paper sp36-7 strength of high-rise shear walls

PAPER SP36-7

STRENGTH OF HIGH-RISE SHEAR WALLS - RECTANGULAR CROSS SECTION

BY ALEX E. CARDENAS DONALD D. MAGURA

Synopsis: The results of a laboratory investigation on the strength of shear walls for high-rise buildings are presented. Six large rectangular shear wall specimens were subjected to static loads representing gravity and wind or earthquake forces. Variables were the amount and distribution of vertical reinforcement and the effect of the moment to shear ratio.

Results indicate that the flexural strength of rectangular shear walls can be calculated using the same assumptions as for reinforced concrete beams. Also, the strength of high-rise shear walls containing minimum horizontal shear reinforcement is generally controlled by flexure.

Keywords: axial loads; bendinp moments; deformation; ductility; earthquake resistant structures; failure; flexural strength; framinp. systems; high rise buildings; laterallressure; loads (forces); multistory buildinps; reinforced concrete; relnforc.np, steels; research; shear proDerties; shear strength; shear tests; ~ ~· -- --

119

120

response of multistory

concrete structures

to lateral forces

ACI member Alex E. Cardenas is c.onsulting- oogineer, Lima, Peru. He received his CE degree from the Universidad Nacional de Ingenieria, Lima and MS and PhD degrees in structural engineering from the University of Illinois. From 1968 to 1972, Dr. Cardenas was a research engineer with the Portland Cement Association. Currently he is a member of ACI-ASCE Committee 426, Shear and Diagonal Tension and ACI Committee 442, Lateral Forces.

ACI member Donald D. Magura is senior design engineer, ABAM Engineers Inc., Tacoma, Wash. He received BS and MS degrees in civil engineering from the University of Illinois. From 1962 to 1969, Mr. Magura was aresearch engineer with the Portland Cement Association. Currently, he is chairman of the PCI committee on prestress losses.

HIGHLIGHTS

There is limited information ~egarding the strength of shear walls in buildings. Prior to the publication of ACI 318-71 (1), only the Uniform Building Code (2) contained design provisions for shear walls. The UBC provisions were based on shear tests of deep beams (3, 4) with and without web reinforcement.

To develop basic information, the Portland Cement Association initiated a laboratory investigation of reinforced concrete shear walls in high and lowrise buildings. The main features of the high-rise wall tests are:

1. Tests of six large rectangular shear wall specimens. 2. Consideration of gravity and lateral loads. 3. Distribution of lateral loads to simulate interaction

between frames and shear walls.

Results obtained from these six tests and seven others on low -rise walls* were used to develop design provisions for shear walls (5), The provisions are included in Section 11. 16, Special Provisions for Walls, of ACI 318-71.

CONCLUSIONS

The following conclusions can be drawn as a result of this investigation:

1. The strength of most rectangular reinforced concrete shear walls in high-rise buildings is governed by flexure rather than shear.

* Cardenas, A. E., "Strength of Low -Rise :'ltear Walls - Rectangular Cross Sections, 11 to be published by the Portland Cement Association, Skokie, Illinois.

121

strength of high-rise

shear walls

rectangular cross sections

2. Design for flexural strength of rectangular shear walls can be carried out on the basis of Section 10. 2, Assumptions, of ACI 318-71.

3. Design for shear strength of rectangular shear walls can be carried out on the basis of Section 11. 16, Special Provisions for Walls, of ACI 318-71.

4. The amount and distribution. of vertical reinforcement in high-rise rectangular shear walls has a definite influence on load-deformation and energy absorp-tion characteristics.

BACKGROUND

Concrete walls in high-rise buildings are often used to carry lateral loads in conjunction with frames or frame-tubes (6, 7). Since they carry the story shear they are generally called "shear walls." However, this terminology does not indicate that the carrying capacity of the wall is controlled by its shear strength.

An investigation of shear wall structures can be subdivided into three parts: determination of the loads, analysis of the structural response and design of the structural members. ·

Basic design information on the nature and magnitude of wind and earthquake loads has been described in detail (2, 6, 8, 9). The analysis of the response of shear wall structures has also received wide attention. Some of the papers presenting analytical methods are contained in Ref. (10-14). Computer programs intended for use in design are also available (15, 16).

Research concerning the behavior and strength of shear walls is scarce. A number of investigations have been conducted in Japan. However, only limited information ( 17 -20) is available in English. In the United States, the only systematic investigation concerning the strength of shear walls was carried out by Benjamin and Williams (21-24) at the University of Stanford. The test program considered only low -rise shear walls surrounded by a reinforced concrete frame and subjected to static loads. A continuation of this investigation for dynamic loads was carried out by Antebi, et. al., (25) at MI'r.

EXPERIMENTAL INVESTIGATION

Shear .walls for high-rise buildings are usually designed to interact with other structural elements. One of the most common systems found in

122


concrete structures

to latera I forces

practice is that of a frame* interacting with a shear wall.** Figure 1a shows a frame-shear wall structure subjected to a system of lateral forces due to wind or earthquake,

Because of the different lateral stiffness characteristics of the frame and the wall, the frame may tend to pull the wall in the upper stories and push it forward in the lower stories (11, 12). This interaction causes a distribution of shear forces between the frame and the wall similar to that shown in Figs. 1b and 1c. Bending moment and shear force diagrams resulting from these forces acting on the shear wall are shown in Figs. 2a and 2b. The location of the point of contraflexure in the shear wall depends on many variables discussed elsewhere (11, 12),

The forces acting on that portion of the shear wall below the point of contraflexure are shown in Fig. 2c. They are: axial stresses, ncf' representing the effects of dead and live loads; a shear force, V cf' representing the resultant shear force of the upper stories; and story shears, f, distributed between the point of contraflexure and the base of the wall.

