The moment-magnifier method applied to brick walls

4 . b. 3
THE MOMENT -MAGNIFIER METHOD APPLlED TO
BRICK WALLS
CARL TUR KS T RA
JOSE OJINAG A
Department
of
Ci,)il Engineering and Applied Mechanics , UcGill University , !1ontreal , Canada
TllE MOMENT- MAGNIFIER METHOD APPLIED TO BRICK rvALLS
DIE MOMENTEN-VERGROESSERUNGSMETllODE
IN DER ANi.'ENDUNG AUF ZIEGEV1AUERWERK
This paper summarises the results
of
a study of the
ultimate capacity of vertically loaded brick walls .
The study is based on the moment - magnifier method
von Versuchen zusammen, die die Bruchlast von verti-
which is used in steel and concrete column design in
kal belastetem Mauerwerk bestüwnen sollte? Der Unter -
North America . Extension to brick mas onry design
would provide a con s istent approach in limit states
grunde , wie sie auch für den Entwur f von Stahl - und
design methods presently under development in Canada .
Betonsáulen in den USA angewandt wird .
In the method, bending moment- axial force inter action
Eine Uebertragung dieser Methade auf den Entwur f von
relation ships for shor t walls are used .
However , the
Diese Untersuchung fasst die Ergebnisse einer Reihe
suchung liegt die Momenten- Vergrosserungsmethode zu-
Ziegelmauer wer k WÜY'de zu einer konsequenten Annâne-
bending moments found from conventional structural
rung an die derzeitig in Kanada entwickelten Entwurf9-
analysis are multiplied by a magnification facto r de -
methoden fún r en . In dieser '4ethode wird das Zusammen -
pending on wall height, stiffness and end constraints .
wirken von Biegemoment und Axialkraft bei kurzen
Mauerl<)erksteilen zugrunde gelegt . Jedoch we1'den die
In the paper the basic assumptions
of
the method ar e
aus üblichen Untersuchungen gefunderten und bekannten
presented briefly and r elevant in f ormation on stress -
Biegemomente mit einem Vergrosserungsfaktop multi-
strain characteristics and br ick wall behaviour are
pliziert , der von der 'Iandhohe , der Steifheit und
r eviewed .
der Einspanmmg abhá·n gt .
The method is applied to a large collection
of published test data from Europe and North America
which has been set up in a computerised data bank .
Test data includes a variety of brick- mor tar combi nations, wall slenderness and end conditions , and load
eccentr1:ci ties .
The limits of applicabil i t y
In der vorliegenden Untersuchung werden die der
Methode zugrunde gelegten Annahmen erortert. Es
f olgt eine kurze Uebersicht úôer Charakterika der
Spannungsbeansp~Achung
und úôer das Verhalten von
Mauerwerkskorpern . Die Methode bez ieht sich au f eine
of
the method ar e di scussed
and conclusions drawn as to the advantages and di sadvantages of the approach in wall design o
grosse Anzahl ver off entlichter Versuche au s EUr opa
und den USA , die in e1:ner l<omputeY'ge steueY'tc<n Datenbank zusammengef asst wurden .
Die Versuchsdaten schliessen verschiedenartige Mortel kombinationen , Schlankheiten, Einspannungen und ausmittige Lasten ein .
Die Gr enze der Anwendbarkeit dieser Methode wird dis kutiert und schliesslich werden Folgerungen füp den
Entwurf von Mauerwepkskó'rpern gezogen .
4 . b . 3-0
LA METHODE DU " MOMENT - MULTIPLICATEUR "
DE METHODE VAN DE "MOMENT- VERMENI GVULDIGING "
APPLIQUEE A DES MURS EN BRIQUES
TOEGEPAST OP BAKSTEENMUREN
Cette communication résume les résultats d 'une re-
Deze mededeling vat de resultaten samen van een
cherche de la capacité limite des murs en briques
onderzoek naar de grenskapaciteit van vertikaal
chargés verticalement .
