hontal plateau of constant stress at %G of

masonry prism strenth , which are defined by the followine!uations

f m and m E compressive stress and strain in

masonry1 f m Ecompressive prism strenth of masonry1 and f jcompressive strenth of mortar. Cowever, 6riestley and *lder$+: did not suest any method to estimate f

m to be used

in the abovee!uations.

2c


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(i#) &) *ffect of water absorption and initial rate of absorption

on compressive strenth of bricks Cr Ecorrelation coefficient!xperimental ,ro#ram

"everal tests were carried out in order to evaluate the uniaxialcompressive stress-strain curves of brick units, mortar cubes,

and masonry prisms constructed with different combinationsof bricks and mortar rades. Jocal bricks from four differentmanufacturers desinated as 2,B, ", and K were used, havinapproximate lenth, width, and heiht as :%, $$%, and /

mm, respectively. #3( and 5( tests were performed on brickunits to et information about the !uality of bricks. 2asonry

prisms and mortar cubes were sub;ected to monotonicallyincreasin displacement loadin strain controlled at their topwhich was applied vertically by a % k< load and L$

mm displacement capacity 2T" servo-hydraulic actuator.Cowever, brick units were tested in a ,%%% k< universaltestin machine under stress- controlled loadin.

*ach specimen was instrumented with an *psilon extensom-eter to record the displacement response durin the tests. TwosiHes of extensometers were used in the studyMa bier one withaue lenth of %% nm and L$mmpeak displacement capacity

was used in prism testin and a smaller one with aue lenthof mm and L mm peak displacement capacity was used

in brick and mortar cube testin. #n masonry prisms the displace-ment was recorded across three mortar ;oints as shown in=i. $ a to include the deformations in bricks and mortar ;ointsin the total deformation. #n the case of brick units and mortar

cubes, the displacements were recorded on their faces as shown in

=is. $ c and d . The vertical load and displacement readins atspecified locations in all the tests were directly recorded usin acomputer-based data ac!uisition system.

"tress-strain curves reported in the paper are arrived at by the

double averain method, i.e., averaed strain values are plottedon the abscissa aainst the predetermined stress values on the

ordinate control points , which are also averaed across differentspecimens. The hihest and lowest values in a set of data are notconsidered while averain that particular set of data. 2odulus ofelasticity is calculated from stress-strain curves by measurin the

slope of a secantbetween ordinates correspondin to and ::Gof the ultimate strenth of the specimens 2">) %% .

Tests for WA and IRA of Bricks

Total water absorption capacity of the brick material is iven bythe 5( test. The absorption of moisture by capillary action in the

bricks produces a suction effect that draws water from mortar andthis characteristic is defined by #3(. The rate of absorption can

have an important effect on the interaction between freshly laidmortar and the brick units. #3( is measured in order to assist in

mortar selection and material handlin in the construction pro-cess. #t is measured in terms of mass of water absorbed perminute by the brick material per unit area of brick immersed in

about : mm deep water, which is kept constant by addin waterdurin the test, as per ("T2 ) &/-%% ("T2 %%$c . #":4#" $b was used to perform a 5( test whose provisions aresimilar to those iven in ("T2 ) &/-%% ("T2 %%$c .

=i. shows the variation in compressive strenth ofbricks f b with #3( and 5( and Table $ ives the correspondinsta- tistics. 5( was found to vary from $$ to $:G mean

$.:G, coefficient of variation )K? %.$: and #3( varied from%./ to

.4 k' m ' min mean $. k' m ' min, )K? %.:4 1 lower#3( values were found for bricks with hiher f b. #n thepresentstudy, a much better correlation was observed between #3(

and f b correlation coefficient F%.// than that between 5( and f bcor- relation coefficient F%.4 . Too hih or too low an #3( isdetri- mental to achievin a ood initial and final bond between

brick and mortar, which not only affects the masonry flexuralstrenth, but also its water tihtness and durability. #t wasobserved by 7rysdale et al. $4 that if #3( is less than

%. k' m ' min, which is a case for low absorption or low-suction bricks, then such bricks may tend to flow on mortar,

particularly if the bricks are damp. Kn the other hand, for

hihly porous and absorptive bricks #3( $.k' m ' min ,a poor brickAmortar bond may result for thin mortar ;oints withless waterAcement ratio because of rapid suction of water inmortar by bricks.

