Analysis of Elastic Lateral-Resistant Stiffness of Steel Plate Shear Wall

Transcription

1 Analysis of Elasti Lateral-Resistant Stiffness of Steel Plate Sear Wall Tiejian LU, Zan Yao *, Silong Yang Sool of Civil Engineering Central Sout University Cangsa,Hunan,Cina Abstrat Te main funtion of te steel plate slotted in te steel plate sear all is resisting orizontal fores, Terefore, estimating its lateral-resistant stiffness plays a very important role in analyzing te reation of te ole struture under orizontal fores. Tis paper analyzes te resear on te elasti lateral-resistant stiffness of steel plate sear all. Firstly, basing on analyzing te interation of te slotted-in steel plates and te boundary frame, te teoreti expression of te lateral-resistant stiffness of steel plate Sear all is derivated. Next, some finite element models of samples are given by using Abaus. Finally, Te of analysis based on Abaqus and te teoretial ere ompared, it sos tat te teoreti expression of te lateralresistant stiffness of steel plate Sear all is aurate and reliable. Keyords-Steel plate sear all; Lateral-resistant stiffness; analysis I. INTRODUCTION Steel plate sear all an be lassified into stiffened steel plate sear all and unstiffened steel plate sear all based on eter stiffened or not; and it an be lassified into ombined steel plate sear all and bukling-restrained steel plate sear all based on te metod ombining embedded steel plate it te onrete slabs on bot sides. Unstiffened steel plate sear all is omposed of embedded steel plate and edge frame; ile as for bukling-restrained steel plate sear all, tere are onrete slabs equipped on bot sides of steel plate to prevent embedded steel plate bukling. Unstiffened steel plate sear all easily bukles under te ation of orizontal loads, but it still ould provide stiffness and sear apaity after bukling; so during design, steel plate's post-bukling properties an be used, so as to adequately play steel plate's role during design. At present, several researers ave arried out studies regarding unstiffened steel plate sear all's post-bukling properties, and Canada is te first ountry tat uses unstiffened tin steel plate sear all [1]. Torburn [] first put forard te onept using unstiffened steel plate sear all's postbukling property in 198. In onsideration of te interation beteen embedded steel plate and edge frame, Sabouri [] put forard frame-steel plate interation model. Trompos and Kulak [4] obtained unstiffened tin steel plate sear all's ystereti urve by lo frequeny yli loading test. Cem [5] studied steel plate sear all's elastially lateral stiffness, and gave to lateral stiffness alulation metods. Karrazi [6] studied steel plate sear all's analysis and design metods, and obtained steel plate sear all's elastially lateral stiffness aording to its sear foredisplaement relation urve. Zouming [7] put forard unstiffened steel plate sear all's unified equivalent model, and studied sear proportionality oeffiient and gave speifi expression by vieing embedded steel plate's meanial arateristis as a superposition of "only searing filed" and "only tension field". Guo Yanlin, Zouming and Dong Quanli [] gave bukling-restrained steel plate sear all's sear apaity formula based on numerial analysis of finite element; provided its elastially lateral stiffness expression based on teoretial analysis, and analyzed and ompared it it finite element result. Hoever, steel plate sear all is not idely used in our ountry, and its design metod and design teory need furter improvement. As bukling-restrained steel plate sear all's meanial properties ave been proved to approximate to tat of unstiffened tik steel plate sear all, in tis paper, bukling-restrained steel plate sear all and unstiffened steel plate sear all are lassified into one ategory and taken as te study objet. [7-8] Steel plate sear all's elastially lateral stiffness is studied in tis paper. First, steel plate sear all's teoretial lateral stiffness expression is dedued based on analyzing te interation beteen embedded plate and edge frame. Ten, several alulation ases' finite element model is establised using ABAQUS softare; and at last, finite element analysis are ompared it teoretial. II. THEORETICAL ANALYSIS OF STEEL PLATE SHEAR WALL'S ELASTICALLY LATERAL STIFFNESS Unstiffened steel plate sear all an be lassified into tree ategories aording to ommon eigt-tikness ratio. Tat is: (,0.8] Tik plate / ( 0. 8, 1. ] Moder at e t i k pl at e n y r (1., ) Ti n pl at e n is ommon eigt-tikness ratio, embedded steel plate's sear yield stress, and embedded steel plate's ritial yield stress. Analysis of tin plate's lateral stiffness. y r is is DOI /IJSSST.a ISSN: x online, print