L ' étude est basée sur la
belaste baksteenmuren .
De studie is gebaseerd
méthode du " moment - multiplicateur " largement
op de 'moment- magnifici " methode welke in Noord-
utilisée en Amérique du Nord pour le calcul des co-
Amerika veel gebruikt wordt voor de berekening
lonnes d 'acier et de béton .
Une extension de cette
van staal en betonkolommen .
Uitbreiding van deze
méthode à la maçonnerie serait une étape importante
methode tot metselwerk ware een belangrijke stap
dans la direction du calcul des valeurs limites qui
in de richting van de grenswaardenberekening die
sont actuellement développées au Canada .
thans ontwikkeld wordt in Ranada .
Dans cette méthode on part du rapport moment de
In deze methode wordt uitgegaan van de verhouding
flexion - force axiale pour des murs courts .
buigmoment - axiale kracht bij korte muren.
Les
moments de flexion trouvés par les méthodes de cal-
De
buigmomenten gevonden door konventionele reken-
cul conventionnelles sont toutefois affectés d ' un
methoden worden echter vermenigvuldigd met een
multiplicateur, basé sur la hauteur de paroi , la ri -
multiplikator, gebaseerd op wandhoogte , stijf-
gidité et les tensions limites .
heid en randspanningen .
Dans cette communication les hypotheses de base de
In de mededeling worden de basishypothesen van de
la méthode sont brievement présentées ainsi que d ' im-
methode kort voorgesteld, samen met de belangrijk-
portantes constatations en liaison avec le rapport
ste vaststellingen in verband met de verhouding
tension - transformation et le comportement des murs
spanning-vervorming en het gedrag van baksteenmu-
en briques .
ren .
La méthode est appliquée à un grand ensemble de ré -
De methode wordt toegepast op een grote verzameling
sultats qui ont été traités par ordinateur et publiés
van resultaten gepubliceerd in Amerika en Noord-
en Amérique et dans le Nord de l ' Europe .
Les données
d ' essai comprennent une grande variété de combinaisons
Europa die in een computer behandeld werden .
De
proefgegevens omvatten een grote variatie van bak-
de mortiers - briques, d 'élancements de murs et de
steenmortelkombinaties , muurslankheden en randvoor-
conditions limites , ainsi que d ' excentricités .
waarden alsmede excentriciteiten .
Les limites du champ d 'application de la méthode sont
De grenzen van het toepassingsgebied van de methode
discutées , de même que les avantages et inconvénients
worden besproken alsmede de voor- en nadelen voor
pour le projet de maçonnerie .
het ontwerpen van metselwerk .
4 . b . 3-1
have bean excluded .
I [HRO OUCTIO~J
To de velop m8thods of limit states design procedures
for preoictlng average ultin~te load capacity. a know la dge of ths va riability of capacity about these
aV3ratSS mUSL ~8 estaol ishe d . The objective Df thls
paper is to sxamlne the LHe Df the momant magnifier
a~pro a ch i n tne special ca se of singl o wythe unre illforc8d brid, \·la 11s subjected to 8ccentric vertical
end loads .
The design prob lem involved is the conventional one
of relatin~ sactio n capac it y to loa ding conditions .
end constraints, l'lull geomet r y. and the properties
Df st a ndard reference specimens . However. the
problem ia rela~iv9 1y difficult in orick wall design
bar:ause of the ;,xis tence of two components with
different ms chanical properties leadi ng to complex
strGss distribution s and failure criteria [1,2) . For
til e case considered . a numb5r Df simplified theories
(3. 4 .5. 6 . 2) and emp iri ca l metilods (7) have been deveL::ped .
PraGtical design methods should be relatively simple
and consi ste nt ~ ith princip18s of strL~tural mechanics
so that s ituations beyond test conditions can be
tro~cod.
Df cünsiderabls interest is the possibility
Df using tne morr.ent -magnifier approach suggested by
Yoke l. Ma they and Dikkers [8 . 91 for concrete b lock
rr. ~ 3'Jnry and b rick mesonry (10).
