of Brick Walls Subject to Axial Compression and Bending · 2015-04-28 · Iransverse slrength of brick wall constrllclion. Delails of rhe bricks, morlar, melhod of conslruction of

19.~Strength of Brick Walls Subject to Axial Compression and Bending

ABSTRACT

Unreinforced brick ",ali panels, 4-in. Ihick, 4-f1 \Vide, and 8-f1 high, ",ere resled by app/ying uni/orm transverse loads, uniform axial compresshle loads, ar a combinalion of bOlh Iypes of loading. Companion prisms were 0150 tested lo determine Iheir strength in compressioll and ftexure. Data from both lhe wall and prism tesls were IIsed 10 del'elop ana/y/ieal pro­cedl/res for predicling lhe slrenglh Df walls slIbjected to axial compres­sion and bending.

A new ona/y/ical approach is proposed to el'a/uate both strength and slendemess effects in masonry walls. The applicalion of Ihis approach would lead to new design procedures, c/ose/y parallelillg similar procedures recenlly introdl/ced in lhe USA for olher engineered malerials, such as sleel and reinforced concrete.

NOTATION

by R. D. DIKKERS and F. Y. YOKEL

National Bureau 01 StOlulards, Washington , D.e.

Résistance de Murs en Briques, Soumis à des Eiforts de Comp"ession Axiale et de F1exion

Des pallneaux de murs en briques non armés, de 10,2 cm d'épaisseur, 1,2 m de large el 2,4 111 de 10llg 011/ essayés par application de charges trans­rersales uniformes. de charges de compression axiale uniformes ou d'ulIe combinaisol1 des deux types de charges. Paral/elemellt , des essais de résistance à la compressiolJ et à la flexioll Ollt été exécutés jur des prismes. Les résultats d'essai obtellus tant sur les murs que sur les prismes ont seni de point de départ à /'élabo­ration de méthodes allolytiques destinées à prél'oir la résistollce mécanique de murs soumis à une compression axiale et à une flexiono Une nOllvelle approche analytique est proposée pour él'aluer à la fois la résistance mécanique et les eJJets de /'élancement dans des murs en maçollner;e. Son applicQtioll devrait condllire à de nouvel/es méthodes de calcul, étroitemem paraI/eles à des méthodes allalogues introduiles récemmellf aux Etats- Unis pour d 'alllres matériaux industrialisés leIs que I' aeier et le béton armé.

Die Festigkeit von Ziegelmauern unte,' achsialem Druck und hei Biegung

Unbewehrte Ziegelmauerp/atten, rund 10·2 cm dick. 1·2 m breil IIml 2·4 m hoch, wurden gleichformigem Quer­oder Achsialdruck bzw. einer Kom­binatioll beider Be/asfUl1gen ausgeselzt. G/eichzeitig wurde Oll prismatischen Probekorpem die Druck- IInd Biegefestigkeit bestimml. Aus dell Ergebnissell der Wand- lInd Pr;smell­Versllche wurde ei" analy tisches Verfahren zur Vorherbestimrmmg der Wandfestigkeit unter achsialem Druck ulld Biegebeanspruchung ent­wicke/t. Ein neues analytisches Ver­

fahren zur Berechmmg der Festigkeit IInd Wirkllng des Schlankheilsgrades in gemauerten W iinden wird l'orge­sch/age". Die Anwelldullg dieses Verfahrens würde Zll neuen KOlIslruk­tionsmethoden führen, die iilm/ichen Melhoden fasl gleichen, die kürzlich in deu Vereiniglen Staoten für anderes KOl1struklionsmaterial wie Slahl /lnd Slahlbelon eingeführl wurden.

a = ftexura l compressive strength coefficient af'm= flexural compressive strength of masonry

Mo= maximum moment caused by transverse load under pin ended condit ions

M'o= maximum moment in lhe direction of tbe trans­verse loads caused by lhese loads lInder given conditions of end fixity

em = moment correction coefficient E= modulus of elasticity E;= initial tangent modulus of elasticity e=eccentricity relative to centroid af section

j'm = compressive slrength of masonry determined from axial prism tests

j',=lensile strenglh of masonry delermined from modulus of ruplure lests

h = unsupported heighl ofwall 1= moment of inertia of section

/11 = moment of inertia of section based on uncracked net section

k = reduction coefficient lo account for end fixity kh = unsupported height of wall reduced for end fixity M = moment Me= maximum moment capacity, computed using

linear stress gradients Mk = moment developed by Pk, applied at the edge of

the kern 125

P = applied vertical compressive load ; also denotes resultant force on wall section