The laboratory specimen and the load distribution selected for this investigation were intended to simulate the conditions existing in the lower portion of a high-rise shear wall as shown in Fig. 2c. In addition, the distribution of shear forces was chosen such that 50 percent of the total shear force, V, at the base of the wall, was applied at the point of contraflexure, V cf' The remaining shear force was equally distributed between the point of contraflexure and the base of the wall.

Ranges for variables such as amounts of vertical and horizontal reinforcement, magnitude of the axial stresses, concrete strength and reinforcement grade were determined from a survey of high-rise buildings designed and built in the Chicago area and on the West Coast.

For convenience of testing, the shear wall specimens in the laboratory were rotated 90° with respect to the vertical position of a shear wall in a building, In describing the specimen characteristics and test results on this report, however, .reference is made to the orientation of a shear wall in a building rather than its position in the laboratory,

Figure 3 shows dimensions and test setup for four of the six specimens tested. The depth of the wall was tw =6ft. 3 in. (1. 91 m) and the thickness, h = 3 in. (7. 5 em). The height of the specimen, representing the portion of the wall between the base and rx>int of contraflexure, was ~ = 21 ft. (6. 40 m),

* A frame, as defined here, includes all beams, spandrels and floor systems contributing to lateral stiffness.

** A shear wall comprises one wall or a combination of shear walls extending ove.r all or part of the height of the structure.

123


shear walls


Two other specimens having the same cross sectional dimensions, but with a height of 12 ft. (3, 66 m) were also tested.

The part of the specimen labeled "restrained area" in Fig. 3 was intended to represent the restraint condition at the base of the wall. In the design of the test rig and loading equipment, particular care was taken to provide a fixed end condition at the base of the wall. In addition, instrumentation was provided to measure base rotations due to elastic deformations of the restrained area and the loading equipment.

Figure 4 shows the test rig used for the specimens with a height~ = 21ft. (6. 40 m), The loading rods going through the laboratory test floor apply the lateral forces to the wall specimen. Post-tensioning rods shown longitudinally in the figure, apply the gravity loads. The vertical steel tubes attached to each side of the wall were used to simulate lateral restraint and prevent large lateral deflections. A more detailed explanation of materials, instrumentation and test procedures used is given in Appendix A.

TEST RESUt.TS

Specimen Characteristics

Dimensions and material properties for the six high-rise shear wall specimens tested are listed in Table 1. All specimens had the same rectangular cross section, 3 in. by 75 in. (7. 5 em by 190 em).

Specimens SW-1, frvv-2, and SW-3 had the same height, ~=21ft. (6.40 m). Their corresponding moment to shear ratio calculated at a distance tw/2 from the base of the wall was M/V = 2. 0 tw. The only variable was the amount of uniformly distributed vertical or flexural reinforcement which ranged between 0. 27 and 3. 0 percent.

Specimens 'i:NJ-4 and SW-5 had a height of~ = 12ft. (3. 66 m). The corresponding moment to shear ratio was M/V = 1, 0 tw. Both specimens were designed for the same flexural strength but containing different distributions of flexural reinforcement. Fig. 5 shows the two distributions of flexural reinforcement used. Specimen SW -4 had uniformly Qistributed reinforcement, while SW -5 had concentrated reinforcement.

Specimen SW -6 was similar to SW -3 except for the distribution of flexural . reinforcement. In SW -6, the bars were concentrated near the ends in the same manner as for SW-5.

Shear or horizontal reinforcement was constant for all six specimens at 0. 0027 times the concrete gross area. All reinforcement used met requirements of ASTM Designation: A-615-68, Grade 60 (4200 kgf/cm2 ). The

124


concrete structures

to lateral forces

nominal concrete compressive strength was 6000 psi (420 kgf/cm2 ) while the axial compressive stress in all specimens was nominal 420 psi (29 kgf/cm2 ).

Table 2 summarizes the test results for all six specimens. The mode of failure for each specimen is also listed.

Load-Deformation Relationships

Moment-curvature or load-deflection relationships of shear walls are significantly influenced by the amount and distribution of vertical reinforcement and the presence of axial load. Fig. 6 shows idealized moment-curvature diagrams for rectangular shear walls with different amounts of uniformly distributed vertical reinforcement. For these diagrams, no axial load was considered and the shear capacity was assumed to be adequate to develop the flexural strength.

For comparison purposes, the flexural strength and ultimate curvature of a shear wall with an amount of vertical reinforcement, Pv == 0. 25 percent, were assumed to be 100 percent.

Figure 7 shows idealized moment-curvature relationships for walls with vertical reinforcement concentrated near the edges. As in Fig. 6, the curve for Pv == 0. 25 percent represents minimum reinforcement uniformly distrib-uted across the wall. Comparison of trends in Figs. 6 and 7 show that, for the same total amount of vertical reinforcement, shear walls having more reinforcement near the ends have both higher moment capacity and ultimate curvature than those with uniformly distributed reinforcement. The inelastic range of deformations is also improved by the concentration of the reinforcement. As a result, concentration of reasonable amounts of vertical reinforcement near the ends of tall shear walls may prove advantageous.