Such an app roa ch
would provi de cons istency with steel and reinforced
concrete de sii~ matho ds . Mo reover, it would provide
a r3tion al basis fo r consideration of general wall
end ~nnditio ns. l~ading . and pcssibly the effects Df
r einfCl r cing .
This paper examines application Df the simplest
posslble form Df tlle momen t-rrlag ni fi el' appT'oach tog2ther with re15ted wall p r operties. Attention is
restr i cted to variations in wall capacity . The
question Df safa ty factors to be used in design is not
considered.
SHORT SECTION CAPACITY
Fundamen tal to any study Df wall beha viour is the
capacity Df a short sRctl on subj ec tod to an axial
f orce F' and a bending moment M about the centroidal
axis . For brick wal ls. several cases must be considered dape nding on whether the section is in comprassion through its thickness or axp erien c es tensil e st r ain . In the latter case . bahaviour depends
on ~hether or not the tensile capacity has been exceeded .
For an assumed linear strain variation through the
wall . resultant axial forces and bs nd ing moments
can readily be calculated for any assumed stressstrajn charactgristics . Shovin in Fig . (2) are the
axial fo rc e - banding moment relationships for the
three ideal1zations Df Fig . (í) for cases corresponding to a ttainment Df the u ltimate rupture strain
E.
on the compression face . Results have been nondimensionalized using the reference ca~acity Po an d
the conventional linear kern bending moment Po t/12 .
Also sh:Jwn are wall test results fro rn Ref. (7) wi t :,
a slanderness ratio kl/r less tnan 40 for walls
tested axially . witn one end flat . or in double curvature, and lass than 30 f or single curvatura sonditions . Such walls can be expact~d to havB somewhat
less than the short section capacity .
Comparison Df the analytical results show that nonlinearity reduces the kern Bccentricity and inCI'eilSeS
axial load capacity fo r a gil/en eccentri city . The
ex periment a l resul t s in dicate t ha r cólpaclty decreases
less rapidly with eccentricities up to t/3 tnan even
a linear-recta ngul ar stress-strain diagra!l1 without
te nsile stI'ength would predict . A simi l ar "straingradient effect " was noted by Yakel et aI (8) fo r concrete block masonry . Such effects may be oue to
changes in transverse stress patterns under ncn-uniform strain and suggest thet the a xially 10i:l ded prism
is an inadequate measure Df mechanical properties.
REFERENCE PROPERTIES
THE MOMENT - MAGNIFIER METHOD
In the absence Df reliable models rela ting masonry
prcperties to the properties nf bricKs and mDrtars .
s mall piers or prisms hava be8n used as a standard
measure Df masonry behaviour . The choice Df a standard rsfer8nce lnvo l v8s considp.ration Df the effects
Df test conditions together with t he easo of fabrication and is somewhat arbitrary . I n this st udy . the
single wythe prism with a haight to thickness ratio
Df 5 te sted between flat rigid plates (11) was adopted
as a practical reference . Al I wa ll capacities P per
unit length are referred to the capacity P per unit
length of s lJch prisms .
o
Numerous tests (12 .13 . 14 . 15) have shown that the
stress-strain chBracteri stics Df brick masonry is
generally non - linear . Some tests sugg es t that segments Df a parabola may be used out the behaviour
in the region Df high compressive stresses does not
saem to have heen extensi ve ly investigated . Tensile
stress capacity has not been well defined . In
exarnina tion Df short section behaviour the three
idei:llize d stress - stra i n diagrams Df Fig . (1) were
used.