2 Extremely tin steel plates get sear bukling very easily under te ation of orizontal sear, steel plate's fore an be seen as a "only tension field", and effet of steel plate on outside frame's fore is as son in Figure 1. Figure 1. Te fore of edge frame Compared it general frame olumns, tere is additional inter-olumn load for edge olumns' fore. As fore of te tension zone formed by tension fields is uneven, te inter-olumn load of edge olumns is not even load. No let te inter-olumn load beome equivalent to uniformly distributed load by introduing edge olumns' uneven loading influene oeffiient, ten edge olumns' simplified fore figure is son in Figure. It is ort noting tat te pre-assumed struture's fore in tis paper is rigtard, tus, in design, any edge olumn sould be alulated for bearing apaity as rigt olumn and left olumn, respetively. Wen determining te overall stiffness, alulation sould be done it one edge olumn of steel plate sear all taken as left olumn and te oter as rigt olumn. m q q m Et sin os q Et sin os m Figure. Te fore of edge pillar E is steel plate's elasti modules, is steel plate's tikness, is tension zone's dip angle, and 45 an be taken for it, is frame olumn layers' eigt, is te eigt t a of outside frame olumn setion, and is olumn top's side displaement Te relation beteen olumn bottom's sear fore Fleft, Frigt and olumn top's displaement an be obtained as follos by fore metod: F 右 F 左 1 EI (1 ) Et 1EI (1 ) sin os os ( sin ) 1 Et sin os os ( - sin) 1 1uEI GA is edge olumn's sear deformation influene oeffiient, if it is not neessary to take its sear deformation into onsideration, an be set at 0; u is setion sape fator, its value is 1. and 10/9 for retangular setion and I irular setion, respetively. is edge olumn's setion inertia moment. Aording to te onept of lateral stiffness, left and rigt edge olumn's lateral stiffness an be obtained: 1EI k 左 (1 ) Et sin os os ( sin ) 1 1EI k右 (1 ) Et sin os os ( - sin) 1 For steel plate, steel plate tension filed effet is obvious, fore of te tension zone formed by tension fields is uneven. Embedded steel plate's lateral stiffness an be obtained as follos after steel plate's uneven loading influene oeffiient is introdued: Etb 4 In tis paper, it is reommended tat bot edge olumn and steel plate's uneven loading influene oeffiient are 0.6. Terefore, tin steel plate sear all's overall lateral stiffness is: k k k k total left rigt 4EI Et si n os Et b (1 ) (1 ) 4 Analysis of tik plate's lateral stiffness. DOI /IJSSST.a ISSN: x online, print