Axial compression on shear walls increases the moment capacity. Axial tensile loads decrease it. However, axial compression reduces the ultimate curvature. Consequently, neglecting the presence of compressive loads in the design of shear walls may result in an overestimate of ultimate curvature and energy absorption.

Figure 8 shows measured moment-curvature relationships for the four test specimens with M/V == 2. 0 t . Figure 9 shows similar relationships for the two specimens with M/V == 1':'0 i.w, Moments were measured at the base of the shear wall and curvatures in Fig. 8 are average rotations measured by LVDT' s over a 40-in. (1. 00 m) gage length near the restrained area. Curvatures in Fig. 9 are average rotations measured over a 12-in. (30 em) gage length. Values of measured and calculated ultimate moments and curvatures and ratios of ultimate to yield moments and curvatures are listed in Table 3. Calculated values for ultimate moments and curvatures were based on a limiting concrete compressive strain of 0. 003, strain compatibility and measur.ed materiaLpraperties.

125


shear walls


Increase in ductility due to the concentration of reinforcement is apparentfrom the results in Fig. 8 of tests on specimens W -3 and W -6. At ultimate, the curvature of W -6, with concentrated reinforcement is almost twice that of specimen W -3 with uniformly distributed reinforcement. Results for specimens W -4 and W -5 shown in Fig. 9 also illustrate the influence of reinforcement distribution on the moment-curvature relationship. In this case, however, the potential ultimate curvature of W-5 was not attained due to a premature shear failure.

Modes of Failure

There were, in general, three distinct modes of failure observed in these tests. Two of these can be classified as flexural while the third can be defined as a shear failure precipitated by the formation of a 11flexure-shear11 crack (27.)

Specimen W -1 reached its flexural strength by fracture of some of the tension reinforcement at the base of the wall. A close-up of this fracture zone is shown in Fig. 10. As a result of the low amount of reinforcement used, pv = 0. 0027, and the relatively high cracking capacity of the shear wall, only one crack formed at the base of the wall. After the full elongation of the tensile reinforcement was exhausted, the bars fractured.

Figure 11 shows the flexural hinge observed in most of the other test specimens. The behavior of this specimen is typical of an under-reinforced section. Its strength is reached by crushing of the concrete in the compression zone after considerable yielding of the tension reinforcement. This type of behavior produced a more uniform spread of cracks near the base of the wall as shown in Fig. 11. All specimens, except W-1 and W-5, exhibited these characteristics.

The third type of failure observed in these tests was designated 11flexureshear11 failure. As seen in Fig. 12, the inclined crack in these specimens initiated from a flexural crack that started at a distance about equal to the depth of the wall, tw, from the base. With increase in load, the flexural crack turned toward the support at an angle of about 45°. At ultimate, some of the shear reinforcement across the inclined crack fractured and the concrete crushed in compression.

ANALYSIS OF TEST RESULTS

Flexural Strength

The calculated flexural strengths listed in Table 2 were based on Section 10. 2, Assumptions, of ACI 318-71. In addition, the effect of strain hardening of the reinforcement was taken into account. Moment-curvature relationships and flexural strength based on these assumptions were calculated viith the aid of a computer.

126


concrete structures

to latera I forces

For hand calculations, a simplified equation for flerural strength was developed. The development of this simplified approach is described in detail in Appendix B. The flexural strength of rectangular shear walls containing uniformly distributed vertical reinforcement and sub-jected to an axial load smaller than that producing a balanced failure condition can be approximated as:

.... (1)

where

Mu == design resisting moment at section, in. -lbs.

As == total area of vertical reinforcement at section. sq. in.

fy specified yield strength of vertical reinforcement, psi.

~ == horizontal length of shear wall, in.

Nu design axial load, positive if compression, lbs.

c distance from extreme compression fiber to neutral axis, in. (See Appendix B)

¢ capacity reduction factor Shear Strength

Calculated and measured nominal shear stresses at failure for all specimens are listed in Table 2. Calculated values are based on the ACI 318-71 shear strength equations for shear walls. The value of¢, the understrength factor, was assumed equal to 1. 0. Measured values represent the nominal shear stress at a section located at a distance Lw/2 from the base of the wall.

Nominal shear stresses observed atyltimate varied between 1. 7 ./f~ and 7. 8 .;r:;; psi (0. 451 ,jf~ to 2. 07 J£6 kgf/cm2 ). As indicated in -Table 2, the two specimens that failed in flexure-shear, fJW-3 and fJW-5, had developed a shear stress greater than that calculated for ¢ == 1. If the recommended value of ¢ == 0. 85 had been used, the measured to calculated shear strength ratios of specimens W--3 and fJW -5 are 1. 33 and 1. 35, respectively. It appears then, that the ACI 318 -71 equations for shear strength of high-rise shear walls provide a conservative estimate of the strength of these specimens. Furthermore, no reduction in shear strength due to the proportions of the specimens, such as that postulated by Kani ('Zl ), was observed in any of these tests.

Energy Absorptio.D

127


shear walls-


The area under the moment-curvature, M - 1/J, diagram is a measure of the energy absorbing capacity of reinforced concrete members. Consequently, the variables that affect the energy absorption of walls are the same as those affecting their moment-curvature characteristics.

