Equivalent Frame Method Applied to Concrete Shear Walls by Angelo Mattacchione

5/12/2018 Equivalent Frame Method Applied to Concrete Shear Walls by Angelo Mattacchione

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E q u iv a le n t F ra m eM eth o d A p p lie d toC o n cre te S h ea rw a lls

uildings t hat incorporateconcrete shearwalls as struc-tural elements to resist bothvertical and lateral loads arecommonplace. Shear wall and cou-

pled shearwall structures have beenfound to be economical up to the.30

tion to their stiffness. The methodtakes into consideration the contri-bution made to the shearwalls bythe bending and shear in connectingbeams. It is a hand method that inits pure form is tedious, but graph-ical methods proposed by research-

quickly becomes time conand complex as the sizestructure increases. Like thanalyzing a structure in matris ideally suited to the digiputer. The matrix method osis is less computation in


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. t l J L ' I 2 ' I I M 1 J-~ !Lr :. b 1 - L2 l'

Fig. 1 - Coupled shearwall subject to horizontalloadi.ngwith equivalent frame superimposed."

Ai, II ----+-+------,.. t~: . . 1 . .

EquivalentFrame

O utli n e o f c ou pl e ds he ar w a II ( d e fie cle ds ha pe u nd er la te ra l 1 0a d)

- - - ,~..~..

_ _ _ _ _ _ _ _ _ _ _. ~ t: :

Fig. 2- Coupled shearwall and concrete frameequivalent frame superimposed


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H-I-H--+-+-+-H~IL ~o_S,-++-+-+-H-+-H-++--f-++-+--H,1-t---t-t--:J,-=I-++--1-++--J,-"F-.O,75+-r-+-+-+-+-~-+--t-I-++-f---+-l

V 1,OO'++-+-++-r--t-+-r-+A-+-H-+-I-t:t-'9+H--+-t-7++-++-l-+l,2S++-e-++--1-1H-I-H-----J,...f4--H-I-H=*"'F++-H--f::".!~~'


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including the connecting elements,interaction with frames, supportcondi tions, symmetry, to rsion, andvarying opening widths.Connecting elementsWhere the connecting elements incoupled shearwalls are well definedbeams, the section properties of thebeams are as discussed previously.But in many residential buildingsand hotels, the flat concrete floorslabs are the connecting elements.The interactiort that occurs betweencoupled shearwalls depends on thebending stiffness of the connectingelements. In the case of flat slabs,the depth of the connecting ele-ments is merely the floor slab thick-ness, but the width is not quite asobvious.An assessment made bySchwaighofer on a system com-prised of two 21.3 ft (6.50 m) wideby 194.4 ft (59.25 m) high concrete

shearwalls spaced 5.3 ft (1.63 rn)apart, and connected by 8 in. (203mm) thick concrete floor slabsshowed little difference in shearwallinteraction when using a slab width

era! investigation'S with respect toslab widths. This comparisonshowed effective widths varyingfrom 20 percent of the slab width togreater than the full slab width (Fig.4)9. In 1988 Ca no and Klingnercompared different analysis proce-dure for two way slabs, which in-cluded the effective Width method(Khan and Sbarounis), the ACIequivalent frame method, and theextended equivalent column andslab methods (Vanderbilt). 10 The re-sults ftom the various analyses werecompared to test results from asmall scale multistory flat plate. testspecimen prepared by the NationalResearch Council of Canada.Fat lateral drift, the effectivewidth method provided the mostaccurate results, with the othermethods giving similar results, butover estimating the drift. Thus, likethe effective slab width in coupledshearwalls, the determination of aneffective slab width far frames isleft to the discretion of the engi-neer.Support conditions

to model inclined rollerspring supports, and supstrained partially againstIn the event that an enginnot have access to such athese support conditions casonably approximated .1clined faller can be modeleshort, stiff, pin-ended meclined at the required angleSpring supports (used tospecific soil conditions forcan be modeled with pimembers whose propertiesmate thespring constant(Fig. 6). Partial rotational(somewhere between a fixpinned condition) can bsented with an element pelar to the actual member ttially restrained, with propeproximating the degree of(Fig. 7).SymmetryThe engineer can take advabuildings that possess a sstructural layout by appothe lateral forces to all sand frame bents in a sing


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r--- S tru ct ure b ein gsupported

Shor t , stiff ( la rg e a re a )p in ende d m em ber slopeda t a ng le to simulatein c ll n e d roller

Clockwise from above left:

Fig. 8 ~ Lateral force distribution between ele-ments (for symmetric plan layouts, distribution 01lateral loads can be achieved in a single opera-tion by linking elements.)

Fig.5 - Model for inclined roller."Fig.6 - Model for spring supports."