3 Under te ation of orizontal sear, tik steel plate's sear yield is anteedent to overall yield, steel plate presents a state tat te plane is loaded it sear stress evenly; only additional eentri fore is applied by steel plate to edge olumns, and te effet of steel plate on outside frame's fore is son in Figure. Ignore te influene generated by edge olumns' axial deformation, ten edge olumns' simplified fore figure is given in Figure.4. Figure. te fore of edge frame m m Figure 4. te fore of edge pillar Gt m.4 G is steel plate's sear modulus, t is steel plate's atual tikness, is te eigt of outside frame olumn setion, is olumn top's side displaement. Te relation beteen olumn bottom's sear fore Fleft, Frigt and olumn top's displaement an be obtained by fore metod: 1EI 5Gt F F left rigt (1 ) 1(1 ) Aording to te onept of lateral stiffness, left and rigt edge olumn's lateral stiffness an be obtained: 1EI 5Gt k k left rigt (1 ) 1( 1 ) It is found by analysis tat steel plate's tension field effet disappears, and steel plate is seared evenly. Referene [7] gives embedded plate's lateral stiffness as follos: Gtb 1. Te above formula is atually steel plate's sear lateral stiffness; oever, in steel plate sear all, embedded steel plate ats togeter it edge frame, steel plate sear all's deformation is divided into edge frame's bending deformation and steel plate's sear deformation. Wile in general, set overall inter-layer side displaement as an unknon quantity, ten steel plate's lateral stiffness is: Gtb 1. Were, is steel plate sear all's sear deformation ratio. Regarding 's value, dedution proess is as follos: Steel plate sear all's deformation: f s Were, is steel plate sear all's overall inter-layer f side displaement, is inter-layer bending deformation, and s is inter-layer sear deformation. Inter-layer bending deformation: N Gtz /(1.) s f dz b 0 EA N Gt s EA ( b ) 1.EA ( b ) Were, N is te axial fore generated under ation of te orizontal fore at top of edge olumn, A is edge olumn's setional area, and rest parameters are te same as above. Te axial fore at top of outside frame olumn is: D N b 1EI D (1 ) So: s 1 B 1 A Were, parameter A and B are as follos: Gt A 1.EA ( b ) D B EA ( b ) Terefore, tik steel plate sear all's overall lateral stiffness is: k k k k total left rigt 4EI 5Gt Gt b (1 ) 6(1 ) 1. Analysis of moderate-tik plate's lateral stiffness. As for moderate-tik plate, its fore an be seen as a superposition of "only sear" and "only tension field" by a DOI /IJSSST.a ISSN: x online, print

4 ertain ratio. Tat is, moderate-tik plate's fore= "only sear field"+ (1- ) "only tension field, ere, is "only sear field" partiipation fator. Zouming gave sear proportionality oeffiient's expression: 1.0, n ( n 0.8), 0.8 n / n, n 1. Wit te edge olumn and embedded steel plate's fore arateristis under bot "only field" and "only tension filed" meanism tat ave been dedued in tis paper and te "only sear filed" partiipation fator, moderate-tik steel plate sear all's fore arateristis an be easily obtained. Te relation beteen olumn bottom's sear fore Fleft, Frigt and olumn top's displaement an be obtained by fore metod: 1EI (1 ) Et sin os F左 [ ( sin (1 ) os 5 Gt ) ] 1 1(1 ) 1EI (1 ) Et sin os F右 [ ( sin (1 ) os 5 Gt ) ] 1 1(1 ) Aording to te onept of lateral stiffness, its lateral stiffness an be obtained as follos: 1EI (1 ) Et sin os k 左 ( sin (1 ) os 5 Gt ) 1 1(1 ) 1EI (1 ) Et sin os k右 ( sin (1 ) os 5 Gt ) 1 1(1 ) As for steel plate, its fore an be seen as a superposition of "only sear" and "only tension filed" by a ertain ratio, so embedded steel plate's lateral stiffness an be obtained as follos: Etb Gtb ( 1) 4 1. Terefore, moderate-tik steel plate sear all's overall lateral stiffness is: k k k k total left rigt 4 EI ( 1 ) Et si n os (1 ) (1 ) 5 Gt Et b Gt b (1 ) 6( 1 ) 4 1. Analysis of bukling-restrained steel plate sear all's lateral stiffness. As for bukling-restrained steel plate sear all, sine tere are onrete slabs on bot sides of embedded steel plate and tere onrete slabs ould bind steel plates, troug reasonably designing te onrete slabs on bot sides, it an be ensured tat steel plate's yield lags beind steel plate's sear yield, ten its fore arateristis also an be seen as "only sear", like tik steel plate sear all. So tey on't be overed again ere. III. FINITE ELEMENT ANALYSIS Te teoretial expression of steel plate sear all's overall lateral stiffness is dedued above. In order to verify te dedued ' orretness and reliability, use general finite element softare ABAQUS to analyze and ompare tem it teoretial to verify teir auray. A. Finite Element Model Sine moderate-tik plate's fore meanism an be seen as a superposition of "only sear filed" and "only tension filed", referene [9] as verified its orretness and gave te sear proportionality oeffiient, and also beause bukling-restrained steel plate sear all's fore meanism is te same as tat of tik plate, ten it is only neessary to verify teoretial formula's orretness under "only tension filed (tin plate)" and "only sear field (tik plate)". Take te model provided in referene [10] as te basi model, and ange oter parameters to form omparison models. Basi model (model 1-1)'s model parameters are as follos: frame olumn's size is 40 mm 50 mm 0 mm 15 mm; as edge beam is bound by upper and loer steel plates, its stiffness an be seen as infinity; beam's setion is 500 mm 500 mm; steel plate size is 700 mm 1800 and 4500 mm 1800 mm; steel's onstitutive model is an ideal intensifiation model, it yield strengt, elasti modulus Es and intensifiation modulus of 40 MPa, MPa and 0.01Es, respetively. Tin plate's model parameters are given in TableI, and tik plate's model parameters are given in Table II. Establis 1 models using ABAQUS finite element analysis softare, respetively. Outside frame uses entity element, adopt equivalent pull rod model for tin steel plate, tat is, truss element is used; adopt sell element for tik steel plate. Embedded steel plate is onneted it edge frames by means of sell-entity oupling. TABLE I THE MODEL PARAMETERS OF THIN STEEL PLATE SHEAR WALLS Model Size/mm ratio of eigt to tikness span-dept ratio DOI /IJSSST.a ISSN: x online, print