P' = resultant campressive force aCling on wall section Pcr=critical load for stability indllced compression

failure, computed on the basis of a modified E/, accounting for section cracking and reduced stiffness at maximum stress

Pk = vertical load capacity when load is applied atthe edge of the kern of a wall section

P,= short wall axial load capacity determined on the basis of prism strength

1= thickness of wall 11= uncracked thickness in cracked section V = horizontal reaction IV = distributed transverse load .d = maximum transverse deftection 3 = transverse deflection

126 Strength of Brick Walls Subject to Axial Compression and Bending

1. INTRODUCTION Recently a research effort was inilialed by lhe Nalional Bureau of Slandards lo oblain dala on the fiexural srrengrh of masonry walls of various types of consrruc­tion. subjecled simullaneously to transverse loads and vertical compressive loads. The results oftesrs ofthirty-six brick masonry walls were reported at the First Interna­tional Masonry Conference.' The data from these tesls and from tesls on lifry-four walls of orher Iypes of masonry construction2 are used as a basis for the develop­ment of analytical procedures ro predict the strenglh of masonry walls subjecled lo axial compression and bending.

A new analytical approach is proposed to evaluare bolh strengrh and slenderness effects in masonry walls. The application of this approach would lead ro new design procedures, closely paralleling similar procedures recently introduced in the USA for orher engineered materiaIs, such as steel and reinforced concrete.

2. EXPERIMENTAL Six or more wall panel specimens, 4-in. thick, were buiIt from each of four Iypes of consrrllction; brick A wirh I : I : 4 (Portland cemenr :Iime: sand) morlar and bricks A, B and S wilh high-bond mortar. The walls were resled by applying uniform axial compressive loads, unifonn Iransverse loads or a combinarion of borh Iypes af loading. The wall specimens were nominally 4-fl wide and 8-ft high except for the axial compressive specimens which \Vere 2-fI wide and 8-ft high.

For each wall system, companion brick prism speci­mens were tested for compressive and flexural strength. The daI a from bolh the wall and prism lests are used to develop analytical methods for lhe dererminarion of rhe Iransverse slrength of brick wall constrllclion.

Delails of rhe bricks, morlar, melhod of conslruction of lhe walls and lesting procedures have been given elsewhere.1.2 Compression tests were conducted on live-brick-high prisms. Flexural lesls \Vere conducled on seven-course brick prisms tested as beams with the 8-in. dimension of lhe brick horizontal, loaded aI the Ihird poiuts Qver a 16-io. clear span .

A summary of lhe wall lesrs is given in Tables I and 2. The Iransverse load and midspan defleclion corresponding lo lhe poinl where lhe load-detlection curves deviated from Jinearity and lhe maximum transverse load and deflection are given for respective values of compressive load. Table 3 gives average values of prism compressive and fiexural strengths.

3. THEORETICAL DISCUSSION 3.1 Cross-sectional Momenl Capacity Equations for lhe relarionship belween verrical load and momenl capacily for solid, hollow and asymmetrical wall cross-seclions have been developed. 2 This relarion­ship can be plotted in lhe form of inreraclion curves between vertical-load capacity and moment capacity.

Figure 1 shows an interaction curve for a solid pris­malic secrion. The plot is non-dimensionalized by dividing vert icalload by P., lhe axialload capacily, and momenls by M k, lhe momenl capacity when a verlical load is applied at rhe edge of lhe middle third of lhe section (kern). The inleraclion curve is based on rhe assumption thal fiexural compressive strengrh equals lhe compressive slrength uoder axial compression (af'm=f'm) As discussed elsewhere,2.3 this is a conservative assump­tion . Typical slress dislributions, associated with different portions of lhe curve, are shown in Figure I. The upper, linear portion of the curve, is associaled wilh uncracked

TABLE 1- $uMMARY OF TEST REsULTS ON BRICK-A WAUS

Devialioll from a lillear load-def!eclioll Cllrve

occurred aI :

Wall Compl'essive Trallsverse Midsp(III Maximul1I Midspan Panei· load [oad defleclioll Iransvel'se def!eclüm

lood ar maximllm trallsverse

load (lbf x la') (lMi,,') (il/.) (Ibfli,,') (ill.)

