IN-PLANE ANALYSIS OF MASONRY INFILL MATERIALSBy Roger D. Flanagan1 and Richard M. Bennett,2 Members, ASCE ABSTRACT: Simple methods for determining the corner crushing strength and the in-plane stiffness of masonry infills are developed. The methods are applicable to structural clay tile, clay brick, and concrete masonry infills and to both steel and concrete bounding frames. The corner crushing strength is determined as a function of the infill thickness and the infill prism compressive strength. The stiffness is determined using a stepwise function of the displacement and is a function of the relative stiffness of the infill to the frame. The only infill material property required for the stiffness is the modulus of elasticity. The methods were developed by looking at a wide variety of tests as reported in the literature. INTRODUCTION mining the strength of an infill with respect to the shear Masonry infills can be a main contributor to the lateral limit state. The method is based on bed joint shear strength and stiffness of a building, particularly of older strength, and the net collapse load of the infill is deter- buildings that have little other lateral resistance. Seismic mined as performance of masonry infills has generally been good, Hult = An fve (1) with infills often preventing collapse of buildings (Flan- agan et al. 1996). However, no consensus method of mod- in which An is the net mortared section of the infill and eling infills and determining their strength and stiffness is fve is the expected shear strength of the masonry infill. The available, in spite of significant experimental and analyt- value of fve may be determined from in-place shear tests ical research on the in-plane behavior of masonry infills. as follows: This paper presents simplified methods for determining the stiffness and corner crushing strength of solid masonry infill materials. Forces generated in the bounding frame 0.75 S 0.75vte 1 AnD PCE fve = (2) have been covered in another paper (Flanagan and Bennett 1.5 1999). There are two main failure modes of masonry infill ma- in which vte is the average bed joint shear strength and terials: shear failure and corner crushing. A shear failure PCE is the vertical compressive force on the wall. FEMA is characterized by sliding along the bed joint. Shear fail- 273 (1997) only considers the shear strength of the infill ures are typically more predominant in concrete frames and not the corner crushing limit state. than steel frames. A corner crushing failure is character- Several methods have been proposed to determine the ized by the compressive failure of the masonry. Although corner crushing strength of masonry infills. Stafford-Smith the term corner crushing has been used in the literature and Coull (1991) and Mainstone (1971) developed meth- and is used herein to be consistent with the literature, the ods based on an equivalent strut analogy. Liauw and actual crushing of the masonry can occur in parts of the Kwan (1983) used plastic collapse theory to determine the infill other than the corner. A third limit state that is some- infill strength. To account for the nonideal plasticity of the times considered is diagonal cracking. This is more of a masonry, Wood (1978) suggested a penalty factor. Another serviceability limit than a strength limit state. The diag- analytical method was recently proposed by Saneinejad onal cracking strength is related to the size of the infill, and Hobbs (1995). However, all of these methods indicate and for large infills the diagonal cracking strength can be a higher influence of frame properties and geometry on greater than the corner crushing strength. If this is the the corner crushing capacity than observed in recent tests case, there is a drop in load after diagonal cracking, but (Flanagan and Bennett 1999). Based on a series of large- the infill continues to carry load until corner crushing oc- scale tests with steel frames and structural clay tile infills curs. that covered a wide range of frame and geometry param- FEMA 273 (FEMA 1997) presents a method for deter- eters, a simplified method for determining the corner crushing strength was proposed by Flanagan and Bennett 1 Asst. General Mgr., Bechtel Nevada Corp., P.O. Box 98521, MS (1999) as follows: NLV101, Las Vegas, NV 89193-8521. 