Figure 13 shows idealized M -1/J relationships for two rectangular shear wall sections subjected to bending. In constructing these curves, it was assumed that the amount of shear reinforcement was sufficient to develop the full flexural strength of the two walls. One of the sections considered was assumed to contain vertical reinforcement placed near the extreme tension and compression fibers. For the other case, the reinforcement was assumed to be uniformly distributed along the cross section. The total area of vertical reinforcement provided is such that both sections have the same flexural strength.

The energy-absorbing capacity of the shear wall with reinforcement near the rmds only can be calculated on the basis of the equations presented by Blume, Newmark and Corning ( 9).. The equations are based on the simplifying assumptions that the yield moment is equal to the ultimate moment and the M - 1/J relationship is elasto-plastic.

For the shear wall with the uniform distribution of vertical reinforcement, the simplifying assumptions of Ref. (9) cannot be directly applied. As shown in Fig. 13, the moment at first yield is appreciably lower than that at ultimate. Consequently, the transition from the yield to the ultimate capacity requires an increase in load. This increase in load depends on the amount of vertical reinforcement and the presence of axial load.

In practice, most rectangular shear walls contain a distribution of vertical reinforcement which is intermediate between those illustrated in Fig. 13. As a result, the shape of their M - 1/> relationship lies somewhere between the boundaries illustrated.

Table 3 lists the moment-curvature characteristics for the six specimens tested in this investigation. Characteristics of each specimen and measured and calculated test results are presented in Tables 1 and 2. For specimens fNJ -1, fNJ -2 and fNJ -3 containing increasing amounts of uniformly distributed vertical reinforcement, the ductility ratio 1/1 I 1/J decreases with increasing amounts of reinforcement. Measured value~ ale the average curvature over a 40-in. (1. 00 m) gage length near the base of the walls. Calculated values were obtained taking into account strain hardening of the reinforcement and using the assumptions of Chapter 10 of ACI 318-71.

The influence of concentrating some of the vertical reinforcement near the ends of the cross section is illustrated by the results of specimens fNJ -3

128

response of multi·story

concrete structures

to lateral forces

through fN\/-6. Specimens fN\/-3 and SW -4 contained uniformly distributed vertical reinforcement while fN\/-5 and SW -6 represent an intermediate distribution between uniform and concentrated. Comparisons of curvature ratios of SW -3 with SW -6 and fN\/-4 with fN\/-5 show the increase in ductility when reinforcement is concentrated near the ends of shear walls.

CONCLUDING REMARKS

The results of this investigation have provided basic information on the behavior and strength of rectangular reinforced concrete shear walls for highrise buildings. Important observations of these tests are listed at the beginning of the report under CONCLUSIONS.

Although no load reversals were considered in these tests, it is expected that the test results would not be affected because of the relatively small magnitude of the shear stresses. For earthquake resistant design, particular emphasis should be placed on good detailing of the reinforcement, adequate anchorage and splice lengths, construction joint details, among others, in order to obtain a satisfactory performance.

The effect of gravity loads acting on shear walls should also be considered. Neglecting these loads does not necessarily lead to conservative designs.

ACKNOWLEDGMENTS

This investigation was conducted at the Structural Development Laboratory of the Portland Cement Association under the direction of W. G. Corley, Manager. The authors thank E. Hognestad, Director, Engineering Development Departman and J. M. Hanson, Assistant Manager, Structural Development Section, Portland Cement Association, for their constructive criticisms made throughout this investigation.

Laboratory Technicians B. J. Doepp, B. W. Fullhart, W. H. Graves, W. Hummerich, Jr., and 0. A. Kurvits performed the laboratory work.

REFERENCES

1. ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI 318-71)," American Concrete Institute, Detroit, 1971, 78 pp.

2. Uniform Building Code, International Conference of Building Officials, Pasadena, California, 1970.

3. dePaiva, H. A. R. and Siess, C. P., "Strength and Behavior of Deep Beams in Ehear," Proceedings ASCE, V. 91, No. ST5, Part I, October 1965, pp. 19-41.

4. Slater, W. A., Lord, A. R. and Zipprodt, R. R., "Shear Tests of Reinforced Concrete Beams," National Bureau of Standards, 1926.

129


shear walls


5. Cardenas, A. E., Hanson, J. M., Corley, W. G. and Hognestad, E., "Design Provisions for Shear Walls," to be published in the ACI Journal.

6. ACI Committee 442, 11Response of Buildings to Lateral Forces," ACI Journal, Proceedings, V. 68, No. 2, February 1971, pp. 81-106.

7. Frischmann, W. W. and Prabhu, S. S., "Planning Concepts Using Shear Walls," Tall Buildings,Pergamon Press, 1967, pp. 49-99.

8. Davenport, A. G., "The Treatment of Wind Loading on Tall Buildings," Tall Buildings, Pergamon Press, 1967, pp. 3-45.

9. Blume, J. A., Newmark, N. M. and Corning, L. H., "Design of Multistory Reinforced Concrete Buildings for Earthquake Motions," Portland Cement Association, Skokie, Illinois, 1961, 318 pp.

10. Rosenblueth, E. and Holtz, I., "Elastic Analysis of Shear Walls in Tall Buildings," ACI Journal, Proceedings, V. 56, June 1960, pp. 1209-1222.