4-1 o 0'12 0·01 0·20 0·02 4-2 o 0'20 0·03 0·20 0·03 4-3 100 2·21 0'12 3·38 0·51 4-4 200 3·70 O· IB 5·20 0·54 4-5 250 2·82 0·16 5·48 0·61 4-6 300 3·90 0·31 5·14 0·58 4- 7 350 ]'78 0·10 4'47 0·55 4-B 562j - - - -4-9 5761 - - - -5- 1 o 0·60 0·02 0·80 0·03 5-2 o 0'58 0·02 0 ·80 0·03 5-3 100 2·70 O·l! 3·88 0·42 5-4 200 4·88 0·20 6·84 0·65 5-5 250 4·90 0·21 7·00 0'53 5-6 300 5·62 0·31 6·90 0 '59 5-7 350 5-44 0·31 0·73 0 ·59 5- 8 400 5·10 0·23 8·29 0 ·67 5- 9 844j - - - -5- 10 872 j - - - -

• Senes 4--1:1:4 mortar. remamder hlgh-bond. t Actual test was performed on 2-ft-wide panel and values were adjus led

for 4-ft width .

R. D. Dikkers and F. Y. Yokel 127 TABLE 2- SUMMARY OF TEST RESULTS ON BRICK-B AND BR1CK-S WALLS WITH HIGH-BOND MORTAR

Deviatioll from a linear load-

defleClioll curve occurred ar:

Walf Brick Compressive Transverse Midspan Maximum Midspan panel load /oad dej1ecriofl transverse defiecliol1

/oad atmaximum traflsverse

load (Ib/x iO') (Ib/l ill ' ) (in.) (Ib/l ill ') (ill.)

6- 1 O 0 -40 0 -02 0 -40 0-02 6-2 O 0-45 0 -02 O-54 0-03 6-3 5 140 2-95 0 -20 3-94 O-58 6-4 220 4·02 0-28 7-10 0-72 6-5 290 4-08 0-24 7-10 0 -72 6-6 350 4-94 0 -29 7-]3 0-60 6- 7 400 3-99 0 -22 6-94 0-69 6-8 1088' - - - -6-9 1050· - - - -

7- 1 O I-lO 0-03 I- !O 0-03 7- 2 O 1-34 0-04 1-34 0-04 7- 3 160 4-67 0-13 6-91 O-56 7-4 B 320 7-98 0-21 11 -29 O-59 7- 5 320 6-54 0 -25 9-68 0 -70 7- 6 600 6-52 0-23 11 -21 0 -63 7- 7 948* - - - -7-8 970· - - -- -

• Actual test was performed on 2-ft-wlde panel and values were adJusted for 4-ft wldth.

TA8LE 3- MEAN STRENGTHS OF SAMPLES OF THREE PRISMS

Brick Compres.iive Flexural s/rengfh sIreng/h

(gross area) (gras.'! area) (lb/l ill ' ) (lbflin ' )

5-course brick prisms A 5400· -A 6240 -B 7650 -5 7320 -

7-course brick prisms A - 35' A - 370 B - 430 5 - 220

• I : 1 : 4 mortar, remainder high-bond.

cross-sections. The broken line, shown as the cracking line, is the loeus of all load-moment eombinations that cause the tension face of tbe wall to crack. Note that after section cracking, the cross-section develops addi­tional moroent resistance before failure oceurs. The entire curved portion of the interaction curve, to the right of the cracking line, is associated with cracked sections.

3.2 Slenderness Elfects

Slenderness efreets on the moment eapaeity of walls are illustrated in Figure 2_ This figure shows the free body of lhe upper half of a detlected wall subjeeted lo axial and transverse loads. The effective moment at any point along the height of this wall will be determined by lhe location of the line of action of the vertical force. reI ative to the localion of lhe detlecled cenlre·line of lhe wall.

0_.

0_' ~o õ:: o.

0_2

I I p,'li!! .,,p-

0'-'0-c2f'<::-",-",7iQ4.--.i0_".-0'<_õ.--i'_"0--I'_2;--!'_4 ~ M/Mk

FIGURE I-Cross sectional capacity af a solid prismatic section at f ',= O· If'm .

Hence the moment acting on any section of the wall is magnified by an added momenl equal lo lhe producl of the axial force and the centre-line deftection.