2 Prof., Dept. of Civ. and Envir. Engrg., Univ. of Tennessee, Knox- Hult = Kult tf9m (3) ville, TN 37996-2010. Note. Discussion open until April 1, 2002. To extend the closing date in which Hult is the corner crushing strength of the infill, one month, a written request must be filed with the ASCE Manager of Kult is an empirical constant, t is the net thickness of the Journals. The manuscript for this paper was submitted for review and infill, and f9m is the prism compressive strength of the ma- possible publication on April 3, 2000; revised February 27, 2001. This paper is part of the Practice Periodical on Structural Design and Con- sonry. The thickness, t corresponds to the prism test result, struction, Vol. 6, No. 4, November, 2001. qASCE, ISSN 1084-0680/ f9m; if the gross area is used for f9m, then the gross thickness 01/0004-0176–0182/$8.00 1 $.50 per page. Paper No. 22156. is used; if the net area is used for f9m, then the net thickness 176 / PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION / NOVEMBER 2001 240 2. the empirical constant does not represent the divided by height).240 W250 3 67 W310 3 52 Single wythe. Brief descriptions to develop a simple means for determining the in-plane of each of the tests with comments are given in the fol- stiffness of the infill. it is proposed that actual displacement be used indepen- umn. t is the thick.315 6. the capacity given is the net infill capacity. strong axis Push—305 Pull—286 21 195 2. with the rest of C for a wide variety of masonry are presented in the being from the column bearing against the infill (Flanagan paper. indicator of performance than in-plane drift (displacement are length. In a small number (1963). (1994)—1 2 Unreinforced 201 ness of the infill. The coefficient of variation of the ratio of ex. lowing sections. weak axis Push—266 Pull—310 17 195 3.240 W250 3 45 W310 3 52 Single wythe.240 2.240 W250 3 45 W310 3 52 Single wythe.240 2. EI is the flexural rigidity of the 4 Shear connectors 191 columns. Unless noted.240 W250 3 18 W310 3 52 Single wythe.240 2. but the corner crushing load.240 2.240 W250 3 45 W310 3 52 Single wythe. infills are replaced by equivalent diagonal on a single bay performed using an actuator at the top struts for analysis purposes.840 2. and Bennett 1999). Only infills in which corner crushing equivalent diagonal strut was first proposed by Polyakov was the failure mode are considered.240 W410 3 60 W460 3 67 Double wythe. actual bearing contact length of the infill along the col. weak axis Push—204 Pull—177 H 330 7. lh lh = h Î 4 Em t sin 2u 4EIh9 (4) TABLE 2. The corner crushing load is what rather varies with applied load or displacement. weak axis Push—205 Pull—280 2 195 2. Although the units of the empirical constant. The concept of using an corner of the infill. u is the angle of the infill diagonal with 3 Shear connectors 212 respect to the horizontal. and h9 is the height of the infill panel. The other purpose of this paper is the literature are given in Tables 1–5. the diagonal cracking load was larger than the equivalent strut area (or modulus) is not constant. weak axis Push—149 Pull—149 is used. where sufficient information was pres- equivalent strut area is expressed as a function of the rel. weak axis Push—330 Pull—288 4 330 2.2 m high infill.240 2. state of the infill. TABLE 1. weak axis Push—238 Pull—262 9 195 2. be determined as 8 Reinforced every course 212 El-Ouali et al. weak axis Push—252 Pull—162 5 330 2. One purpose of this paper is to extend (3) to clay brick CORNER CRUSHING STRENGTH and concrete masonry infills and to infills with concrete frames. ent. Kult. Often the is reported herein. Values ferred through shear along the top boundary. or the ative panel-to-frame-stiffness parameter. Stafford-Smith and Carter (1969) recognized that of the tests.240 W410 3 39 W460 3 113 Double wythe. Em Hendry and Liauw Unreinforced 198 is the modulus of elasticity of the masonry. 