774

EARTHQUAKE RESIST ANT DESIGN OF BRICK INFILLED FRAMES

HASSAN A MOGHADDAM PATRICK J DOWLING

Civil Engineering Department Imperial College, London SW7 2BU

ABSTRACT

The predominant and largely beneficiai effect of masonry infills on the lateral response of structures has for long been recognized by researchers, yet the role of infills as earthquake resisting elements is often ignored by design engineers . In this paper various parameters influencing the strength and stiffness of infilled frames are discussed and some of the existing methods of analysis reviewed. The difficulties of implementing these methods in the aseismic design of infilled structures are discussed, and an aseismic design method for uncracked low rise buildings is suggested . The effect of cracking on ductility is illustrated by the results of shaking table tests on cracked reinforced and unreinforced infilled frames .

E E· , 1

d

h

Ih

Q

w

li

À

Àh

e

o"c

T

F

Ff

NOTATION

modulus of elasticity of infill and frame, respectively .

diagonal length

infi 11 height

column moment of inertia

infill length

infill thickness

effective width of the diagonal strut

lateral deflection

scaling factor

relative stiffness parameter

tan- 1 h/Q

compressive strength of inrill material

shear strength of infill material

compressive strength strength of diagonal strut

resistance of bare frame

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1. INTRODUCfION

In spite of the significant contribution of infills to the stiffness and lateral strength of

structures, they are frequently ignored in current design practice . This results in an

inaccurate analysis and gives rise to unrealistic designs . The current methods of

earthquake-resistant analysis are- dependent on a proper estima te of the natural period of

structures (1, 2). Polyakov (3) reported that in a 14-storey building wind loads gave rise

to substantial measured stresses in the plane of the walls. Measurements taken in several

such buildings in Moscow showed that when the wind speed is small the actual stiffness of

a building exceeds the stiffness of the bare frames by 10-20 times. The neglect of infills

also violates an important principIe of earthquake-resistant design; that is, to avoid

unnecessary mass and to utilize the available mass to increase the earthquake-resistant

resistanct< of the system.

2. CHARACfERISTICS OF INFILLED FRAMES

2.1. Mode of Failure

The following modes of failure are observed in infilled frames:

i) Interface Cracking (separation of the infill panel and the frame except at the

compressive comers)

ii) Diagonal cracking

iii) Comer crushing

The first mo de occurs at load magnitudes considerably below the ultimate. Up to

the onset of interface cracking the system behaves elastically and monolithically similar to

a composite plate . The second mode is characterized by a sudden crack through the wall,

essentially on the compression diagonal. The third mode is usually accompanied by the

formation of plastic hinges either in the column or in the beam.

2.2. Strength

The strength of infilled frames is dependent on numerous parameters and a full discussion

is given in reference (4). Some of the important parameters are as follows:

i) Compressive strength of infill material, (Tc - the strength is usually assumed to be

proportional to (T c'

ii) Relative stiffness parameter, Àh - this parameter was studied by some investigators

(5-7) and it will be considered hereafter - this only affects the comer crushing strength.

iii) Height to length ratio has a reducing effect on strength.

iv) Bending moment capacity of the frame has an enhancing effect on the strength.

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v) Interface bond condition - experimental and analytical investigations indicate that

the interface shear bond does not influence the cracking strength markedly, but it increases

the comer crushing strength.

vi) Lack of fit - for a small lack of fit of a few millimetres the ultimate strength is not

significantly affected, whereas the cracking strength is usually reduced.

2.3. Stiffness

In contrast to the strength, the stiffness of masonry infilled frames is very sensitive to

factors such as workmanship and lack of fit, and thus it is very scattered. In general, as

shown in Fig. I, the load-deflection curve of can be distinguished according to the modes

of failure. Some of the influencing parameters are as follows:

i) Aspect ratio - on the basis of the experimental results of Benjamin and Williams

(12), and the analytical results of Riddington and Stafford-Smith (6), the current authors

(4) have shown that the stiffness is almost constant for aspect ratios less than 0.5 and it

decreases linearly for aspect ratios greater than 0 .5.

ii) Mortar strength and curing have significant effects on stiffness.

iii) Type of frame

corresponding steel frames .

infilled concrete frames are generally much stiffer than

iv) Lack of fit greatly influences the stiffness, especially if the gap is located at the

loaded comers.