A similar problem has been analysed for lhe case of eccentrieally loaded reinforced concrete columns,4 where it has been shown thal lhe externaI momenls acting on a column are magnified and tbal , Ihis efreel ean be predicled quile reasonably by lhe following equalion :

em Me = Mo.,---,.~~

l -(P/P,,) (1)

where em is a moment eorrection factor, depending on lhe ratio af the end momenls and lhe shape af lhe primary moment diagram and

(2)

128 Strength of Brick Walls Subject to Axial Compression and Bending

T h/2

w ---, , ----'

I I

---.l I I

---.l I I

---.l I I

---t I I

---t '-

I -l

p

p

--v P·e .. YIl -~+P.d

2 4 i, :E Mo +p.ó,

' \ I ' . \ I ' , \ I ' I ! I I

FIGURE 2- Slenderness effects on equilibrium.

is the axialload Ihal will cause a slabilily-induced com­pression failure. This melhod of computing lhe lotaI mament is designated as lhe mament magnifier method . A similar method may be applied lo lhe loading conditions of lhe tests reporled herein.

Figure 3 shows lhe momenl diagram aCling on a wall

w -

I kh

1 (b)

FIGURE 3- Slenderness effects : (a) moment distribution ; (b) partial end fixity.

which is subjected to combined axial and lransverse loading. If il is assumed thal lhe wall section is pin-ended. lhe moment due lo transverse load will be parabolically dislributed over lhe heighl of lhe wall wilh a maximum momenl ai mid-height,

1 Mo= - wh 2

8 (3)

If il is in turn assumed that the deftection curve of th, wall is also parabolic,' the added moment caused b: the action of the axial load on the deftected wall , n will also be distributed parabolically wilh a maximun momenl piJ at mid-height. Thus, the maximum tota momenl acting on lhe wall aI mid-heigbl, which a fai/ure will equal lhe seclion capacily M" equals:

M ,= M ,+PiJ (4)

If it is assumed lhal the stillness EI is constanl ave, the heighl of lhe wall, il has been shown' that lhe equa· tion for section capacity for pin-ended conditions is :

(5)

Under condilions of partial end-fixity the deftection curve, and Ihus lhe magnitude of the added moment, will change. For lhe parlicular case of transverse loading, the equation for pin-ended conditions can be modified by sllbstiluting lhe 'e/feclive' wall heighl, kh, at which a pin-ended member of equal sti/fness (EI) would develop similar slenderness e/fecls, for lhe wall height h. E/feclive heighls for di/ferent conditions of end-fixily for braced members, as well as members which are free to sway at the top may be convenienlly delermined by referring to lhe Jackson and Moreland alignmenl charts. 5

Parlial end-fixity is illustrated in Figure 3(b), aod eqo. (I) lhus becomes:

, I M,= M ' I - (P/P,,) (6)

where P" is the axial load thal will cause a stability­induced compression failllre (eqn. (2» aod M ', is the maximum mament in lhe direction af lhe transverse loads aI the giveo end-fixily.

The equation must be modified for seclion crackiog (change in 1), and change in E with increasing slresses. For a malerial wilh a relatively small leosile streogth, the sectioo will be cracked within lhe range of vertical loads where section capacily is governed by the ultimate momeot for a cracked section. Thus, lhe sti/fness (EI) of lhe sectioo is a function ofverlicalload. Consequenlly, EI in lhe mament magnification equation is a function of PIPa.

11 has been shown for IightIy reinforced concrele columns 4 that slenderness effects can reasonably be approximaled by using an 'equivalen!' EI of Etl. /2·5. Ob­servation of lhe magnitude of deftections of the slender brick walls tested in Ihis study iodicales that at axial loads up lo aboul O·25P, an 'equivalent' EI of E"./3 will fit the test resulls reasonably well. For this case, eqn. (6) can thus be modified as:

where :

M 'o= M. (1 -:.) (7)

;t2Edn P" o= 3 (kh)'

This equalion accounls also for partial end-fixity. The above equalion is a good approximatioo for lhe

range of verlical loads belween P = O aod P = O·25P, .

• A parabolic curve is a dose approximation lO the aclual defiection curve.

R. D. Dikkers and F. Y. Yokel 129 For higher verlical loads lhe seclion capacity is under­eslimaled by eqn. (7). Closer examination of the test results on brick walIs indicated Ihat an equivalent Elof:

EI = E,I. (0'2+ :.) .;; 0 ·7 Ed. (8)

will approximate the actual test results of slender walls over the entire range of vertical loads.

Reduced interaction curves cao be developed by plotting M,-PA for each value of P. Such reduced curves will show the value of M'., the moment that can be imposed 011 the wall by externai forces at any particular valueof P.