Stress-Strain Curves forBricks

The tests were performed in accordance with ("T2 ) &/-%%("T2 %%$c and #" :4 #" $a . The experimental setupable *) "ummary of Test 3esults for Brick Units

Brick type

f b26a =ailure strain Eb26a 5(G #3(k' m ' min2 $%specimens $/./ %.: a %.%%/ %.$+ ,:%% %.$ $. %.$$ .& %.$B $%specimens $&.$ %.%+ %.%%&% %.$ ,%:% %.:4 $:.% %.$$ .4 %.%K $%specimens +. %.: %.%%/% %.: /,$& %.& $$.4 %.$ %./ %.:4" $%specimens %.& %.$/ %.%%/ %.+ &,:4 %.$% $$.+ %.% $.+ %.4(verae 4%specimens %.+ %.:: %.%%& %.:4 &,% %. $.: %.$: $.% %.:4


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a=iures in brackets indicate coefficient of variation.

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(i#) .) Typical failure modes of0 a brick units1 b mortarcubes1

and c , d masonry prisms

for testin and the characteristic crushin failure of bricks isshown in =is. $ c and : a , respectively. =i. 4 a shows thestress-strain curves for the four types of bricks obtained by aver-ain the stress-strain data from ten samples of each type of

brick. The bricks were found to be behavin linearly up to aboutone-third of the ultimate failure load after which the behavior

became hihly nonlinear. (n averae stress-strain curve for all thebrick types used in the study is also shown in =i. 4 a . Thesummaryof results includin f b, failure strains, and modulus of

elasticity Eb are iven in Table $. =or different bricks used

in the study, mean values of f b varied from $&.$ to +. 26a

mean%.+ 26a, )K? %.:: . 2ean values of failure strain recorded inthe brick specimens were found to vary between %.%%/ and%.%%/ mean %.%%&, )K? %.:4 and Eb was found to vary be-tween ,%%% and /,%% 26a mean &,% 26a, )K? %. .?ariation of Eb with f b is shown in =i. a , and it is seen thatEb varies between $% and %% times f b. (n averae value of Ebmay be determined by

(i#) 0) )ompressive stress-strain curves for0 a brick units1 bmortar cubes1 and c masonry prisms

(i#) 1) ?ariation of modulus of elasticity of0 a bricks1 b mortar1and c masonry with correspondin compressive strenths

Eb :%%f b1 )K?%.: 4Eb and f b are not very well correlated as evident fromsinificant scatterin of data in =i. a 1 the coefficient ofcorrelation, Cr E %.:1 therefore *!. 4 should be used withcaution.

Stress-Strain Curves for Mortar Cubes

Three different rades of mortar cement0lime0sand by volumewere used in the study, viH., $0%0& weak , $0%0: strong ,and

$0%.04. intermediate and mortar cubes of % mm siHe weretested after + days of castin to obtain theircompressive stress-strain curves. The procedure for obtainin the compressivestrenth of mortar cubes is iven in ("T2 ) $%') $%2-("T2 %%$a and #" % #" $ . *xperimental setup andtypical failure of mortar cubes are shown in =is. $ d and: b ,respectively. )ompressive strenth of mortar depends upon thewaterAcement ratio and cement content. 5aterAcement ratiore- !uired for preparation of mortar was strictly monitoredeven thouh not controlled, and it was observed that the ratio

varied from %./ to %.+ for various mixes to obtain workablemortar in a very hot and dry climate about 4 N ) . =i. 4 b

shows the compressive stress-strain curves for the threerades of mortar obtained by averain the data from nine

specimens of each rade. #nitial straiht portion of the stress-


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strain curve up to about one-

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samples. "train readins on the fallin branch of the stress-strain K +. %.$ %.%%/ %.:& ,$ %.%curve could not be recorded for the weak mortar because of its " /.& %.$/ %.%%% %. 4,% %.44

brittle and explosive crushin failure after reachin the ultimate (verae /. %.$+ %.%%: %.4$ 4,%% %.:+

able &) "ummary of Test 3esults for 2ortar )ubes able .) "ummary of Test 3esults for 2asonry 6risms