3. METHODS OF ANALYSIS

Methods of analysis can be categorized as follows: finite element, finite difference, stress

functions, plastic method, and simplified methods . As a result of the nature of the

scatter of the strength and stiffness, the most sophisticated methods do not, in general,

produce much better results than the simplified methods . Thus, from the design point of

view, the latter methods may be preferable.

3.1. Plastic Method

In 1978, Wood (13) presented a plastic method of analysis, and the same concept was

employed by Laiuw (14). He postulated three modes of failure as shown in Figure 2, and

the corresponding expressions for collapse loads are given in Table 1.

3.2. Equivalent Diagonal Strut (EDS)

Holmes (15) was the first to suggest the EDS concept in 1961. Since then a number of

investigators have attempted to modify and develop the method (8,16-19). The infill panel

is replaced by an equivalent compressive diagonal sfrut with an effective width of w.

The strength is calculated as foIlows:

H = Ff + F.cos8,

where

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O)

F - (wt).~c - compressive strength of the diagonal strut, (2)

Ff - Resistance of bare frame

Ff can be calculated by assuming a value for the lateral displacement of the frame at

the cracking load. For example, Polyakov (3) suggests

[6] = 1.2 x 10-3 to 7 . 9 X 10-3

~ crack (3)

Holmes suggested a value of d/3 for the effective width, w. The current authors'

experiments. on brick infilIed frames suggest a value of d/6 as being more realistic.

Mainstone (8) suggested the foIlowing semi-empirical relationship for w which accounts for

the relative stiffness of the frame and infilI.

(4)

where (5)

Stafford Smith and Riddington (21) assumed a value of ElE = 1/30 for brick infiII

in a steel frame, and substituted it into the above relationship. This gives

w = 1.12 [~]-o.~~ cos 8

30lh (6)

3.3. Scaling Method

This method has been suggested by the first author in reference (20). For a particular

type of construction, the strength is dominated by the following factors; the infiII

compressive strength (~c). geometry (h, Q, t), aspect ratio (h/Q) and scaling factor, À.

It has been shown, (4), that the cracking and uItimate strengths can be related to the

aspect ratio by the foIlowing approximate relationship.

r· a h/Q ( 1.0 Hc H,c [1 + (3c O - h/Q) 1 {3c

0.4 h/Q > 1.0 (7) {I. O h/Q ( 1.0

Hu - H,u [1 + (3u O - h/Q) 1 {3u -0.4 h/Q > 1.0

where Hc, Hu cracking and ultimate strengths respectively

H,c, H,u cracking and ultimate strengths at h/Q = 1.0

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It was also shown (4) that the scaling effect can be accounted for by using the

following relationship.

where

H/À2 ~ Ho[1 + a (1 - À)]

H, Ho the strength of model scale and full scale panels

respectively

(8)

À scale factor taken as the ratio of infill thicknesses

a empirical coefficient

From Benjamin & Williams' results (12), conservatively, a 0.75, hence,

H/À2 ~ Ho [1 + 0.75 (1 - À)] (9)

Assuming that a large scale test has been carried out on a frame infilled with a

certain type of brick wall, it is possible to estimate the strength for a similar type of

infill construction but with a different geometry and material strength. Assume the

parameters of the specimen which has been tested are as follows: Q, h, t, r, U c and

similarly, the parameters of the infilled frame whose strength is to be estimated are as

follows. Q', h', t', r', u'c. The strengths of the two structures are denoted by H and

H'.

To account for the difference in the aspect ratio, H should be multiplied by A,

where

A ~ [1 + ~(1 - hYQ')]/[1 + ~(1 - h/Q)]

where ~ is taken from equation (7).

To account for the scale effect H is multiplied by B, where

B

B

À2[1 + 0'(1 - À)]

I/[À2[1 + 0'(1 - À)]]

À h'/h if h' < h

À ~ h/h' if h' > h

(10)

(11 )

Finally, to account for the difference in thickness and material strength H is

multiplied by C, where

Hence,

Cc

Cu

[ t ' I t . (h' Ih) ] . (r ' I r)

[t' It. (h' Ih)] . (u' c!uc )

H' A.B.C.H

for cracking strength

} (12) for ultimate strength

(13 )

In the absence of the shear strength of the infill material, r, it may be assumed that

it is proportional to the infill compressive strength, uc ' i.e.

r'lr u'cluc • (14)

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4. EARTHQUAKE-RESIST ANT DESIGN

The design of infilled frames to resist earthquake excitation can be based on two

approaches, namely, Elastic Design and Cracked Design.