These interaction curves can be used to determine the moment capacity of slender walls since they have been in e/fect corrected for e/fects of deflections. Red uced interaction curves usiog eqns. (7) and (8) are compared with test resulls in Section 4.

4. ANALYSIS OF TEST RESULTS

4.1 Discussion of lhe Tesl Conditions In the test set-up and the loading condilions used,I.2 the top of lhe wall is free lO rol ale bul is restrained from laleral movemenl and may be considered as pin con­necled. The bottom of the wall rests on a fibreboard which does permit rotation but may impose some restraint on the rotation, particularly lInder large vertical loads. While these lest conditions attempl to simulate actual conditions in a structure, they a150 impose a varying degree of restraint on lhe wall base, which will tend to reduce the maximum momenl caused by super­imposed loads when compared to a wall with a pinned base.

In the subsequenl inlerpretation ofresuIts,2 il has been assumed that partial end restraint reduced moments in lhe walls lo 68 % of the pin-ended moments. Slenderness e/fects for these conditions were assumed lo correspond lo an 'e/fective' wall height of 80 % of actual height (k=0'8) Wall strength computed in Ihis way will be the lowest strength Ihat the walls could have developed.

4.2 Comparison of Brick Wall Syslems

Figure 4 shows a comparison of the tesl resulls on two wall systems. The solid cireles are lesl results of Iype-A brick walls with I: I : 4 mortar and lhe hollow cireles are test resulls of type-A brick with high-bond morlar. Moments plotted are the moments imposed by trans­verse loads. The curves show lhe average Irend of lhe lest results. NOle Ihal Ibe walls wilb high-hond mortar developed significantly higher load capacilies.

At zero verticalload lhe two walls wilh I: 1:4 mortar developed momenls of 5500 Ibf/in., which correspond to lensile strengths of 50 Ibf/in2. This value compares with an average tensile slrenglh of 35 Ibf/in2 developed by lhe seven-brick beam specimens. The IwO high-bond mortar walls tested ai zero compressive loads developed momenls of 22000 Ibf in., which correspond to tensile strengths of 210 Ibf/in2. This compares wilh an average tensile strength of 3701bf/in 2 predicled by seven-brick beam leSiS. Thus, in this case, the high-bond mortar walls developed 57 % of the tensile strenglh predicted by prism tests , and the I: 1:4 mortar walls exceeded lhe prism strenglh.

Figure 4 also lists lhe short-wall axial load capacily

I~'r-------------~~~~~--~ AXIAL LOAO CAPACITY PREDICTED BY PRISM

200

5·10

"'9

TESTS'H4 MORTAR. 965 .IO~b' HIGH-BON~ MORTAR' 1105 x 10 lbf

°4-1 5-1 100 200 300 4-25-2

APPLIED TRANSVERSE MOMENT,lbt"n x 103

FIGURE 4- Comparative strenglh of brick-A walls with I: 1:4 and wilh high-bond mortars.

predicted from lhe average prism slrength for lhe Iwo wall systems. The values were nol plotted since one lies o/f lhe figure. The \Valls with I: 1:4 mortar developed an average axialload capacily of567 x lO' Ibe Shorl-wall axial load capacity computed on lhe basis of prism slrenglh would be 965 x lO' Ibf. This result indicates Ihat lhe wall developed only 59 % of the short-wall compressive strength. The high-bond mortar walls developed an average axialload capacily of 858 x lO' Ibf, or 77 % of lhe shorl-wall axial load capacily of 1105 x lO' Ibf, computed from prism teSiS. These results lead 10 lhe conclusion Ihal lhe axial load capacily of Ihese walls is probably limited by stability-induced compres­sion failure, rather than by lhe compressive strenglh of lhe masonry.

The effecl of lhe properlies of the brick units on the Iransverse strength of high-bond masonry walls is illustraled in Figure 5, which shows a comparative plot of the interaclion curves for brick-A, brick-S and brick-B walls. The curves show lhe approximate trend of lhe lest resulls. Tensile slrenglhs of lhe walls, compuled from Iransverse load capacily with zero vertical load and compressive slrenglhs computed from wall failures under axial compressive loads are given in Table 4, with lhe average prism slrenglhs for each wall system.