Ej m Emf j 26a =ailure strain 26a Brick type 26a =ailure strain 26a

a Weak mortarM$0%0& specimens:.$ %. %.%%+/ %.:+ 4 %.:%

b Strong mortarM$0%0: specimens%.& %.%+ %.%$+ %.$ :,/% %.$&

c Intermediate mortarM$0%.04. specimens$. %.%&

%.%/% %.:&

:,:%% %.&

third of mortar strenth is followed by a nonlinear curve,whichextends well beyond the strain limits correspondin to the brick

a 6risms with weak mortarM$0%0& 4 /specimens2 4.% %.$: %.%% %.: ,: %.:%B . %.$/ %.%%:4 %.4 $,/ %.$/K .$ %.$& %.%%+& %.$ ,&:% %.$4" 4.: %.$/ %.%%& %.$4 ,: %.$(verae 4.$ %.4

%.%% %.4:

,:%% %.4

b 6risms withstrong mortarM$0%0: 4 /specimens

2 /.4 %.$% %.%%&/ %.+ :,+ %.$+B &. %.$4 %.%%4$ %.: :, %.

strenth. The crushin failure of two other mortar rade speci-

mens was more ductile and nonexplosive. 2ortar strenth f j, failure strains, and modulus of elasticity Ej of mortarspecimens are shown in Table .

Weak mortar was found to be very weak and soft as comparedto the other two rades with mean f j and Ej of only :.$

26a)K? %. and 4 26a )K? %.:% , respectively. Kn the otherhand, mean f j for strong and intermediate mortar was %.&

26a)K? %.%+ and $. 26a )K? %.%& , respectively1 and meanEjwas :,/% 26a )K? %.$& and :,:%% 26a )K? %.& , respec-tively. "imilarly, mean values of the failure strain at failure

in weak mortar was only %.%%+/ )K? %.:+ as compared tothe values of %.%$+ )K? %.$ and %.%/ )K? %.:& for thestrong and intermediate mortar, respectively. =i. b showsthatEj varies between $%% and 4%% times f j and averae valuemay be determined by

Ej %%f j 1 )K?%.: =or the present data, a very ood coefficient of correlation Cr E %.% was observed between the experimentally observedEjvalues and the values estimated usin *!. .

Intermediate mortar performed well in terms of strenth andductility as compared to the other two rades because of the pres-ence of lime1 f j for intermediate mortar was about :G lessthan that of strong mortar1 however failure strain was about 4Gmore=i. 4 b .Stress-Strain Curves for Masonry Prism

2asonry prisms were constructed usin combinations of fourbrick types and three mortar rades, and stress-strain curves wereobtained by averain the data from seven specimens of each

combination. (pproximate heiht of five-brick hih masonryprism with $%-mm-thick mortar ;oints was about 4%% mm. )om-pression testin was done followin ("T2 ) $:$4-%%a ("T2%%$b and #" $% #" $+/ . Ieneral test setup and typical

failure of masonry prisms are shown in =is. $ a and:c and d ,respectively. The stress-strain curves for masonry prisms are

shown in =i. 4 c and the summary of results includin prism

strenth f m , failure strain, and modulus of elasticityEmare iven in Table :. =ailure of the ma;ority of the prism speci-

mens was due to the formation of vertical splittin cracks alon

their heiht. =ailure of about $%A%G of specimens in each

set took place because of crushin of an odd weaker brickin the prism or bond failure by flexural bendin o

specimens, probably due to poor alinment of the specimenwith the load-


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c 6risms with intermediate mortarM$0%.04. 4 /specimens2 &. %.$ %.%$% %.$/ :,4 %./

B . %.: %.%%& %.4% :,% %.4

K /. %.4 %.%% %.: 4,/$ %.::

" &.+ %.: %.%%&& %.:$ :,: %.&

(verae &.& %.% %.%%+% %.:4 :,+%% %.:in arm of actuator1 these results have not been included in thestudy.

2ean value of f m was found to be 4.$ 26a )K? %.4,/. 26a )K? %.$+ , and &.& 26a )K? %.% for prisms con-structed with weak, strong, and intermediate mortar, respectively.2ean failure strain was %.%% )K? %.4: , %.%%: )K? %.4$ ,

and %.%%+ )K? %.:4 for masonry with weak, strong, and inter-mediate mortar, respectively. 2asonry prisms constructed withweak mortar were found to be weaker and softer with meanEm of