4.1 . Elastic Design - this applies to both i) structures designed for modera te seismic loads,

and ii) low rise buildings which remain uncracked even during strong earthquakes.

The authors are not aware of any specific codified provisions for seismic loading of

masonry infilled structures. In general, the seismic coefficients of loading recommended by

existing codes are much less than the real seismic loads. This is accepted in recognition

of the plastic deformations of elastic-plastic systems during strong earthquakes. Thus a

certa in amount of ductility is assumed although it is not explicitly mentioned in the codes.

For an elastic design, this reduction is no longer valid. The elastic design spectra

recommended by most codes are also unsafe in the range of short period structures (23),

and the designers are recommended to build up special design spectra according to the

regional seismicity. Newrnark and Hall, (22) suggested the following values for the seismic

magnification factor m, for structures with a damping ratio of 0.10 .

m ~ 2 . 0, when 2 ~ f ~ 8

5.7 m 8 ~ f ~ 33 (15 )

Ir m = l.0 33 ~ f

where f is the natural frequency of the structure in HZ.

Low rise infilled frames , up to three storeys, may be conservatively assumed to Iie in

the peak range (2-8 HZ), and a magnification factor of 2.0 is used. The peak ground

acceleration depends on the regional seismicity, for example, the NS component of

EI-Centro 1940 had a peak ground acceleration of 0.34g. Therefore

2.0 x 0 . 34 = 0.70 g (16)

Obviously, the spectral value of acceleration Sa' which is a measure of the inertia

force applied to the structure is much larger than that which current seismic codes

recommend . However, for regions where a higher seismicity is expected , such as Tabas in

Iran, where a peak ground acceleration of 0.9g occurred in 1978 , infilled structures would

be subjected to much larger seismic forces than suggested by the codes.

4.2. Cracked Design - Although infilled frames are much more ductile than ordinary

brickwork structures they cannot be modelled simply as elastic-plastic systems beca use of

their degradation of strength and stiffness under cyclic loading . The authors' dynamic

tests indicate that brick infilled frames have a considerable residual strength even after

cracking and crushing. On the basis of these results a nonliner degrading cubic- plastic

780

mode! was deve!oped (20) and used for a series of parametric studies (cracked mode!).

The maximum disp!acement response of the cracked mode! and the ideal e!astic-p!astic

mode! to the N65E component of Parkfie!d 1966 with varying intensity is shown in Fig.

3(a) and the ratio of responses of the two mode!s is shown in Fig. 3(b). It can be seen

that the disp!acement of the cracked mode! is approximate!y 2.5 times the corresponding

disp!acement of the e!astic-p!astic mode!. Similar resu!ts were a!so obtained by using

other earthquake records. Therefore, it can be conc1uded that a cracked mode! with a

ductility factor of p. corresponds to an elastic-plastic system with a ductility factor of

p/2.5. The seismic spectral value of acceleration for elastic-plastic systems is inversely

proportional to p.. Thus the seismic spectral acceleration of a cracked system is 2.5 times

the corresponding elastic-plastic mode!. This means that the current seismic coefficients

should be multiplied by 2.5 to account for the degrading nature of the cracked infilled

frames. Further analytical and experimental research is needed to verify this preliminary

conclusion.

5. STRENGTHENING METHODS

5.1. Corners - the corners of the infill panels are subjected to concentrations of stress.

The performance of the structure can be improved significantly by strengthening these

corners.

5.2. Concrete Columns - the column section adjacent to the loaded corner is subjected

to a combination of concentrated shear forces from the infill panel, and tensile axial

force. This can result in column failure, and therefore such sections need adequate

reinforcement.

5.3. Horizontal Reinforcement - the state of stress at the centre of a pane! is shown in

Fig. 4. As the aspect ratio increases, (Jy increases and (Jx decreases. Thus the shear

sliding tends to occur in a vertical plane rather than a horizontal plane as the aspect ratio

exceeds 1. The authors measured the deflection of the infill before and during the

diagonal cracking. The results indicate that the occurrence of the diagonal crack is

followed by a sudden vertical slip as shown in Fig. 5(a). Results also indicate that the

vertical shear slip is significantly greater than the corresponding horizontal slip (Fig. 5(b».