There is definile correlation belween tensile slrenglh derived from prism tests and tensile slrength of lhe walls; however, it is evident that lhe flexural prism tests over­estimale lhe lensile slrenglh of lhe walls. Brick-S walls developed 55 % of lhe prism tensile slrength; brick-A walls, 57 % and brick -B walls, 70 %

Comparison of compressive strength data fram full­scale wall tests and from prism teSiS indicates, Ihal while in the prism tests masonry compressive strength increased wilh the compressive strength of lhe brick units, the full-scale walls behaved in a different manner. Brick-S walls developed lhe highest compressive slrength (the same walls had the lowest lensile strength), which was 83 % of the prism strength. As previously noted, the walls probably failed by slability-induced compression failure

130 Strength of Brick Walls Subject to Axial Compression and Bending

rather than by compression. In the latter case the axial load capacity of the walls would be a function of the modulus af elasticity and not af masonry compressive strength , and moduli of elasticity do not necessarily increase with compressive strength af masonry. Data available [rom another research programme conducted at the National Bureau of Standards indicate the fol­lowing average initial tangent moduli af elasticity: Brick A with I: 1:4 mortar, E=3'65 x 106 IbfJin2, and brick A with high-bond monar, Ei= 4·2 x 106 IbfJin2. In Table 5 axial-failure loads are compared with criticai loads (Euler) computed on the basis of ' pio-ended' wall conditions as well as lhe partial fixity conditíons. Stiffness EI at failure is assumed to equal 0'7Ed" in accordance with eqn. (8).

•

1200

1000

800 ,

600

400

200

BRleK B PRISM STRENGTH

BRleK 5 PRISM STRENGTH

BRleK A PRISM STRENGTH

'-, , , \ " , , , ,

BRleK A \

BRleK 5

\ , , "'

•

0~~~-L----~2oo~----~----~4~00~----"

APPUEO TRANSVERSE MOMENT,lb1· ln x 101

FIGURE 5- 1nftuence or brick units on the strength of high-bond mortar waHs.

It appears that axial-failure loads tend to occur within the range ofcomputed criticalloads and are considerably lower thao predicted short-wall strength. 11 can therefore be assumed that wall failures are attributable to stability rather than strength.

4.3 Correlation of Tes! Results with Theory

The correlation between prism strel1gth and the strength of full-scale walls for the four wall syslems tesled is illus­trated in Figures 6- 9. Again, verticalloads are divided by p , which is the short-wall axia l failure load, computed 011

the basis af prism strength , and moments are divided by M k=Pot fl 2, which is lhe theoretical maximum elastic mament resulting when a vertical load is applied at the edge of the kern of the section . A dual scale is used to show actual magnitude of loads aod moments. The part of the moment caused by deftectioll is showo

TABLE 4-COMPARISON OF WALL ANO PRISM STRENGTHS

Wall Prism Walf Pr;SIII Brick fensiJe tel1Sile compresstl'e compressh'e

srrel/glh srrenglh strellglh slreng/h (Ibfl in' ) (Ibfl ilz Z) (lbfl in1 ) (lbfl in' )

A 210 370 4800 6240

S 120 220 6050 7320

B 300 430 5140 7650

TAOLE 5- COMPARISON oFAxIAL-FAILURE LOADS ANO COMPUT ED CRITICAL LoADS

A ver. Compllled criticalload Short-Il'all axial axial failm'e

failure (oael ba5ed Morta,. load Pill ellded Partial fixir)' 01/ prism fest

{ype (Ibfx 10') (Ibf x la' ) (lbf x 10' ) (lbfx 10' )

1, 1,4 567 540 I: 960

J-ligh bond 858 640 990 1110

P/~ '~ ______________________________________________________ ,

1000- r­IO

Q

~

~ o ~

~ ~ u ;=

'" '" >

800-0.8

600-o.

400- 0.4

200- 0 .2

COMPUTED INTERACTION . CURVE,EQ.(8l p .13'-....~ ./EloEi In (O.2+;:;-lSO.7E,l n ~8 ~ ~

Mk • Po 1112

Ej ~3 ' I06Ibflinz

,~. 5 400 Ibf/in 2

,'f ' WALLS 50 Ibf/in z

PRISMS 351bflin 2

/

............. OMPUTED INTERACTION """,CURVE ,EC. (7 )

,,\'~E; I~'I'§~~~ '_ 4·' '- " ................... 4 · 6 ...... 4 ·5

/) 4-4 /'/4-3

MOMENT, Ib,· in }( 103

FIGURE 6---Brick·A waUs wilh j : 1:4 mortar, correlation wilh prism slrength.

