CALCULATION ON DEFORMATION RATIO OF SHEAR TO BENDING FOR

Transcription

1 CLCULTON ON DEFORMTON RTO OF SHER TO BENDNG FOR STEEL RENFORCED CONCRETE SPECL-SHPED COLUMNS Liu Yi, Xue Jianyang, Zao Hongtie, Cen Zongping 3 Candidate for P.D., Sool of Civil Engineering, Xi an University of riteture and Tenology, Xi an Cina Professor, Sool of Civil Engineering, Xi an University of riteture and Tenology, Xi an, Cina 3 ssoiate Professor, College of Civil and ritetural Engineering, Guangxi University, Nanning, Cina liuyi_zzp@6.om BSTRCT: Elasti stiffness sould e alulated wile developing a restoring fore model of steel reinfored onrete (SRC) speial-saped olumn. Weter it is needed to tae te sear deformation into aount due to te irregular setion of speially-saped olumns and its small sear span ratio was seldom studied in te literature. To tis end, it is studied teoretially ased on te meani model wi an simulate real engineering using te lassial meani teory. Te results sow tat wile te sear span ratio is equal to, sear deformation is aout 3%~5% of total deformation. Wile te sear span ratio is equal to.5, te ratio is %~3%. Wile te sear span ratio is equal to.5, te ratio is more tan%. KEYWORDS: steel reinfored onrete, speial-saped olumns, spring stiffness, sear deformation. NTRODUCTON Steel reinfored onrete (SRC) speial-saped olumn is a new-type speial-saped olumn, wi mainly ontains steel wit rigt amount longitudinal ars and stirrups in simple speial-saped setion (L, T, + sape) [Cen Z.P., Zang X.D. (6) ]. For one side, it eeps some advantages of ordinary speial-saped olumn, su as no orner angle, nie-looing, pratial and inreasing te real using areas; for anoter side, it inerits te advantages of SRC struture, su as ig earing apaity, good seismi eavior and deformaility[zao H.T.()]. t is an effetive approa using SRC speial-saped olumn to overome te weaness of ordinary speial-saped olumn wose earing apaity is not ig and seismi eavior is not good[cen Z.P., Zao H.T. (6) ]. n order to study te wole proess reation and failure meanism of te frame onstrution wit SRC speial-saped olumn under eartquae ation, te restoring model of SRC speial-saped olumn must e determined, and te auray of analysis result of seismi response depends on te preision of te restoring model to a ertain degree. Wile SRC speial-saped olumn restoring model is estalised, te alulation of elasti stiffness must e referred to[si J.(), Xue J.Y.()]. Beause te speial-saped olumn is not regular in setion, weter te searing deformation needs to e onsidered or not wile alulating elasti stiffness, it is still a gap to now at ome and aroad. n view of tis, tis paper does some wor in teory for te first time, and offers some important referene data for te estalisment of SRC speial-saped olumn restoring model.

2 . CLCULTON THEORY ON DEFORMTON RTO OF SHER TO BENDNG FOR SRC SPECL-SHPED COLUMNS Te deformation of SRC speial-saped olumn inludes ending, searing and axial deformation under external load. Te axial deformation is very small, generally an e ignored. nd te searing deformation is also very small and an e ignored too, wi is mentioned in lassial material meanis[timoseno S.(978)] wen te ratio of sear span is large omparatively. s te speial-saped olumn is mainly applied to te residential uildings, te eigt of floor is not large generally, and te SRC speial-saped olumn s leg as te arateristi of long and narrow terefore te ratio of sear span is not large. So weter te searing deformation needs to e onsidered or not, in view of tis, it is neessary to arry on te deep resear in teory. Supposing te infletion point is at te middle of te span for te SRC speial-saped olumn wose lengt isl and te following formula an e otained. Searing deformation: Pl δ s = (.) G Were, G is sear stiffness; P is transverse sear fore; l is te lengt of olumn; is te nonuniform oeffiient of sear stress distriuting along te setion. = Were, = te setion area; =te moment of inertia; = te setion widt of te loation were sear stress is requested; S =te area moment to te neutral axis Z of te setion aove or elow te loation requested (Fig. ). S d d (.) z Fig. sape of ross setion Flexural deformation: 3 Pl δ = (.3) E Were, E = flexural stiffness; te oter symols ave te same meaning as aove. Te equation (.) Compare wit (.3): n order to alulate onveniently it an e simplified as te following: δ ( E) = S = (.4) δ ( G) l