It can be concluded that the suppression of diagonal cracking requires the containment of

both the vertical and horizontal slips. As shown in Fig. 6, the horizontal reinforcement is

ineffective in preventing vertical slip . The authors investigated the effect of combining

horizontal reinforcement and a RC beam as shown in Fig. 7 . This method resulted in

the full suppression of diagonal cracking and, as shown in Fig. 8, the strength and

stiffness were improved.

•

--

FIG URE 1 Typical Joad-deflection

behaviour of masonry infilIed frames

H

'""' ::; ::; W tf)

30 z O CL tf) w a:: ::; 15 => ~ X co:: ::;

w O I 1 I-

A

A - Interface crackin, B - Diagonal crackin, C - Ultinate stren&th

8

FIGURE 3(a)

CRACKED ~ODEL ELASTO-PLASTIC t.lODEL

4 7 INTENSITY

10

FIGURE 4

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FIGURE 2 Plastic failure modes of

single-storey infilIed frames

5 O

~ a:: -l2. w O O ::;

O 2

a - strong beam b - strong column c - strong frame

FIGURE 3(b)

5 e 11 INTENSITY

State of stresses at the centre of panel

FIGURE 5(a) Vertical displacement of a course of brick at mid-height

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FIGURE 5(b) Horizontal and vertical slips of bricks along diagonal

E 0.4 E

c e 02

~ ~ '6

.~ ~

B

• Vtr1 'COI d.splocrmcrnt ofter 1hcz firs1 d iO}:)OO 1 crock

o VczrtiCQI disploc.rmcznt be:torc •.

1300

1500 (!)Vrrtic 01 {Shrar slips ot ' .1 mm of ~ 0Horizontol fromr 10frrol displQcrmrnt

FIGURE 6 Effect of vertical sliding on horizontal reinforcement

FIGURE 7 Brick infilled frame reinforced by horizontal reinforcement and reinforced concrete beam

R~nforCEmQ'n t bending octicn

~"""~.o,_~

~,----,=-_---"------,,L3

H kg

5000

/' reinfor

concrete

........... _-v-v-y--

m

-- unreinforced

.-- -- reinforced

11

j

K

11

JL I

20 HH

11

N li

11

11

11

11

FIGURE 8 Comparison of the load-deflection behaviour of reinforced and unreinforced brick infilled frames_

0' 0 •

I I

J! JI I I

JI JI I

II 11

M I

----f---l

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6. CONCLUSIONS

6.1 . A simple way of predicting the shear strength of an infilled frame by extrapolation

from the known characteristics of another infilled frame has been proposed.

6 .2. It is suggested that existing codified provisions for seismic loadings are unsafe for

both "elastic" and "inelastic (cracked)" design of infilled frames. Appropriate modifications

fo r both methods have been suggested .

6 .3. The shortcomings of the use of horizontal reinforce ment to enhance in-plane shear

resistance of masonry infilled frames have been highlighted . The resistance can be greatly

improved by insertion of a lightly reinforced beam in the infill.

ACKNOWLEDGEMENT

This project was sponsored by The Science and Engineering Research Council. During

the first year of his postgraduate studies the first author was supported by the Ministry of

Higher Education of the Isla mic Republic of Iran.

gratefully acknowledged.

The contribution of both parties is

1.

2.

Chopra, A .K., Dynamics of Monograph, Earthquake Eng . Moghaddam, H.A., Dowling, of buildings, CESLIC Report December 1985.

REFERENCES

structures. A primer. A monograph pub . by EERI Research Ins!., California, 1981.

P.l . Current methods in earthquake analysis and design EQ1 Civil Engineering Dep!., Imperial College" London,

3. Polyakov, S.V. Masonry in framed buildings. pub . by Gosudarstvennoe Izdatel Stvo Literatury po Stroitel Stvui Arkhitektuze, Moscow, 1956 (Translation into English by G . L. Cairns).

4. Moghaddam, H.A., Dowling, P.l., The State of the Art in Infilled Frames, ESEE Report, No. 87-2, Imperial College, London, Aug. 1987.