The ini ti al tangent modul us E has a significant random
variat io n . Exarr.inat ion Df 142 experimental results
(16) innira~ed a very good correlation with brick comprassive stre ngt h fb . The equation
As wa ll slenderness increases . lat e ral deflect j.ons become s i gn-Lfican t as axial forces act throü"h the deflectians to modify the distribution Df bendirog rnoments along the \~all heigM . As a r"s ul t . the l ocation
and magnitude Df tha maximum moment is va1' iabl e . For
exarnple. an eccentric load within the [,erro at the ends
cm lead to eccontrici ties beyond tile I,ern at mid height . Details Df behaviour depend on the wall
height 1. radius Df gyration r. end condHions. and
the shape of the moment diagram found fro m elementary
anal ysis.
The moment-magn ifier method is a device for converting
the bending moments alo"g the lsngth Df a beam-column
to equi.val,mt short section bendir,g mO!l1ents . The
section is then design e d using the shor~ 3ection interaction relationsh ips. the applied axial forces , and
the larger Df the applied end moments or aqui valent
"magnified " moment o Tha methoo was davelope d for steel
sections and has been ad~pted to concret~ column design (171.
For the load case under study . the equi valent moment
M
can be I-Iri tten in ter-ms Df the axial force and
m~~~mum applied end eccentricity e
in the form
max
M
E
145 . 000
+
220 .6 fb
(psi)
(1 )
had a cor rel ation Goeffici ent Df 0.941 and a standard
error Df e sti ma~ e of 360 .000 psi . Waak lima mortars
mag
LC Pe
max
(2)
tl . b . 3-2
S t ress
S tre 5S
Stress
+-.
E
.
TE.
E.
I
Str ain
(a)
( b)
Li near
Strain
Paraboli c
FIG. 1 rDEALI ZED
E.
2
St r ain
I
(c)
Linear
Rectangle
STRESS STRAIN DIAGRA MS
Axia I Force
1.0
0 .5
1.0
FIG~
E r ror (% po )
15
10
...
-5
... ...
O X
X
O
... ...
...
... X
...
""
150
X
X
...
X
Length Factor
K = I
K
0.7
K = 05
200
Slenderness
Ratio = _k_1
r
X
O
-2G
FIG. 3
SHORT SECTION INTERACTION DIAGRAMS
X
... 5 0
X
- 10
- 15
...
...
5
Effect ive
2
ERRORS FO R AX IALL Y LOADED WAL LS
2 .0
3 .0
4 .b . 3- 3
where
1
(31
----- p- -
L
1 -
p-
c,
c
( 41
p
( 51
cr
ll18 fectur L ll1r: l uooc; the effect. s of r'lateri éll stiffnass tllrough ths fIlodulus Df e lasticity t: , section
goome try through Lhe moment Df i nertjoa I , the length
x" emd en,J s'Jpoo,-t condi1: io n th l'ougn the effective
lsngth filet!),- :'. . -;-he shape Df the e lfomentary í11Dme nt
oiagralil l5 introouced b", the faetcr C. To dea l with
nominally axiéllly loaded Cilses, a mllumum a r acci d",ltaI anel dccentri cit y G1l1s t be i ,-,troducB-J .
lhe n~ thud was deve lope d fGr lineilr sl a stic sections
,;iLh c:onsta nt c r us s-s e C1:i OrI3 an d melst be approached
~ fth caution in mason r v as in concrete design o
Non :Lj r,e ari ty Df mechan ica l pl'operties can increase
l~ Leral deflections relativs cO an al ysis based on the
j ~ itial tangent mod ulus.
le nsi 18 cracking before
failure Jea ds to var iatLuna in c:ross-sectional geo metry ':ln d can lead t,) stability failures n ot con ,, 1dered 1.;'1 the method .
In con c rete design these
pf +ects hciVO ~een i nclujed by the ~SB Df modified
fl~x urAl riRid ities t I and J i rrdtations on the range
'o r app ] il' 6t LJiI l i: p recIedo ~;t clbi Iit:, f aj lures .