Q x

~

õ <l ~

~ ~ u

" '" w >

Q x

li

P/Po I

1000-

O. 5-10

R. D. Dikkers and F. Y. Y okel

Mk = PoI/l2

Ei :4'I06 I bf /in2

f~ : 6 240 IH fin 2

800-

'·9 '"" 'VPVTED CURVE,

f; ' WALLS 210 Ibf/in2 PRISM 370 Ib"in 2

0.6 EC.le) 600- .~.

COMPUTED CURVE, _____ / EO.l7) \ OA '·8

400-'·7 ----- ) -, ,., ,

0.2 \ . 200- //

-"'-;::::;!. 5-3

0-,~~~~---t.,---~,---~----~--~~---7~--~ o 5-1 0.2 0.4 0_6 0_8 1.0 1.2 1.4 M/Mk 5-2 I I I I I I

o 100 200 300 400 500

FIGURE 7- Briçk-A walls with

P/Po

MOMENT,lb1-in x 103

high-bond mortar, çorre[ation with prism strength.

1.0""'---------------------------, 1200-

O. 000-

800-0.6 COMPUTED CURVE

·VEQ.(8)

Mk" Po 1/12

Ei-4'106Ibffin2

f:n- 7320 I bf /in 2

f't 'WALLS 120 IH /in 2

PRISMS 2201bf!in 2

Õ

COM~. ~ O ~

~ ~ o

" '" w >

600-

0.4

400-

0.2 200-

I CURVE \ EC.(7) ----- ,

- ............ " <:-:-__ 6:..;;:4~~ ___ ,.:

46-3

6·7

....-:::;;.._ ... 0--~0~·~'.~2~-~~--~===-~c-----~------~----~~----~~----~~~~~

0.2 0.4 0 .6 Q8 1.0 l2 1.4 M/Mk I I I I I I I I

O 100 200 300 400 500

MOMENT,Ib1-in xlO)

FIGURE 8-Briçk-S walls with high bond mortar, correlation w i th prism strength.

1200-

P/Po

1.0"""-----------------------,

0.8

·8 7-7

Mk=POI/12

Ei = 4 ·10 6 Ibf/in 2

fm" 7650lbf/in 2

f' 'WALlS 300 Ibf/in 2

PRISMS 430lbt/in2

M. 0.6

'"' 800-'" COMPUTE O CURVE

......... / EO.(,)

õ ~ O 0 .4 ~

~ ~ o

400-to w > 0.2

.-.........

"-. cOMPUTED \ /CURVE

-<'_ EQ. (7) , ---- ) --, \ ,

7·6

7·4

J 7·3

o O 7-1 0 .2 OA 0.6 0.8 la 12 IA M/Mk I I I I I I I I I I

O 100 200 300 400 500 600 MOMENT, Ibf·in )( 103

FIGURE 9-Brick-B walls with high-bond mortar, correlation with prism slrength.

131

132 Strength of Brick Walls Subject to Axial Compression and Bending by a solid horizontal line. The left end of this line rep­resents the momenl caused by transverse loads alone. The righl end represents the ultimate momenl aCling on the wall aI failure. Thus, the magnitude of lhe measured slendemess e!fect can be clearly seen by the length of the solid line. The figures illuslrate the greal magnilude of the added moment caused by defleclions, which represents the slendemess e!fec!. Figure 6 shows the lesl resulls on brick-A walls wilh convenlional mortar. The righl-hand end of the solid horizontallines represenls ullimate momenl capacity and should be compared wilh the solid curve marked M , which was computed on lhe basis of prism strength. Note Ihat lhe lotaI ultimale moments developed by the walls closely follow the pre­dicled shorl-wall interaction curve.

Theorelical reduced moments were compuled by lhe Iwo methods represented by lhe following equations:

where:

and

(I)

or

(2)

,,2 EI P,,= (0'8h)2

Edn EI= -

3

EI = Edn (0'2 + :J .; 0'7 Edn

(7)

(8)