11. Khan, F. R. and Sbarounis, J. A., "Interaction of Shear Walls and Frames," Proceedings, ASCE, V. 90, ST3, June 1964, pp. 285-335.

12. "Design of Combined Frames and Shear Walls," Advanced Engineering Bulletin No. 14, Portland Cement Association, Skokie, Illinois, 1965, 36 pp.

13. Tall Buildings, Pergamon Press, 1967.

14. McLeod, I. A., "Shear Wall Frame Interaction - A Design Aid with Commentary," Special Publication SPOll. OlD, Portland Cement Association, Skokie, Illinois, April 1971, 62 pp.

15. Derecho, A. T., "Analysis of Plane Multistory Frame-Shear Wall Structures Under Lateral and Gravity Loads," Computer Program Series, SR097. OlD, Portland Cement Association, Skokie, Illinois, 1971, 90 pp.

16. Schwaighofer, J. and Microys, H. F., "Analysis of Shear Walls Using Standard Computer Programs," ACI Journal, Proceedings, V. 66, No. 12, December 1969, pp. 1005-1007. ·

17. Tomii, M., "Introduction and Summary Design Procedures of Concrete Shear Walls," especially edited for United States - Japan Joint Seminar, February 1967.

130


concrete structures

to latera I forces

18.

19.

20.

21.

22.

23.

Muto, K. and Kokusho, K., rrExperimental Study on Two-Story Reinforced Concrete Shear Walls,U Muto Laboratory, University of Tokyo, Tokyo, Japan. Translated by T. Akagi, University of Illinois, Urbana, Illinois, August 1959.

Ogura, K., Kokusho, K. and Matsoura N., "Tests to Failure of TwoStory Rigid Frames with Walls," Part 24, Experimental Study No. 6, Japan Society of Architects Report No. 18, February 1952. Translated by T. Akagi, University of Illinois, Urbana, Illinois, August 1959.

Tsuboi, Y. , Suenaga, Y. and Shigenobu, T. , "Fundamental Study on Reinforced Concrete Shear Wall Structures - Experimental and Theoretical Study of Strength and Rigidity of Two -Directional Structural Walls Subjected to Combined stresses M. N. Q. 11 Transactions of the Architectural Institute of Japan, No. 131, January 1967. PCA Foreign Literature Study No. 536, November 1967.

Williams, H. A. and Benjamin, J. R., "Investigation of Shear Walls, -Part 3 - Experimental and· Mathematical Studies of the Behavior of Plain and Reinforced Concrete Walled Bents Under Static Shear Loading," Department of Civil Engineering, Stanford University, Stanford, California, July 1953, 142 pp.

Benjamin, J. R. and Williams, H. A., "Investigation of Shear Walls, -Part 6 - Continued Experimental and Mathematical Studies of Reinforced Concrete Walled Bents Under Static Shear Loading," Department of Civil Engineering, Stanford University, Stanford, California, August 1954, 59 pp.

Benjamin, J. R. and Williams, H. A., "The Behavior of One-Story Reinforced Concrete Shear Walls," Journal of the Structural Division, ASCE, V. 83, No. ST3, May 1957. Also Transactions, ASCE, V. 124, 1959, pp. 669-708.

24. Benjamin, J. R. and Williams, H. A., "Behavior of One-Story Reinforced Concrete Shear Walls Containing Openings," ACI Journal, Proceedings, V. 55, November 1958, pp. 605-618.

25. Antebi, J., Utku, S. and Hansen, R. J., "The Response of Shear Walls to Dynamic Loads," MIT Department of Civil and Sanitary Engineering, (DASA - 1160), Cambridge, Mass. , August 1960, 290 pp.

26. Bresler, B. and MacGregor, J. G., "Review of Concrete Beams Failing in Shear," Proceedings, ASCE, V. 93, No. ST1, February 1967, pp. 343-372.

131


shear walls


27. Kani, G. N. J., "How Safe are Our Large Reinforced Concrete Beams?" ACI Journal, Proceedings, V. 64, No. 3, March 1967, pp. 128-141.

28. Hognestad, E., Hanson, N. W., Kriz, L. B., and Kurvits, 0. A., ''Facilities and Test Methods of PCA Structural Laboratory," Journal of the Portland Cement Association, Research and Development Laboratories, V. 1, No. 1, pp. 12-20 and 40-44, 1959; V. 1, No. 2, pp. 30-37, 1959; V. 1, No. 3, pp. 35-41; PCA Development Bulletin D33.

29. Hanson, N. W., Hsu, T. T. C., Kurvits, 0. A., and Mattock, A. H., "Facilities and Test Methods of PCA Structural Laboratory -Improvements 1960-65," Journal of the Portland Cement Association, Research and Development Laboratories, V. 3, No. 2, pp. 27-31, May 1961; V. 7, No. 1, pp. 2-9, January 1965; and V. 7, No. 2, pp. 24-38, May 1965; PCA Development Bulletin D91.

PCA R/0 Ser. 1498

132


concrete structures

to latera I forces

APPENDIX A

DETAILS OF TEST SPECIMENS

This appendix describes the fabrication, instrumentation and testing of six shear wall specimens. Methods and procedures employed were those normally used at the PCA Structural Laboratory ( 28, 29).