1\3 cn ir.:!.tiiJl stap i. n , ~\/Jluc t i'l n CJ f 'thc app l ication
DF t~, e approach t u prEH.dc·;:. :i..l.lrl of \Jariat.ions j.n wall
r:'lr,Bc it y , the sjompl e st possibln fo r ;]', wa s a pplied to
plJblished wall data in ,,J hich uricK 3trength , pris:n
stcength, a nd test condit1ons w a~8 elearly stated .
oI ,;a ini tial modu l us frClm Eq o (1; ,483 uscd tog et her
cá th a linear st r 2ss -s tr aJn ,j ~agr a rr" zero te nsi l e
~apacity and ~r:e un cracked s8c~io n r ad i us af gy ,'at i on .
In p;enera l, íour caSE,S rêust toe sxam j.ned lef1dir,g to
the fo llowing fo~r eq~etjO "5
Case 1
Fcr the give n values Df th e anti ecco n t~ i c 1ti 8s , the
t heorstir:al capac i ty reduction fa e i,c r (P/P ) TH is t he
least of tM8 fou r Bol utio ns t o these equat ~~n~ .
To cC I~pa ct the re ~IJ I te for ô var'Lety uf brick dnd
mor t ar strengtl's the deviatüm Df the theo r etical
capa ci t y from the exp eri me ntal ca pacity hós oean
calcu15ted as a p e rc e ntage cf tha pris m c~pa c it~ to
obtai~ tl18 relativ8 8r rc r
( 101
A negati v8 valu8 cf t hi s Rrror in djcates
vative tn eor8 tic~1 predi utio n .
~
conser -
As mentioned pre viously , ml. nl mUm eccentrtcities must
be assumed to predict the heha viour uf nomi nal]y
axially loaded walls . Since the form J& such eccen tricities a long t he height of ô wa ll mu st aIs o be
assumed , a va riety Df ch o ices are possiole . In
analysis it was conservat.ivel y assume d that the rúni mum eccentricity was constant A1Dng th e height 18arl ing
to single curvature .
Show n in Fig . (3) are the errors ob cair led for t h e da ta
cf Ref . l71 wi t h a min i mum eccentricity 8f ~ per c8n t
Df the wal l thickness . lt can be seen that lhe methcd
generally predicts the v ariati on Df capacit y wi th
heig h t end end conditi o ns with an abso lut e error thdt
mi ght docrease with slenderness . tiy su i ;:able cho ice
of mi n imum e ccentri c iti es , t hB grror i n p~ediction c an
be adjusted tow ar ds more cons8 rv~t t lie r2su l t s ~nd the
variat i cn with slerderne~ s ca n be 0'':lr:ged .
ECCENTR IC.A,LL'( L.O,\,Jéll
!t/.A, ~
LS
In the case Df eccentrically 10 30",rj 'NC" ls, t!,fe. bd~ Le
variables are the effective Rlend e~ne s s r dti n kt/r ,
t h e r e lati ve end eccentricities eJe~ ,md the maxin:um
8nc1 eccentricity e
. Shown ü , F i ~ . (dl ""re U-,e absolu te predic ti~n ~~~ors obt~inB ~ fo r the Ja ta oi'
Ref . ( 7 , 181 . These data indicat e t:hilt 'lhR rnethod is
gensrally conse rv ê:ti V2 wi t I"! A i") q rl' ~ r 7 t:bt Ch::c:'Ra:::y,;
with sle ndernBss ,
~n d
Uncracked S8ct i on . Fai lure Rt
DISCUSSIClN
[ ~ 01=
c
Ca'-ip 2
0.5 <
1
+
6 e
I!lax
~-
/t
< 1
( 61
o
Uncrilcked ::J8cti.Cln , Failure Al c n g I-ieight
<' ~
n. 5 __
p
_<
(7)
o
Case 3
Crilcke d Saction , Fai l ure a t En d
~
L
Célse 4
4
[1 -
Crack ~rl
2 8 /t l
max
<[J . 5
0 -< ~
p -
( 81
u
SRc t i on , Fai l ure Along Length
[J<~
<0 . 5
o
(9)
In evaluation Df the ability of th'l morr.enr. - m,~gni fi8 1 '
me th od to pre~ ic t ~aria tions in wall capaclty, th9
assumptio lls adopted rnust be considered . {l,s shovm iq