3 E G E = β (.5) For te speial-saped olumn wit inds of layout steel te value ofβanges from.3 to., wile te steel ratio varies from 3% to 5%; aording to te alulation results and referring to te Japan Code, te stiffness of steel setion is less tan te stiffness of reinfored onrete setion for te ordinary SRC struture, so it an e approximately onsidered as te following: G E E (.6) G G E Were, = ( + μ), μ is Poisson ratio, and usually it is. for onrete. G Troug te formula (.), (.3), (.6), te following equation an e otained: Were, ξ = δ s 8.8ξ = = (.7) δ l S d ; Oter symols ave te same meaning as aove. 3. CLCULTON METHOD ON DEFORMTON RTO OF SHER TO BENDNG FOR SRC SPECL-SHPED COLUMNS Beause speial-saped olumn setion is not regular, ot te nonuniform oeffiient of sear stress and te moment of inertia are related to loading diretion. n atual onstrution, te struture wit speial-saped olumn may suffer from every diretion s ation. n tis paper it is mainly researed along engineering axis, 45 and 35 diretion, and every speial-saped olumn s leg as te same eigt, as Fig. sows. For L and + setion only one situation ((), (4) in Fig.) an e onsidered eause of symmetry wen loading along engineering axis diretion. For T setion two situations an e onsidered along wing (() in Fig.) and we ((3) in Fig.). Wen loading along 45 diretion only one situation ((5), (6), (7) in Fig.) of +, T and L setion an e onsider. Te numer (8) is only for L sape along 35 diretion. () () (3) (4) (5) (6) (7) (8) Fig. Te setion of speial saped olumns and te loading diretion

4 Tae + sape setion as an example for te situation of loading along engineering axis diretion, as Fig.3 sows. Wen / y /, Wen y /, / / z = y dy, ξ = {( / y) [ y + / ( / y)]} dy / / / z = y dy ξ = {/ ( ) [ / + / 4( )] + ( / y)[ y + / ( / y)]} dy / = ( + ) (3.) z z z ξ = ( ξ + ξ ) (3.) l = λ (3.3) Were, λ = ratio of sear span; = effetive dept of setion; y y y dy dy y z z (a) () Fig.3 Te figure of omputation Taing equation (3.), (3.), (3.3) into (.7), te ratio of searing deformation to ending deformation an e alulated. Similarly, oter setions loading along te engineering axis diretion an e alulated. 4. NLYSS OF THE CLCULTON RESULTS n tis paper, all speial-saped olumns ave te same setion eigt of olumn leg; mm and 4mm ommonly used in atual projet are osen as te setion tiness of olumn leg. nd.,.5, 3., 3.5 and 4. are osen as te ratio of setion eigt to setion tiness of olumn leg;.,.5,. and.5 are osen as te ratio of sear span λ. Te alulation results are sown in Tale to Tale6. Te alulation results is totally te same for L sape olumn loading along te engineering axis diretion and for T sape olumn loading along

5 te we diretion, tey sare te Tale togeter. Similarly, Te alulation results is also te same for + sape olumn loading along te engineering axis diretion and for T sape olumn loading along te flange diretion, tey sare te Tale togeter. Fig.4 to Fig.9 sow te relationsip among te deformale ratio of sear and ending, ratio of sear span and ratio of setion eigt to setion tiness of olumn leg for L sape wit mm setion tiness loading along te diretion of engineering axis, 45 and 35. Tale te ratio of deformation of sear and ending in T sape loading along te flange (m) / ( - m 4 ) λ =. λ =.5 λ =. λ =.5 λ = Tale te ratio of deformation of sear and ending in T sape loading along te we (m) / ( - m 4 ) λ =. λ =.5 λ =. λ =.5 λ = Tale 3 te ratio of deformation of sear and ending in L sape loading along te diretion of 45 (m) / ( - m 4 ) λ =. λ =.5 λ =. λ =.5 λ = Tale 4 te ratio of deformation of sear and ending in L sape loading along te diretion of 35 (m) / ( - m 4 ) λ =. λ =.5 λ =. λ =.5 λ =

6 Tale 5 te ratio of deformation of sear and ending in T sape loading along te diretion of 45 (m) / ( - m 4 ) λ =. λ =.5 λ =. λ =.5 λ = Tale 6 te ratio of deformation of sear and ending in ross sape loading along te diretion of 45 (m) / ( - m 4 ) λ =. λ =.5 λ =. λ =.5 λ = λ=. λ=. λ=.5 λ=3. / λ=. λ=. λ=.5 λ=3. / Fig.4 T olumn deformation ration loading in flange Fig.5 T olumn deformation ration loading in we λ=. λ=. λ=.5 λ=3. / λ=. λ=. λ=.5 λ=3. / Fig.6 L olumn deformation ration loading in 45 Fig.7 L olumn deformation ration loading in λ=. λ=. λ=.5 λ=3. / λ=. λ=. λ=.5 3 / Fig.8 T olumn deformation ration loading in 45 Fig.9 + olumn deformation ration loading in 45