,:%% 26a )K? %.4 as compared to those constructed withstrong and intermediate mortar with mean Em of 4,%% 26a)K? %.:+ and :,+%% 26a )K? %.: , respectively. The stress-strain curve was found to be linear for up to about one-third off mafter which cracks bean to form in the bricks introducin the

nonlinearity. =i. c shows that Em varies between % and$,$%% times f m , and an averae value ofEm may be determined

by

Em %f m 1 )K?%.:% &=or the present data, a relatively ood coefficient of correla-

tion Cr E%.&: was observed between the experimentally ob-served Em values and the values estimated usin *!. & ,which was found to be in line with internationally accepteddocuments and codes, e.., =*2(:%& =*2( $ , whichalso proposesEm %f m . #nternational Buildin )ode #B)%%: and the 2">) document 2">) %% recommend Emas /%% times f m , while 6aulay and 6riestley $ and*urocode& )*< $& suest conservatively hiher values ofEm /% and $,%%% times f m , respectively . The )anadianmasonry code ":%4.$ )"(%%4 recommends Em as +% times f m with an upper limitof

%,%%% 26a. 7rysdale et al. $4 plotted Em and f mobtained

from past experimental studies and showed that Em variesfrom$% to $,&/% times f m.

=i. 4 c shows that the behavior of masonry prisms con-structed usinstrong and intermediate mortar was !uite similar inthe linear reion, while the best performance was shown by

prisms with intermediate mortar, which has lime content)0J0"E$ 0%. 0 4. . (lthouh, f m was found to be about$:G

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(i#) 2) )omparison of stress-strain curves for brick units, mortar

cubes, and masonry prisms for different rades of mortar0 a weak1b strong1 and c intermediate. 7ata points represent experimentalresults and solid lines represent correspondin trend lines.

less for prisms with intermediate mortar than those with

strong mortar, the failure strain was about %G more. Thus,there is a sinificant improvement in the ductility of masonry incompres- sion without any considerable compromise with thecompressive strenth because of lime in mortar. Therefore, the

ae-old practice of usin lime in mortar, which has beendiscontinued in many parts of the world for various reasons,appears to have a role in improvin performance and its useshould be re!uired.

=i. & and Tables $ and show that a ma;ority of the bricksused in the present study were stroner and stiffer than the mortar

used. =i. & a shows that the stress-strain curves of masonryconstructed with weak mortar falls in between those of bricks andmortar. Kn the other hand, for masonry constructed with interme-diate andstrong mortar =is. & b and c , the stress-strain curves

of masonry fall onthelower side of those correspondin to bricksand mortar. Therefore, the enerally believed go-between com-

pressive behavior of masonry may not be applicable for all thecases, especially when the strenth and stiffness of bricks andmortar are comparable.

=is. / a and b show that f m increases with f b and f j forall the brick types and all the mortar rades, however theincrease is more prominent when weaker mortar is used in

constructin masonry. This characteristic behavior of masonryhas also been reported in past studies 7rysdale et al. $4 .

Therefore, althouh some minimum strenth of mortar isre!uired for strenth and to ensure ade!uate durability, other

considerations such as better workability of the fresh mortarand a more deformable mortar to

(i#) %) 3elationship between0 a masonry prism strenth and brickcompressive strenth for different mortar rades1 b masonry prismstrenth and mortar compressive strenth for different bricks

accommodate differential movements have led to the commonadvice of not usin a hiher strenth mortar than is re!uired forthe ;ob.

Control ,oints Definin# Stress-Strain Cur$esof Masonry

Based on the limit states proposed by *win and 8owalsky%%4 , six control points were identified on the stress-straincurves of masonry in the present study, which correspond to theexperimentally observed six significant events representin com-

pressive stresses in masonry and the correspondin compressive

strains. The six control points represent ::, /, %, and $%%G off m on the risin part, and % and %G of f m on the fallinbranchof stress-strain curve as shown in =i. +. "train values used to

define the control points depend larely upon the mortar radeused in prisms. #n the case of prisms constructed with weak mor-tar, strain readins in the descendin part of the curve could not

be recorded after the compressive stress reduced to about &%G of

fm after reachin peak because of brickAmortar bond failure

inmost of the cases, and sudden and brittle failure of the specimens.