Fabrication

Because of the relatively large size of the specimens, 28 ft. 9 in. (8. 76 m) by 6ft. 3 in. (1.91 m), and the small thickness, 3 in. (7. 5 em), all specimens were cast in a horizontal position. This procedure facilitated both the manufacture of formwork and placement of reinforcement and concrete.

Figure A1 shows one of the specimens before casting. The formwork consisted of a double 3/4 -in. plywood base supported on 2x4 and 2x6 stringers. The stringers were supported on 2x4 vertical struts properly braced. The height of the struts was selected to accommodate a tilt-up assembly underneath the double 3/4-in. plywood base.

Reinforcement conforming to ASTM Designation: A-615-68, Grade 60 (4200 kgf/cm2 ) deformed bars and annealed deformed wire was used in all specimens. The deformed bars were used as flexural (vertical) reinforcement and the annealed wire as shear (horizontal) reinforcement. Deformed bar sizes were No. 4 and No. 5. Measured yield stresses for specific groups of bars used in each specimen are listed in Table 1.

The D4 (A = 0. 04 sq. in. == 0. 26 sq. em) deformed wire reinforcement used conformed\o ASTM Designation: A-496-64. Because of the relatively high yield stress of the wire, it was necessary to anneal it to obtain a yield stress of about 60 ksi. Results of trial runs in the laboratory indicated that annealing the wire at 1100° F for one hour would provide the characteristics needed. Based on these results, all deformed wire reinforcement was commercially annealed at 1100° F in a gas-fired furnace for a period of one hour.

Yield stresses obtained for individual groups of reinforcement are listed in Table 1. Figure A2 shows representative stress-strain curves for both the deformed bars and deformed wire reinforcement used in all specimens.

The normal weight concrete used was made with a blend of Type I cement and 3/4-in. maximum size Elgin aggregate. Design cylinder compressive strength at test age, usually 10 days, was 6000 psi (420 kgf/cm2 ). Measured concrete strengths are listed in Table 1 in the text. Concrete quality control was based on a measured slump of 3 ± 1 in. All specimens were cured under polyethylene sheets for a period of 3 days.

Instrumentation

133


shear walls


Reinforcing bars were instrumented with electrical resistance strain gages. Vertical bars were instrumented at a section near the base of the wall and also at a section a distance tw from the base of the wall. Instrumented ver-tical bars permitted measurement of the strain distribution along the wall at these two sections. Several horizontal bars placed within a height Jw from base of the wall were also instrumented. These gages provided an indication of the strains produced by the shear deformations.

Gages were also placed on the concrete surface. These gages were located near the base of the wall and at the extreme tension and compression fibers. other gages were placed at mid-length of the wall.

Rotations near the base of the wall were measured with LVDT1 s placed near the extreme tension and compression fibers of the specimens. The LVDT1 s were connected to directly measure angle changes. Gage lengths for measured average rotations were 40-in. (1. 00 m) for the 21-ft. (6. 40m) high walls and 12-in. (30 em) for the 12-ft. (3, 66 m) high walls.

Lateral deflections of all specimens were measured at 3 ft. (91 em) or 18-in. (45 em) intervals from the base of the wall. Graduated scales were read with a precision level (28) that has an optical micrometer reading to 0. 001 in. Out-of-plane deflections were measured near the cantilever end of the wall using mechanical dial gages reading to 0. 001 inches.

Applied axial and lateral loads were measured with load cells. Reactions at the restraining portion of the specimens were also measured with load cells. All of this instrumentation was connected to continuous oscillographic recorders or strain indicator boxes as required. Figure A3 shows some of the locations where instrumentation was used in the specimens.

Test Procedure

After the specimens were set in the test rig, readings were taken to assess the effects of dead weight and loading equipment. The axial compression force was then applied in increments. At the end of each increment, outof-plane deflections were checked. When necessary, adjustments were made in the position of the hydraulic rams to insure that no large out-ofplane deflections occurred.

After the full axial load was applied, lateral load was applied by hydraulic rams. The number of increments of lateral load to obtain failure was usually between 10 and 15. After each increment, all instrumentation was read and cracks were marked and recorded. In addition, load versus deflection and load versus maximum compressive strain were continuously monitored on X-Y recorders throughout the test.

134


concrete structures

to latera I forces

APPENDIX B

EQUATIONS FOR FLEXURAL STRENGTH

As a part of this investigation, a simple equation to calculate the flexural strength of rectangular shear walls with uniformly distributed vertical reinforcement was developed. The solution is developed in accordance with Section 10 .. 2, Assumptions, of ACI 318-71 (1).

Figure B1(a) shows the cross section of a rectangular shear wall subjected to combined bending and axial load. The total area of reinforcement, A , is assumed to be a continuous line of steel albng the fulll€mqth of the wa11. The assumed strain distribution at ultimate is shown in Fig. B1(b). This distribution implies that the load producing failure is smaller than that at balanced failure conditions.