5 Reinforced alternate courses 211 6 Reinforced alternate courses 193 Flanagan and Bennett (1999) proposed that a piecewise 7 Reinforced every course 204 linear strut area. A. all tests were static tests Typically.223 W250 3 49 W410 3 54 Double wythe.450 2. Approximately 50% of the force in an infill is trans. In examining the behavior of a 6. Clay brick masonry—95 mm thick 91 pt (1991)—2 A= (5) Cl cos u 5 Lime and sand masonry—95 mm thick 184 6 Lime and sand masonry—47 mm thick 204 in which C is an empirical constant that varied with the Benjamin and — 196 Williams (1958) in-plane drift displacement and is an indicator of the limit PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION / NOVEMBER 2001 / 177 . Lacking further experimental studies.2 m perimental corner crushing load to the analytical corner high versus a 2. Specimen Summary of Clay Brick in Steel Frame Tests Description Kult (mm) in which h is the height to the centerline of the beam. weak axis Push—267 Pull—295 3 195 2.240 W250 3 45 W310 3 52 Single wythe. dently of infill height to determine the value of C. Flanagan and Bennett crushing load was much smaller using (3) than for other (1999) determined that in-plane displacement is a better methods. Summary of Structural Clay Tile in Steel Frame Tests Panel thickness Panel length Panel height Description Kult Specimen (mm) (mm) (mm) Column size Beam size (including column orientation) (mm) 1 195 2. It will be shown that (3) is applicable to a wide The results of various experimental tests as reported in variety of conditions. 67 Monotonic 293 0 185 4 weak hollow 0. Results from Mehrabi et al. the infill was reported. two with lime and sand Structural Clay Tile Infills in Steel Frames bricks.67 Cyclic 196 98 176 6 strong hollow 0.67 Monotonic 196 98 197 10 weak hollow 0. which also indicates the value of Kult. of 19.48 Cyclic 196 98 324 11 weak solid 0. Each frame was 2. 4 45-mm thick infill 322 as indicated in Table 2. TABLE 3. An increasing cyclic load was applied to the are given in Table 1.250 mm high by 200 m thick clay the size of the specimens tested by Flanagan and Bennett brick infill in a pinned steel frame. El-Ouali et al. Based on the given unit strength creasing displacement controlled loading to capture the and the relationship between unit strength and prism hysteretic behavior.48 Cyclic 196 98 248 12 weak solid 0. displacement.48 Cyclic 293 147 261 178 / PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION / NOVEMBER 2001 .3 MPa was assumed.’s (1994) Concrete Frames with Concrete Masonry Infill Tests TEST CHARACTERISTICS Vertical Load (kN) Aspect ratio Kult Specimen Type of frame Type of masonry (height/length) Lateral load Columns Beams (mm) 3 weak solid 0. The columns and beam were (1994)—3 0.200 mm high. Results from Dawe and Seah’s (1989) Steel Frames with Concrete Masonry Infill Tests Frame Characteristics Polyethylene Mortar packed between membrane Joint column flanges Panel-to-column between panel Sandy. All infills were 2. (1991)—3 90-mm thick infill 204 the strong axis.500 mm long and 1. labeled as a spec. poor Kult Specimen reinforcement and panel ties Bond beams and frame quality mortar (mm) WA1 u u — — — — 261 WA2 u u — — — — 241 WA3 u u — — — — 265 WA4 — u — — — — 295 WA5 u u u — — — 264 WA6 u u — u — — 291 WB1 u u — — — — 286 WB2 u — — — — — 253 WB3 u — — — — — 259 WB6 u — u — — — 180 WC1 u — — — u — 200 WC2 u — — — u u 170 WC7 — — — — — — 242 WD7 u — — — — — 294 TABLE 4. The tests included a variation of 78 specimens until failure. which was approximately three times 3. Benjamin and Williams (1958) monotonically tested a imen H in Table 1. and two with concrete bricks. Results of Kult are given in Table times in the moment of inertia of the columns. reported is a test by Henderson (1994). with a coefficient of variation of 4%. Summary of Concrete Masonry in Steel Frame Tests Clay Brick Infills in Steel Frames Kult Hendry and Liauw (1994) monotonically tested eight Specimen Description (mm) clay brick infills in steel frames. The mean value of Kult for these tests strength given in Drysdale et al.4% vertical reinforcing 308 long and 1. with a coefficient of variation of 24%. TABLE 5. single and 2 for the clay and lime and sand bricks. Also for the concrete bricks. and in Table 4 double wythe infills.8% vertical reinforcing 258 100 3 60 3 6 mm tubes. with both the col- The results of eight tests performed on structural clay umns and the top and bottom beams being W150 3 37 tile infills in steel frames by Flanagan and Bennett (1999) members.67 Cyclic 196 98 225 5 weak solid 0. Various types of reinforcement were used. and varying lengths of infills.500 mm high.67 Monotonic 196 98 302 9 weak solid 0. (1994).025 mm Hendry and Liauw (1994)—1 Unreinforced 322 (1994)—2 0. All of the structural clay tile tests involved in.67 Cyclic 196 98 335 8 weak hollow 0.67 Cyclic 196 98 314 7 strong solid 0. a prism strength is 246 mm. with the columns bent about El-Ouali et al.260 mm long by 2. The average value of Kult for Hendry and Liauw’s maximum load minus the bare frame load at the same tests