Fig.7 - Model for spring supports."E LE VA TIO N O F EQU IV AL EN T F R AM E S

:\

S h o o.p i n e niri


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SvmmetryUney ,W/2

~. i ~]I , Ll,2 , I , L2.3,

Only half of frameis analyzed

Roller supports restrainingvertical movement are addedat each f lo o r_< - : S;".-~

A b~ ,4 ~ A b2,3! A b4,S ~Abl,2:------lii3;;f~-Ib2;3 -----i---lii4;5;'lf.-i;i:

- -- - -, c ,; j T - - - -- - .- - - -- - .- - .- - - -.c: 0;


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shear at a given level is the alge-braic sum of the story shears fromthe column above and below thefloor. The. final second order deflec-tions are calculated from the firstorder deflections as follows:

1 - .r ,PI1i1Hhwherer,P = cumulative vertical loadf).i = first order story swayh = story heightH = horizontal shear The additional story shears areadded to the applied loads, and thestructure is re-analyzed (first orderanalysis), using the new lateral

Symme,rytineX

Movernen l iny directionrestrained .

D l r e c t i C l f l

Fig. 11 - Symmetry lor 3D frame.'

. . . . . . . . . . _Symmetry

t.tne

; X "Moy d,---~ __re:s

,.------- Moz dres

structure, It can also be used in the


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4. Glanville, John I., and Hatzinikolas,Michael A., "Engineered Masonry Design,"Winston House Enterprises, Winnipeg, Can"ada, 1989, p. 160.5. Hall, A.S~, An Introduction to the Me-

chanic, of Solid" John Wiley & Sons Aus-tralasia Pry Ltd, Sydney, Australia, 1969, pp.116-124.6. Schwaighofer , Joseph, "Shearwall

Structures." Structural Concrete Sympo-sium, University of Toronto Department ofCivil Engineering & Port land Cement Asso-ciation., Toronto, Canada, May 1'3&14,1971, pp. 118-145 ..7. Taranath, Bungale S., Structural Anal-

ysis and Design of Tall Buildings, McGraw-Hill Book Company, New York, 1988, pp.491-535, 675-686.8. Khan, Fazlur R., Sbarouuis, John A.,

"I uteraction 0r Shea [walls and Frames,"Journal of the Structural Division, ASCE, V.90, SD, June 1964,pp. 285-335.9. Vanderbilt, M. Daniel, and Corley, W.

Gene, "Frame Analysis of Concrete Build-ings," Concrete International: Design &Cons/ruction, V. 5, No. 12, Dec. 1983, pp.33-43.10. Cano , Mary Theresa, and Klingrier,

Richard E,., "Comparison of Analysis Pro-cedures for Two Way Slabs," AC! Struc-tural Journal, V. 85, No.6, Nov.-Deo. 1988,pp, 597~608.11. LUlZ, Leroy A., "Computer-Aided

Analysis and Design," Building Structural

Desing Handbook, Richard N. White andCharles O. Salmon, editors, John Wiley &Sons, New York, 1987, pp. 530-541.12. MacLeod, lain A., "Shearwall-Frarne

Interaction: A Design Aid," EngineeringBulletin, Portland Cement Association, Sko-kie, 1970, 17 pp,13. ACI Committee 318, "Building Code

Requirements for Reinforced Concrete (AC]318-89) and Commentary - (AG 318R-89),"American Concrete Institute. Detroit 1989,pp.117-129.14,. Coull, Alexander, and Choudhury, J.

R., "Stresses and Deflections in CoupledShearwalls,!' ACI JOURNAL, Proceedings, V.64, No.2, Feb. 1967, pp. 65c72.15. Coull, Alexander, and Choudhury,

J. R., "Analysis of Coupled Shearwalls ,"ACI JOURNAL, Proceedings, V. 64, No.9,Sept. 1967, pp. 587-593.16. Coull, A., and EI Hag, A. A., "Effec-live Coupling of Shearwalls by Fl00r Slabs,"ACI JOURNAL, Proceedings, V. 72, No.8,Aug. 1975, pp, 429-431.17. Duchesne, D, P. J., and Humar, J, L.,

"Erigi neeri ng So ftware - a Consul ta nt'sPerspective.' Canadian Journal oj Civil En-gineering, V.IS, Apr. 1991, pp. 303-311,18. Falk, Howard, "Microcomputer son-

ware for Concrete Structural Design," Con-crete lruernationai: Design & Construction,V. 7, No.6, June 1985, pp. 49-56.19. Khan, A.H .. and Stafford Smith, B.,

"Simplified Method of Analysis for Deflec-

lions and Stresses in Wall- Frlures." Buildirig and EnvironmenNo. I,1976, pp. 69-78.20. Kong, F.K., et al, Editor",oj Structural Concrete, Pitman

ited, London, 1983, pp. 31-1 to21. Schwaighofer , Joseph, a

Michael P. "Experlmernal Sludyhavior 0r Rein fo reed ConcreteSlabs," ACI JOURNAL, ProceedinNo.3, Mar. 1977, pp. 123-127.22. Weaver, William Jr. , and

M., "Matrix Analysis of Framlures," 3rd Edition, Van Nostrhold, New York, 1990.

Received and reviewed under J nscation policies.

ACI. member A n-gelo Mattac-chione is Presi-dent of Prosum En-gineering l.td., ast r uc tu raI oonsu It-ingfirmin NorthYork, Ontario. Hehas been active inthe design of numerous strutimber, structural steel,forced and post-tensioned c

Equivalent Frame Method Applied to Concrete Shear Walls by Angelo Mattacchione

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