From equilibrium of forces as shown in Figs. B1(c) and Bl(d):

pifl (tw - c (1 + /3)] ~ + Nu == 0, 85 f~ {31hc + pJlc (1- {3) fy , .... (1)

where

Pv As/twh

h thickness of shear wall, in.

tw depth or horizontal length of shear wall, in. c == distance from extreme compression fiber to neutral axis, in.

f3 ey~o.003

fy specified yield strength of reinforcement, psi

Nu design axial load at section, positive if compression, lbs.

f~ == specified compressive strength of concrete, psi

f31 a factor defined in Section 10. 2. 7, ACI 318-71

From Eq. (1) the distance from the extreme compression fiber to the neutral axis, c, becomes:

where

c r w

w+a ..... (2) 2 w + 0. 85{31

and

w

Nu 01 =:

J.w hf~

135


shear walls


•••• (3)

.... (4)

The ultimate resisting moment, Mu, of the cross section becomes:

[ ( Nu ) (1 {31 c ) c2 - {! 'J Mu == Asfytw 1 + AI "2' - IT - T \ 1 + 3 - (31 ) s y w w

..... (5)

Equation (5) can be approximated, without significant loss of accuracy, by -eliminating the terms containing c2 I t:V and dropping (31 • Equation ( 5) then reduces to:

.... (6)

Figure B2 shows a comparison of results using Eqs. (5) and (6) for different amounts of uniformly distributed flexural reinforcement. Two values of axial compressive load are plotted: Nu == 0 and Nu == 0. 25 f~ J.wh. The re-sults show that for the case of pure bending, N == 0, the approximate Eq. (6) compares very well with the results of the fAore exact Eq. (5).

The above derivations are limited to rectangular shear walls with uniformly distributed reinforcement and subjected to an axial load smaller than that producing balanced flexural failure. In practice the magnitude of the axial compression load is almost always smaller than Nu == 0. 25 f~ i.wh. Since Eq. (5) is applicable up to Nu == 0. 425 {31 f~ J.wh, the proposed flexural strength equations should apply to most rectangular shear walls found in practice. Similar equations can be derived for different shear wall cross sections and for distributions of vertical reinforcement other than uniform.

136


concrete structures

to lateral forces

c

d

f

~ f' c

~ h

s

APPENDIX C

NOTATION

total area of vertical reinforcement at section, sq. in.

area of horizontal shear reinforcement within a distance, s, sq. in.

distance from extreme compression fiber to neutral axis, in.

distance from extreme compression fiber to resultant of tension force, in.

story shear forces, lbs.

square root of specified compressive strength of concrete, psi

specified compressive strength of concrete, psi

specified yield strength of reinforcement, psi

thickness of shear wall, in.

total height of wall from its base to its top, in.

== depth or horizontal length of shear wall, in.

== design resisting moment at section, in. -lbs.

axial stress at the point of contraflexure

design axial load at section, positive if compression, lbs.

Af/J-hf' s y w c

vertical spacing of horizontal shear reinforcement, in.

nominal permissible shear stress carried by concrete, psi

nominal total design shear stress, psi

shear force at the point of contraflexure, lbs.

total applied design shear force at section, lbs.

N jJ. h f' u w c f.y/0.003

(31

137


shear walls


fraction defining location of the neutral axis, (Section 10. 2. 7, ACI 318-71)

capacity reduction factor (Section 9. 2, ACI 318-71)

== Av/sh

A/.ewh

curvature at ultimate load

curvature at yield load

TABLE 1 -Dimensions and Material Properties of Test Specimens

Concrete Reinforcement Compressive Tensile Vertical Horizontal

Mark Height Strength* Splitting Amount Yield Amount Yield Axial Strength* Stress Stress Stress

~ f' f~p p ** f ph fy Nu/i.wh c v y

ft. psi psi psi psi

'ENJ-1 21.0 7420 660 0.0027 60,200 0.0027 61,300 'ENJ-2 21.0 6880 650 0.0100 65,400 0.0027 61,000 fNV-3 21.0 6780 615 0. 0300 66,080 0.0027 60,000 fJVJ -4 12.0 6740 585 0. 0300 60,000 0.0027 60,000 fNV-5 12.0 5900 565 0.0230+ 60,000 0.0027 60,000 fNV-6 21.0 5950 590 0.0230+ 63,000 0.0027 70,000

-----·-

* Taken as the average of 3 or more concrete cylinders in critical area. A

** flv = .e:h , where As= total area of vertical reinforcement, Lw = 75 in.

h = 3 in.

+ One-third of total vertical reinforcement concentrated within a distance Lw/10 from either extremity of cross-section (amount of reinforcement

in interior region P vw = 0. 01).

(1ft. = 0. 305 m; 1 psi = 0. 07 kgf/cma)

psi

415 430 420 430 425 430

-w 00

@ en "'0 0 :::::1 en CD ..... 0 ii) ..... CD ..... Ill

d' ..... n CD en

TABLE 2- Test Results

Calculated Flexural Strength Shear Streng'.'>.

I Para.."!leters

Moment Ca!cu- Measured

Calculated* Measured lated * * CaiculateC! Mark to Shear Ratio Measured Calculated ' ..... Mo;,ent ! s:~ear at Ratio dftw Moment,~~ Moment, 1\, ~+ Shear, vu' : ~ vc + vs Observed

M/Vu at the tw/2 Mode of at at base at base at tw/2, hd.Jf' .jf~ Base from Failure

at £w/2 ultimate . c

Base from Base kip-ft. kip-ft. kip-ft. kips :

SW-1 2. Otw 0. 58 406 379 356 26.5 1.7 3.9

I 1.07 ! 0.44 Flexure

SW-2 ~:g!w 0.62 675 650 609 41.4 2.8 4.0 1. 04 0. 70 Flexure SW-3 0. 71 1073 1200 1181 66.0 4. 5 4. 0 0. 90 1. 13 Flexure -Shear SW-4 l.Otw 0.71 1077 1139 1108 108.6 7.4

6. 6 I 0. 95 1. 12 Flexure SW-5 1.0£w 0. 78 1078 1121 - 108.6 7.8 6.8 0. 96 1. 15 FleX"Jre-Shear SW-6 2.0~ 0. 78 1179 1154 - 72.5 5.3 4.4 1. 02 ! 1. 20 Flexu.re

L_____ ---- L-- -·

• Based on compressive concrete limiting strain of 0. 003, strain compatibility and measured material properties including strai."l harderJng of steel. Calculated from ACI 318-71 Code shear strength equations.