5. Stafford-Smith, B.S. Behaviour of square infilled frames. Am. Soc . Civ. Engrs . , 1966, 92, No. S.T.1 (Feb.) 381 - 403.

6 . Riddington, 1., Stafford-Smith, B. Analysis of infilled frames subject to racking with design recommendations. Struc!. Engr., 1977, 52, No. 6, 263-268.

7. Mainstone, R.l . , and Weeks, G.A. The influence of bounding frame on the racking stiffness and strength of brick walls. Proc. 2nd In!. Brick Masonry Conf. Stoke-on-Trent, England, 1970, pp. 165-171

8 . Mainstone, R.l. On the stiffness and strengths of infilled frames . Proc. Ins!. Civ. Engrs. Supplementary Volume, 1971, 57-90.

9. Dawe, 1.L., McBride, R.T . Experimental investigation of the shear resistance of masonry panels in steel frames, Proc. 7th In!. Brick Masonry Conf., Melbourne, Australia, 1985 .

10. Focardi, F., Manzini, E. Diagonal tension tests on reinforced and non-reinforced brick panels. Proc. of 8th World Conference on Earthquake Engineering, San Francisco, California, USA, 1984, Vol. VI, pp. 839- 846 .

784

11. Zarnic, R., Tomazevic, M. The behaviour of masonry infilled reinforced concrete frames subjected to seismic loading. Proc. of 8th World Conference on Earthquake Engineering, California, USA, 1984, VaI. VI, pp. 863-870.

12. Benjamin, J .R. , Williams, H.A. The behaviour of one-storey shear walls. Proc. ASCE, ST. 4 (July), 1958, paper 1723.

13. Wood, R.H . Plasticity, compasite actian and collapse design of unreinforced shear wall panels in frames. Proc. Inst. Civ. Engrs., Part 2, 1978, 65, June, 381-411.

14. Liauw, T.C., Kwan, K.H. Plastic theory of non-integral infilled frames, Proc. Inst. Civ. Engrs., Part 2, 1983, 75, Sept., 379-396.

15. Halmes, M. Steel frames with brickwark and concrete infilling. Proc. Inst. Civ. Engrs., 1961, 19, 473.

16. Liauw, T.C., Lee, S.W. On the behaviour and the analysis of multi-storey infilled frames subjected to lateral loading. Proc. Inst. Civ. Engrs., 1977, 63, Sept., 641-656 .

17. Kadir, M.R.A. The structural behaviour of masonry infill panels in framed structures . Ph .D . thesis, University of Edinburgh, 1974.

18. Thiruvengadam, V. On the natural frequencies of infilled frames. Earthquake Engineering and Structural Dynamics, VaI. 13, 1985, pp. 401-419.

19. Smalira, M. Analysis of infilled shear walls. Proc. Inst. Civ. Engrs., Part 2, Vol. 55, Dec. 1973, pp. 895-912.

20. Moghaddam, H.A., Seismic 8ehaviour of 8rick Infilled Frames, Ph.D., thesis, Imperial College, London 1988.

21. Stafford-Smith, 8., Riddington, J .R. The design of masonry infilled steel frames for bracing structures. The Structural Engineer, March 1978, No.1, Vol. 568.

22 . Newmark, N .M., Hall, W.J. l:.annquaKe spectra and designo A monagraph pub. by The Earthquake Engineering Research Institute, Berkeley, California, USA. 1982.

23. Newmark, N.N., and Rasenblueth. FundamentaIs of Earthquake Engineering . Prentice-Hall, 1971.

TABLE 1 Ultimate strength of single-starey infilled frames

Hu For span greater For helght greater I -- than helght than span , "eth !

"'c

When re mbe

beam stronger mln 2 mln ---than eolumn me + ~

tanB 1

m2 + ___ e 6 tan 2 B

mbe "'c

When ~ ---column stronger mln mln than beam

tanB ',an8 1 2 1 2

I ~ +- m +---

• e 6 tan 2, I

Hu - ultlmate strength

"'c - (4Mpe/l1e th2 )o.s

mb - (4Mpbll1eth2)O.S

~e - [2(Mpb + Mpe)/l1eth2Jo.s

Mpb - Plast le moment of the beam

Mpe - Plast le moment of the colurnn