These theoretical curves were developed by reducing the ultimate value of M, shown by the solid curve in Figure 6. For brick A, values of J'm and E used in arriving at these reduced curves were independently derived on lhe basis of prism tesls, except that the value of E; for brick A with Iype I: 1:4 mortar was slightly modified as noted below. For bricks S and B, values for J' m were available only from physical tests . Values for E were assumed to equal the value for brick A with high-bond mortaL The theoretical reduced curves thus computed, which are shown in Figure 6 by the dashed and lhe dash-dotted curves for eqn. (7) and eqn. (8) respectively, should be compared with the left end of lhe solid horizontallines. Examinalion of these lwo Iheoreti­cal curves shows lhal eqn. (7) slightly over-estimales lhe moments aI low axialloads and under-estimates lhe momenls aI high axial load. This di!ference should be expected since cracking will increase with decreasing axialloads, causing a reduction in lhe moment af inertia while aI high axial loads lhe 10lal gross seclion will be e!feclive. Eqn. (8) was derived to fit the te SI results of ali the brick wall syslems and in general shows good agreemenl with test results wilhin the range below 0·2 Pn, which is the maxil11ulTI axial load presently permitted in conventional design, and it has the advantage of greater simplicity. For the mament reduction computations for brick-A walls with I : 1:4 mortar, an E of 3 x lO' Ibf/in2,

rather than the 3·65 x lO' Ibf/ in2 previously mentioned has been used.

Tesl results on high-bond mortar walls are plotted in Figures 7-9 in a similar manner. For alI these wall systems, theoretical reduced mament interaction curves were computed lIsing a modulus of elaslicity of E = 4 X 106 lbf/in2. In general, these specimens developed or exceeded the theoretical moment capacity computed

[rom compressive prism strengtb, indicating that 'a' was greater Ihan I. Computed theoretical reduced curves show reasonably good correlation with lest results, except thal lhe strength of the brick-B walls (Figure 9) was underestimaled. These walls developed deflection curves corresponding to a much higher modulus of elasticity, but their buckling load was ralher low. These walls also exceeded their predicted section capacity by a substantial margin.

5. CONCLUSIONS

The following conclusions can be drawn from the test results on brick walls:

1. The load capacity of the brick waUs tested was closely predicted by the moment magnifier method, using compressive prism slrength as the basis for pre­dicting short-wall section capacity, and a sli!fness EI in accordance with eqn. (7) or (8). The Irend of the relation­ship between vertical loads and moments was correctly anticipated by theoretical interaction curves, and the order of magnitude of slendemess e!fects shows good agreement with the predicted slenderness e!fects.

2. Ali brick waUs tested hehaved as slender walls. They failed by stability induced compression and their moment capacity was significantly reduced by slendemess e!fects.

3. Compressive and flexural tensile strenglhs of prisms built from brick A with I: 1:4 mortar were smaUer than lhe strengths of prisms from the same brick built with high-bond mortar. Compressive prism strength of high­bond mortar prisms increased with the compressive slrength of the brick unils. Flexural tensile strength of high-bond mortar prisms did not correlale with the compressive strength of the brick units.

4. Full-scale walls built with I: 1:4 mortar developed ftexural tensile strength which exceeded the average tensile strength delermined from prism teSlS. Full-scale high­bond mortar walls developed 50 % or more of the prism tensile strength.

5. Walls built of brick A with high-bond mortar developed significantly higher ultimate load capacity under combinations of vertical and transverse loads Ihan walls buill of the same brick with I: 1:4 mortar.

6. Walls built with high-bond mortar and brick B developed significanlly higher transverse slrength Ihan the high-bond mortar walls built wilh lower strength brick. However, under compressive loads alone these walls did nol develop increased strength.

REFERENCES I. GRENLEY, D. G., CATTANEO, L. E. and PFRANG, E. O., Effect

of Edge Load on Flexural Slrength of Clay Masonry Syslems Utilizing Improved MOrlars. Designing, Engineering and Construcling with Masonry Products. Houston, Texas, Gulf Publishing, 1969. pp. 119- 128.

2. YOKEL, F. Y., MATHEY, R. G. and DIKKERS, R. D ., Slrenglh of Masonry Walls Under Compressive and Transverse Loads. National Bureau of Standards, Building Science Series 34, March 1971.

3. YOKEL, F. Y., MATHEY, R. G. and DIKKERS, R. D ., Compressive Strength of Slender Concrete Masonry Walls. National Bureau of Standards, Building Science Series 33 , December 1970.

4. MAcGREGOR, J. G., BREEN, J. E. and PfRANG, E. O., Design of Slender Concrele Columns. J. Amer. Concrete IIIst. 57, (I), 6, 1970.

5. COLUMN RESEARCH CoUNCIL, Guide to Dcsign Cri teria for Metal Compression Members. New York, Wiley, 1966.