+ According to Eq. (1).

++ d used is 0. Btw or greater.

(1 kip-ft. = 0.138 ton-m; 1 kip= 0. 453 ton; ~psi = 0. 265 .jf~ kg:f/cm•)

~ -. (!) ::::'1

(C ..... :::r 0 -(/) :::r gJ

~ ;;;

.... w c.c

140 response to lateral forces

TABLE 3 -Moment-Curvature Test Results

Measured Calculated

1/Ju M 1/Ju 1/Ju u M 1/Ju u Mark Millionths/in. My 1/J; Million ths/in. My lp y

SW-1 223 1. 13 7.0 186 1. 17 4.8 SW-2 116 1. 37 3.6 143 1. 48 4. 1 SW-3 94 1. 29 1.8 103 1. 43 2. 5 SW-4 190 1. 35 2. 5 117 1. 42 2.7 SW-5 225 1. 18 3.3 133 1. 30 3.4 SW-6 186 1. 31 3. 9 120 1.28 3. 1

1 millionth/in. = 0. 4 millionths/em

strength of shear wa lis

Frome Shear Wall _,r----/'----,~

_.r-----~----~.

(a) Loads

141

(b) Frome (c) Shear Wall

Fig. 1. Interaction between frame and shear wall

v\17~ N

(a) Shear Diagram (b) Moment Diagram (c) Forces on Lower Portion

Fig. 2. Forces acting on a high-rise shear wall

142

Post-tensioning representing gravity load

a) Dimensions: Plan View

Arrangement for lateral loads b) Test Setup: Elevation

response to lateral forces

Area

Fig. 3. Shear wall specimen: dimensions and test setup

Fig. 4. Test setup for shear wall investigation

strength of shear walls

tw=75"

~h=3"

fJv =A 8 /\wh

(a) Uniform

60" ~As

(b) Concentrated

Fig. 5. Distribution of vertical reinforcement in test specimens

Curvature, ojl, percent

Fig. 6. Moment-curvature relationships for rectangular shear walls

143

144

1200

1000

800

Moment,M, 600 percent

0

I I I I

p =0.5% v

I I I I \ \ \ \ \

\


r lw=25h

1 fiji

=fO.Itw

__...10.25%

0.8tw

JOI~

~=0.003 u c

Cross Section

Strain Distribution at Ultimate

',~Limiting curvatures

' ....... ....... ---60 80 100

Curvature, ojl, percent

Fig. 7. Effect of reinforcement distribution on moment-curvature

Moment,M, k.-ft.

0 50 100

SW-6

150 200

Average curvature over a 40-in gage length,oj!, millionths/in.

I kip-ft.= 0.138 Ton-m ; I millionth I in. = 0.4 millionth /em.

Fig. 8. Measured moment-curvature relationships

strength of shear walls 145

Moment,M, k.-ft.

1200r----r---,r---.----,----,----,,---.---~--~

0 50 100 150 200 Average curvature over a 12-in. gage length, 1/l,millionths

Fig. 9· Measured moment-curvature relationships

Fig. 10. Failure by fracture of the reinforcement


Fig. 11. Failure by crushing of the concrete

I \

strength of shear walls

Fig. 12. Flexure-shear failure

Moment, M

My

'/lu Curvature, '/1

Fig. 13. Energy absorption of shear walls

't ~JJ ~~

147


Fig. Al. Shear wall before casting

Stress,

ksi

100.---------------------------------------~

Annealed Wire 80

60 Deformed Bars

40

00~----------~~------------~----------~ 0.01 0.02 0.03

Strain

Fig. A2. Reinforcement stress-strain relationships

strength of shear walls 149

. ~

150

lw

~ (a) Cross

Section

0.003

H ~

(b) Strain Distribution; f!y

.B=o:oo3

c


I ,8 ,c __!_

0.851~

H

(c) Concrete Stress Distribution

and Axial Load

fy

H

71 y

(d) Steel Stress

Distribution

Fig. Bl. Assumptions at flexural strength of rectangular shear walls

Flexural 51 rength,

A8 fy\w

2.0

1.0

0

I I I I I I I I I I I I I I \

' ' \ \

fy= 60,000psi (4219kgf/cm 2 )

f~= 4,000 psi (281 kgf/cmZ)

\ '\ Eq.(5)

Eq.(6)~',,.,. -c. Eq.(5) " ..... ..,.:::=:-------------.~---"T---=------======a =0.25 7 a=O

Eq.{6)

1.0 2.0 3.0 Amount of Uniformly Distributed Vertical Reinforcemenl,p, percent

Fig. B2. Flexural strength of rectangular shear walls

paper sp36-7 strength of high-rise shear walls

Documents