Fig. (2) , use Df a linea r stress -st rai n dia gram sV's te mati cally und erestimates section capacity for
8ccentric loads . USB Df the i ni tial modulus Df p Jes ticity to c:a l c ulate criti caI l o a ds le a ds to un ds; estimation Df t h e effe c ts Df lateral deflection s wlth
decreasing erro r as t he slenderness increases, As ~
res ult , the method can be e xpecte d te oe c on se rl:et~ 'ie
for relatively s hort ec c sntrically 10a deG wa l ls , As
s l enderne s s inc r easE:s I.htJ noncor,5el'võtisr.1 Df tnG
effects Df the laterõ o" [J8Fl 8ctiom; comUones w~t,-, the
conservatis!l! of sh ort e e C'tin ll ~ r:)p",; · ti es l Cilding to a
reou ce d total el"rr:('o
The r e sult s Df 'lhis i> t l!dy SLl g6est l.r,at USE c,f Ju,oa r
elastic mode l for h ri.cK masonry 1s no t war('anteo . ,4
more realistic defi ni tion ~f t he st,e s s-strai n charac teristics i s required . S"C'.cessfL!l app l i cõtion Df' t.he
moment-magnifi e r app roacr wi ll ; 'equire coth lmprol/C'c
shol ,t section prc;p8rtios and ~ cetal l ed ~tudy (1f l ateral defl ections TO ystabllsh ~hp val~e5 cf f rlnd r
to De use d in designo
4.b.él-4
Fl nallv ~t shQ~lrl be noted that some variations obtsined resu lt fr nm the fact that prism capa ci ty is
normally found from amall samples . As a result the
ratio (P/r lEXP may indicate a greater vari atio n in
wall capac~ty P than ac t ual l y exists. Related
studies (19 ) and repeoted wall testa suggest t ha t
wall capaci ty may not be as vari able as uni t a nd
priam props rt ies .
REFERE I~CES
1.
Hilsdorf, H.F., " Investigation i nto the Failure
Mechanism of Brick Masonry Loaded in Axial Compression°, Oesigning, Engineering and Co nstructing
with Masonry Products. F . B. Johnson. ed., Gu lf
Publishing Company. Hou5ton , Texas , 1969 , pp . 34 -41.
2.
Sahlin , Se ven, Structural f'lasonry , Englewood
Cliffs , N.J.: Prentic Hall, 197 1 .
3.
Chapman, J . C. and Slatford. J .• "The Elastic Buckli ng of Brittle Co lumns", Pr'oceedings of t he Institution of Civil Engi neers. January. 1957 , Vol.
6. Paper No. 6147, 107-125.
4.
Poulsen, E. and Risager. S " "Tl;e Bearing Capacity
Df Linear Elastic Brittle Colurnns". Bygningsstatiske Medde leser . Vol. 36, No . 3 , Copenhagen .
Oenmark , 1365.
15. SCR . "Compressive and Transverse StrenEth Tests
of Eight-Inc h Brick Walls" . Structural Clay
Products Research Foundation. Research Repurt
No. 10, Geneva , Illinois , october 1966 .
16 . Eskenazi , A., and Ojinaga, J . and Turkstra , C. J .•
"Some Mechanica l Properties of Brick and Block
Masonry ; Interim Report" , St ructura l Masonry
Series 75-2, McGi11 University , 1975.
17 . MacGregor , Jarnes G.• Breen, Joh n E .• and Pfrang.
Edward O.• "Oesign o f Slender Concrete Columns".
American Conc reta Instituto Journal, VaI. 67,
No. 1. January 1970, pp 6-28 .
18 . Watsein, O., and Al l en, M.H., "Compressiv8
Strength of Brick Walls with Large Eccentricities",
A. S.C.E . Nation al Structural Engineering Meeting ,
Meeting Preprin t 1400, Baltirnore, f'la ryland. April
19 -23. 1971.