7 From Tale and Tale, nonuniform oeffiient of sear stress is influened largely y setion type and loading diretion. Te value of is relatively small for T setion loaded along te flange and + setions loaded along te engineering axis; and te value of is relatively large for T setion loaded along te we and L setions loaded along te engineering axis. ording to douments, for te first situation, te maximum searing stress in setion redue (ompared wit retangular setion under te same situation) eause of te existene of flange, and namely searing stress in setion is distriuted uniformly, so te value of is smaller. For te seond situation, te existene of flange doesn t play a orresponding role, so te value of is larger. From te Tale3 and Tale4, for L setion loaded along 45 and 35 diretion te value of is relatively small. From Tale to Tale6, for te same setion and loaded along te same diretion, te deformation ratio inreases as te value of inreases; from Fig.4 to Fig.9 te deformation ratio dereases and urves ange slowly as te sear span ratio inreases. From Tale and Fig.4, for T setion loaded along te flange and + setion loaded along engineering axis, wen sear span is, te deformation ratio is nearly.5, namely te sear deformation aount for /3 of te total deformation; wen sear span ratio is.5, it is nearly /6; and deformation ratio as te tendeny of derease in te eginning ten inrease later as te ratio of setion eigt to setion tiness of olumn leg inreases. From Tale and Fig.5, for T setion loaded along te we and L setion loaded along te engineering axis diretion, wen sear span ratio is, te deformation ratio is more tan.7, and espeial wen te ratio of olumn leg eigt to olumn leg tiness is more tan 3, te deformation ratio varies from.9 to., namely te searing deformation aounts for / of te total deformation; wen sear span ratio is.5, te deformation ratio is.4 and te sear deformation an t e negleted; in addition, te deformation ratio inreases as te ratio of olumn leg eigt to olumn leg tiness inreases. From Tale3 and Fig.6, for L setion loaded along 45 diretion te deformation ratio redues as te ratio of olumn leg eigt to olumn leg tiness inreases; wen sear span ratio is, te deformation ratio is te largest approaing to.4. From Tale4 and Fig.7, te deformation ratio inreases as te ratio of olumn leg eigt to olumn leg tiness inreases for L setion loaded along 35 diretion. Wen sear span ratio is, te deformation ratio exeeds.8 and namely te searing deformation aounts for / of te total deformation; wen sear span ratio is.5, te average of deformation ratio is.44, and namely sear deformation aounts for /3 of te total deformation, wi an t e negleted. From Tale5 and Fig.8, te deformation ratio inreases in te eginning te dereases later as te ratio of olumn leg eigt to olumn leg tiness inreases for T setion loaded along 45 diretion; wen ratio of olumn leg eigt to olumn leg tiness., te deformation ratio is approaing.8. From Tale6 and Fig.9, te deformation ratio dereases as te ratio of olumn leg eigt to olumn leg tiness inreases for + setion loaded along te 45 diretion; wen sear span is. and ratio of olumn leg eigt to olumn leg tiness., te deformation ratio exeeds..

8 5. CONCLUSON Troug te teoretial analysis, te nonuniform oeffiient of sear stress and deformation ratio under different sear span ratio are alulated, and te following onlusions an e otained. () Te value of dereases eause of te existene of we wen loading along engineering axis diretion and sear stress distriute uniformly. () Te value of is small relatively for L sape setion loaded along 45 and 35 diretion; and it is large relatively for T and + sape setion loaded along 45 and 35 diretion. (3) Wile te sear span ratio is equal to sear deformation aounts for 3% to 5% of te total deformation; wile sear span is.5 it is aout %~3%; wile te sear span is. it is aout %, so te sear deformation an t e negleted during teory analysis. Te autors would lie to tan te Foundation of Eduational Department of Saan xi Provine (Granted No. 7JK3) and State Eduation Ministry (Granted No.[7]8) for teir supports of tis resear projet. REFERENCES: Cen Z.P., Zang X.D., and Su Y.S., et al.(6). new type of onrete speial-saped olumns ---study of steel reinfored onrete speial-saped olumns onept system. Siuan Building Siene, 3:, 5-7. Cen Z.P., Zao H.T., and Xue J.Y., et al.(6). Resear on earing apaity of steel reinfored onrete speial-saped olumns, Proeeding of 9t nternational symposium on Strutural Engineering for Young Experts, Fuzou & Xiamen, Cina.. Si J., Bai G.L.() n experimental study on restoring fore arateristis of lattie type steel reinfored onrete frame olumns. Journal of Xi an Higway University, :4, Timoseno S., Gere J.(978). Meanis of Materials, Siene Press,Beijing, Cina. Xue J.Y., Zao H.T.(). Elastoplasti analysis of seismi responses for steel reinfored onrete frame model. Journal of Building Strutures, :4, Zao H.T.(). Steel and Conrete Composite Struture, Siene Press, Beijing, Cina.