was 203 mm. No prism strength for (1999). (1991) tested five steel frames with ma- sonry infills: one with clay brick. which were described in the previous sec. statistic when comparing frame material was 94. Statistical Summary of Corner Crushing Results Specimen Characteristics Statistical Results of Kult Mean Coefficient of variation Infill masonry type Frame Number of tests (mm) (%) Clay tile Steel 18 246 23. can handle dif- ferent configurations of concrete masonry infills in steel ferent sample sizes. TABLE 6. reliable estimate of the corner crushing strength of a ma- sonry infill. The not be rejected at the 5% level.700 mm long by 2. and is robust against different vari- frames. Considering the wide variety of test conditions that mm high. and having a ference between bounding frame material types. and the top beam was a W200 3 46. rejected (U-statistic = 49. Column sections were W250 3 58 bent about rejected. critical U-statistic = 116). termine the strut area. tile in steel frames are given in Table 7 (Flanagan and PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION / NOVEMBER 2001 / 179 . A tistical tests. with a coefficient of material does not statistically affect corner crushing variation of 16%. along with the value of Kult. (5) can be used to de- to be an outlier was the clay brick masonry test of El.8 m high. Other monotonic tests of concrete masonry in steel All tests within steel frames were compared to deter- frames were conducted by Hendry and Liauw (1994). However.2 Concrete Masonry Infill in Steel Frame To statistically compare different frame and infill types. adding bond were compared to the tests with concrete masonry in con- beams to the infill. (3) provides a simple but quite of Kult was 257 mm. In all cases. The average value is not excessive. since there was no statistically signifi- cant difference. In analytical modeling of masonry infills. critical U-statistic = 65). along with the values of Kult. Additional statistical information is given in Table 6 for clay tile and concrete masonry combined (both steel and Concrete Masonry Infill in Concrete Frames concrete frames). the U-test was used.7 All All 58 243 21. Thus. 2. the coefficient of variation of Kult Table 5.3 Clay tile and concrete combined Steel and concrete 47 253 20. including joint rein. the null hypothesis can- are given in Table 3. with a 159. (1991). (1991). The U-test is distribution-free. Other characteristics of the infills are given in this data set represents. (1994) tested several concrete masonry between masonry types is ignored and all tests are com- infills in concrete frames.1 (with outlier removed) 11 201 4. Results of the tests are shown in not be rejected at the 5% significance level (U-statistic = Table 4. A 5% significance level was chosen for the sta- the weak axis. The average value of Kult was 296 mm. mine if there were statistically significant differences be- fills 2. and the bounding frame average value of Kult was 250 mm.5 Brick Steel 12 191 17. If the U-test statistic is greater than and constructed with 190 mm concrete blocks and Type the critical U-test statistic. with Kult of 91. The tests with concrete masonry infills in steel frames forcement versus no joint reinforcement.6 Concrete Steel 19 259 17. The data were checked for outliers using the max. is Dawe and Seah (1989) monotonically tested several dif. This value is not in. Values of C for structural clay cluded in further statistical analysis of the data. The null hypothesis that concrete 8 mm steel tubes were tested with various amounts of masonry infills were different from clay tile infills could vertical reinforcement. the only value determined for the stiffness of the infill. Eq. the null hypoth- coefficient of variation of 11%. variety of conditions were tested.475 mm high in 100 3 100 3 tween masonry types. critical U-statistic = 61). with a coefficient of variation of 23%. strength. be replaced with an equivalent diagonal strut to account At the 5% significance level. In. the infill can imum normed residual test (Snedecor and Cochran 1980). The U- polyethylene bond break between the steel and masonry. Summary Table 6 gives statistical results for values of Kult in terms IN-PLANE STIFFNESS of the type of masonry used in the infill and frame ma- terial. In all tests the infill was 1. and the null hy- frames with concrete brick infills performed by El-Ouali pothesis that brick was the same as concrete