19 . Fisher , K. • "The Effect of Low Strength Bricks i n
High Strength Brickwor~," . Proceedings Df the
British Ceramic Society. Load-Bearing Brickwork
(4), No. 21 . April 1973.
E rror (% Po )
5.
Hallar, P .• " Load Capacity of Brick Masonry" , Oesigning Enginee ring and Constructing wit h Masonry
Products . F.B . Jo hnson, ed ., Gu lf Publis hing Company, Houston. Te xas, 1969.
10
~--------~-----------r---------'~---~---~
7.
8.
9:
Monk, Clarence B., "Column AGtion of Clay Masonry
Wal ls", Oesigning, Engineeri ng and Construct i ng
with Masonry Products , F. S . Johnsoll, ed. , Gulf
Publistüng Cmnpany, Houston , Texas, 1969 .
-3 O
Struct ural [1 ,,'1 Produots Insti tute . Recommended
Practice for En gineered Elri~ f', f1asonry . McLean,
Virgi nia : SCPI , 1969 .
-50
Vokel, Fe l ix V., and Mathey , Rebert G., and
Oikkers, Robert O.• " Compressi'Je Strength of
Slender Concrete Mas onry Walls ", Nati onal Bureau
of Standards , Building Sc~encB Series 33. Oec.
1970.
Vokel. F.V. and Oikkers , R. O.• "Strength of Mason1''1 Walls under Compressive and Transverse Loads ",
National Bureau of Standards (U.S.). Bldg . Sci .
Ser. 34, March 1971.
10. Vokel. F . V. and Oikkers , R. O. , "Strength of Load
Beari rlg Mas on ry Walls ", Structul'al Di vision,
Proceedi ngs Df the A. S . C. E .• May 197 1 . Vol.97,
1593-16Ll9 .
13 . SeR , " Compressiv8 and Transve rse Tests of Five
Inch Brick Wa lls" Structural Clay Products Rosearch
Fou ndatio n. Research Repurt No . B. Gene va ,
11lino1s, May 196 5 .
14 . SCR , "Comp ressive,lrans vérse, and Racking Strength
Tests of Fou r-Inc l; Bri ck Walls " , Structural Clay
Prod ucts Research Feundat ion . Research Re port No.
g, Gbn'l 'J a. Ill1n015 , Aug . 196 5 .
Curvature
X,e Max =t/6
... e Mox = t/3
X
-40
E rror (% pc)
10
50
O
O
-10
-20
-30
11. Canadian Stan dard s Association , "CSA A23.2.13 ,
'1973. Te s t for Compressive Strength cf Moulded
Co ncreto Cyllnders ", Rexd~le, Ont ari o , 1973 .
12. Glõ,',vi lle. W. H. • an d Ba rnett. P , W., "Mechanical
PrOpeI'ti85 of Bricks and Brick\<lOr k Masonry" ,
Oepartme nt of Scientifi c and I ndust r ial Resea rch.
Building Research. Specia l Report No. 22 . Building
Research St atiorl. Ga rston. Watford. Herts, His
Majesty's Stôtiorlery IJffice. London, 1934 .
200
X
e 1 /e2 = LO Single
-20
6.
i50
100
50
- 10
kl
O
X
...
X
"-
... X
8
xlOoA
...
X~ X
XX
X
150'"
200
kl
,--
X
e 1 /e 2 = O
\
"
Max- t /6
... e Max = t/3
O e Max =tl2,4
X
...
...
e
Error (% pol
10
...
-10
...
... ...
-20
X
-30
50
X
...
...
X
...
kl
,&
--r--x-
200
e I le2 = - 1.0 Double Curvatut'e
X e Max = t /6
... e
= t /3
Max
100
150
X
X
FrG, 4
ERRORS FOR ECCENTRICALLY LOADED
~IAU . S