The control points identified durin the tests are as follows0

$. %.:: fm represents the point up to which the stress-

strain curve remains linear. Thereafter, several cracks startdevel- opin in masonry introducin nonlinearity1

. %./ f m is where vertical splittin cracks in bricks startde- velopin at about this stress1 however masonry stillresists loads without much deterioration1

:. %. fm represents the stress level in masonry ;ust before

the failure when the vertical splittin cracks propaateexces- sively throuhout the masonry1

4. f m is the ultimate stress level in masonry after which


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the

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nb j

be hiher than . #n *urocode& )*< $& , the values of and have been specified as %.& and %., respectively, andK variesfrom %.4 to %.& dependin upon brick properties and brickAmortar

;oint confiuration. These values of and are valid for mortarhavin compressive strenth not more than%26a or two timesf b, whichever is less.

Based on reression analysis of data obtained in an experimen-tal study, 7ayaratnam $+/ proposed different values of theconstants K, , and as per the followin e!uation

%. %.

f m

E %./f b f j+

(i#) ') "tress-strain curves for masonry prisms for different rades of

mortar0 stress is normaliHed with respect to prism compressivestrenth for each curve

masonry beins to drop the load and exhibits sudden increasein the strains1

. %. f m 0 the stress correspondin to this control point onthe descendin curve may be considered as the maximum

de- pendable compressive strenth ofmasonry1and

&. %. f m is the maximum residual compressive stress andcor- respondin failure strain observed in masonry.

The last two control points were not recorded in the masonryprisms with weak mortar because of reasons already mentioned.

These control points can be effectively used to define the perfor-

mance limit states of the masonry material or member.

Analytical Model for Stress-Strain Cur$esof Masonry

Estimation of Prism Strengt of Masonry

f m is the intrinsic property of masonry which can be used inthe

Usin experimental results on hollow structural clay tiles, Bennettet al. $/ suested that the masonry prism strenth can beconservatively estimated as three-tenths of the brick compressive

strenth. Based on testin of solid claybrickmasonry, the follow-in e!uation is proposed by 2">) %% for estimatin the ma-

sonry compressive strenth

fm EA4%%DBf b psi

where AE $.% for inspected masonry1 and B varies from %.to%. for different mortar rades. The units of f b in *!. are

psi$ 26a $4psi

.5hen the *urocode& )*< $& relation, *!. / , is applied

with K E %.& Iroup $ bricks as per the code to thepresent data, R and come out to be %.& and $.% 26a,respectively%.+f b was used as the normaliHed strenth of bricks . Knthe other hand, the relation proposed by 7ayaratnam $+/ , *!.+ , ives a poorer match with R value of F%.4 andvalue of .$+ 26a. )learly, e!ual weihtae iven to f band f j E E %. in *!. + is not supported by this study."imilarly, since the expression suested by Bennett et al. $/depends upon the compressive strenth of brick units only,

R comes out to be poor F%.$ and comes out to be

much hiher.%$ 26a . (ain, a poorer match results with the R valueof

F%.$ and the value of .%: 26a when *!. , proposedby2">) %% , is applied withB e!ual to %. to the present data.

R is the coefficient of determinationbetween the experimen-tally obtained values and values obtained by reression analysis

and is thestandard error of estimate, which ives an idea of thescatter of actual data from the value estimated by reression

analysis. ( value of R closetounity indicates a ood fit and thatclose to Hero indicates a poor fit, whereas it is desirable that isa minimum, implyin that the scatter in the data about the

estimated value is a minimum. R and are calculated as5eso- lowsky $/&15onnacottand5onnacott$/

f F f desin of a variety of masonry elements, particularly the walls.f

m

is also used to estimate Em and for plottin the masonrystress- strain curves. Therefore, f m is one of the most basicandre!uired properties that must always be available for a ivenmasonry. Cowever, it is not always feasible to conductcompression testin of masonry prisms. Kn the other hand, f band f j are readily available in the desin codes or can beobtained easily by conductin tests. The three compressivestrenths can be conveniently related

and

RE $ Fi Ri

f i F!f

E i RiF :

$%

$$as done in *urocode& )*< $& as

f m EKf f /where f i and

f Ri E ith experimentally obtained and reression

est mated prism strenth, respectively, !f E mean of the

experimentally


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obtained prism strenths1 and nEtotal nu mber of data points. Thewhere K, , and E constants. #n addition, a few otherfactors have also been specified which take care of siHe andshape of bricks, dry strenth of brick, normaliHed strenth of

bricks, etc.

(s already discussed, f m does not depend upon themortar strenth as much as it does on the brick strenth, therefore

must

divisor nF: is used in *!. $$ rather than n in order to makean unbiased estimation of since three estimators K, , andare re!uired in the calculation.