masonry was et al. tion. the in-plane displacement. ances (Sachs 1984). the infill was 3. the null hypothesis cannot be S mortar. packing mortar between the infill and crete frames to determine if there was any statistical dif- column flanges. Table 6 also gives results if the difference Mehrabi et al. nearly as statistically efficient as the t-test. with the Specific characteristics of 14 solid infills that they tested critical U-statistic being 58. Thus.420 bined. where the constant C varies with Ouali et al. esis that brick was the same as clay tile was rejected (U- Table 4 also shows the results of the two tests on steel statistic = 52.3 Concrete Concrete 10 257 23.6 m long. using column-to-panel ties. the 25 mm limit of displacement. Values of C for Masonry Infill Stiffness C Concrete masonry Displacement Structural clay tile Concrete masonry in concrete (mm) in steel frame in steel frame frames Proposed Typical infill damage 0–4 7 5 4 5 None 4–12 11 9 11 10 Diagonal mortar joint cracking 12–18 14 12 — 13 Mortar crushing and cracking of units 18–25 18 17 — 17 Failure of units (primarily corner regions) FIG. Summary results are presented in terms of hollow and solid block infills. 1 shows the value of C versus infill displacement for the concrete masonry infills in steel frames tested by Dawe and Seah (1989). Solid block infills appear to be slightly stiffer than hollow block infills. and frame 9 from Mehrabi et al. The load at 25 mm displacement value of displacement of 25 mm is used. Experimental Shown in Solid was observed in these tests. Experimental and Analytical Load-Deflection Curves for Frame 2 (Bennett and Flanagan 1999). but there is not a large difference in behavior. Fig. with only a gradual Line. individual tests are not shown for clarity. These C values. Analytical in Dashed Line decrease in load with increasing displacement. 1994). In the case of frame Thus. values of C for these regions are shown in Table 7. the displacement limit of 25 mm. A limiting displacement of 25 mm is used for structural clay tile. the infill will be controlled by Seah (1989). thus only stiff. Fig. FIG. the 25 mm displacement was reached before the masonry are given in column 5 of Table 7. These specimens reached peak loads at smaller displacement levels. TABLE 7. This behavior has been 3 shows both the proposed analytical and experimental observed in experimental testing (Flanagan and Bennett 180 / PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION / NOVEMBER 2001 . the displacement of 12 mm. Using the same displacement regions as for structural clay tile. was taken as a peak load. reached at smaller displacement levels for stiffer columns. proposed values of C to be used with all types of WD7. Fig. A limiting corner crushing capacity.’s (1989) Tests of Concrete Masonry Infills in Steel Frames (1994) Tests of Concrete Masonry Infills in Concrete Frames Bennett 1999). frame WD7 from Dawe and For more flexible columns. along with the corner crushing strength. corner crushing capacity of the infill was reached before The values of C are similar for all types of masonry. Using the same displacement regions as for structural clay tile. agan and Bennett (1999). and Frame 9 (Mehrabi et al. are used to obtain As a general rule. In the case of frames 2 and 9. the strength of the infill will be load-deflection curves for three tests: frame 2 from Flan. Also shown in Fig. however. 1 is a piece- wise linear approximation to the data. Frame WD7 (Dawe and Seah ness values up to 12 mm are shown. Significant ductility 1989). 2. val- ues of C for these regions are shown in Table 7 up to a load-deflection curves. Value of C versus Infill Displacement for Dawe and Seah’s FIG. Value of C versus Infill Displacement for Mehrabi et al. 1. 3. (1994). (1994). 2 shows the value of C versus infill displacement for the concrete masonry infills in concrete frames tested by Mehrabi et al. . All three infills shown in Fig. J..K. 865–876. T.’’ J. G. (1994). A handbook of techniques. (1963). Masonry Conf. R. A. V. Boulder. (1999). D. and Hanson. The only infill material REFERENCES properties required are the prism compression strength and modulus of elasticity. M. B. However. Instn. (1989). Masonry Conf. C. 53–85.’’ J. Colo. Earthquake Engi- neering Research Institute. L. 365–374..’’ Proc. (1987) identified the dissipation of Flanagan. (1994). G. and Noland. infills. 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