#n the present study, K, , and have been obtained as %.&:,%.4, and %.:, respectively, by unconstrained reression analysis

%.0 J!"R#A$ !% MA&ER'A$S '# C'('$ E#)'#EER'#) * ASCE SE+&EMBER 2-


15/23

E f m

able 0) )omparison of past *xperimental 3esults on 2asonry 6risms with (nalytical 6redictions

*xperimentalvalues26a 6redicted values of f m26a3esearch

a f b f j f

m6resent study

*!. $ *urocode&)*< $& 7ayaratnam$+/ Bennett et al.$/ 2">)%%"aranpani $ +. :.$ .: . $%.:

b./ $/.& $.4 &. . /.% 4.4 $.

TomaOeviP $%.% %. .% $.& +. .: $./ %.& . :.% %.% 4.+ $:/."aranpani $%./ 4.$ . :. .% :.4 $+. $.+ . :. $%./ 4. &+."aranpani $%./ $%.& :. 4.: ::.& 4.4 :&. . .& :. %.% 4. .

) %%

are ood for masonry constructed with hih strenth bricks, how-ever for lower strenth bricks, the error in estimatin the masonrycompressive strenth is comparatively hiher. The relation pro-

posed by Bennett et al. $/ depends on the compressivestrenth of brick units only1 therefore it does not take care ofweakness induced in masonry because of the use of low strenth

mortars. The e!uation proposed by 7ayaratnam $+/ ivese!ual weiht to the compressive strenths of bricks and mortar,therefore in most of the cases, the errors in estimation of masonrycompressive strenth is hiher.

The estimation of masonry compressive strenth usin *!.

$ proposed in the present study is consistently better for prism


16/23

fm m m

where f m and m E compressive stress and strain in masonry,re- spectively1 and m E peak strain correspondin to f m .=urther, the parabolic curve can be extended in the descendin

part of the stress-strain curve until f m drops to %G1 thecorrespondin straincan be calculated usin *!. $: . (fter the stress level of %. f mis

reached on the descendin part, the curve can be simplifiedasa

straiht line up to the residual stress in masonry, i.e., %G of f m. ( problem remains in estimatin the value of m for themasonry prism in field applications because it is difficult andcumbersome to do the controlled tests with accurate measurininstruments and loadin machines. #n the present study, thefollowin e!uation is proposed to estimate m by reressionanalysis of the experimental data.

J!"R#A$ !% MA&ER'A$S '# C'('$ E#)'#EER'#) * ASCE SE+&EMBER 2- %.1


17/23

Em j %./

f

(i#) +) 7ependence of masonry strain on mortar strenth

(itness of ,roposed Analytical Model

The proposed analytical model for compressive stress-straincurves is examined for its fitness by comparin it with0 $experimental curves obtained in the present study1

experimental curves obtained in seven different studiespublished in the past"aranapani et al. %%1


18/23

analytical model with those obtained in the present experimental

study is shown in =is. $$ aAc , which show a very close match

between the analytical and experimental curves. f m predictedbythe present analytical model match really well their experimental

counterparts Table 4 . Therefore, =is. $$ aAc show the curves

enerated by the present analytical model usin only the predicted

f m ."tress-strain curves have been enerated by the proposed

model usin f b and f j reported in the past seven

experimental studies and compared with the experimental curvesof the oriinal studies in =is. $$ dA; . The proposed analytical

model clearly demonstrates a reasonably ood prediction ofthe stress-strain curves when compared with the experimental

curves. The proposed model successfully predicts prismstrenths and correspondin peak strain values fairly

accurately. #n most of the cases, failure strains predicted by the

proposed model are sinificantly reater than the correspondinexperimental values. This may be due to the fact that it is

difficult to record the rapidly descendin part of the stress-straincurves experimentally and, therefore, the researchers of these

studies may not have accurately recorded the diminishin curve."aranapani et al. %% used very soft and weak bricks in

their experimental study, therefore prism strenth reported in

their study is also much less, which matches !uite well withtheir predicted values based on the present study =i.$$ d . =or all other studies in which hih strenth brickswere used, predicted prism strenths are observed to be less thantheir experimental counterparts.

*xperimental stress-strain curves of the present study and theseven past studies are also compared with the analytical estima-tion usin the two past models0 the modified 8entA6ark model

proposed by 6riestley and *lder $+: , and the *urocode& )*

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