5 TABLE II THE MODEL PARAMETERS OF THICK STEEL PLATE SHEAR WALLS Model Size/mm ratio of eigt to tikness span-dept ratio B. Comparison Beteen Teoretial Results and Finite Element Analysis Results Compare te teoretial dedued in tis paper it finite element analysis. Comparison of lateral stiffness of tin steel plate sear all's edge olumn and embedded steel plate's lateral stiffness are given in Tale III, Table IV and Table V, respetively. And omparison of lateral stiffness of tik steel plate sear all's edge olumn and embedded steel plate's lateral stiffness are son in Table VI and Table V,respetively. TABLE III THE LEFT EDGE PILLAR S LATERAL-RESISTANT STIFFNESS OF THIN STEEL PLATE SHEAR WALL Model Te formula of tis paper Differ /% TABLE IVTHE RIGHT EDGE PILLAR S LATERAL-RESISTANT STIFFNESS OF THIN STEEL PLATE SHEAR WALL Model Te formula of tis paper Differ /% TABLE VTHE SLOTTED-IN STEEL PLATE S LATERAL-RESISTANT STIFFNESS OF THIN STEEL PLATE SHEAR WALL Model Te formula of tis paper Differ /% TABLE VITHE EDGE PILLAR S LATERAL-RESISTANT STIFFNESS OF THICK STEEL PLATE SHEAR WALL Model Te formula of tis paper Differ /% TABLE VIITHE SLOTTED-IN STEEL PLATE S LATERAL-RESISTANT STIFFNESS OF THICK STEEL PLATE SHEAR WALL Model Te formula of tis paper Differ /% Results in Table III~Table VII so tat tere are ertain errors beteen finite element analysis and teoretial in tis paper, but tey are very little and are all itin 10%, i indiates tat te lateral stiffness alulation formula of edge olumn and embedded steel plate of tin plate and tik steel plate sear all dedued in tis paper is orret and reliable. IV. CONCLUSION (1) In tis paper, steel plate sear all's fore arateristis and te interation beteen edge frame and DOI /IJSSST.a ISSN: x online, print

6 embedded steel are analyzed, and on tis basis, te teoretial expressions of lateral stiffness of tin steel plate and tik steel plate sear all's edge olumn and embedded steel are dedued, respetively, so tat te teoretial expression of overall lateral stiffness of steel plate sear is obtained. () A finite element model for steel plate sear all is establised, and te teoretial expression of elastially lateral stiffness of steel plate sear is verified to be orret by omparing te analyzed by tat finite element model it teoretially dedued. REFERENCES [1] Driver R G, Grondin G Y, Steel plate sear all: No performing on te main stage, Modern steel onstrution, 001. [] Torburn L J, Kulak G L, Montgomery C J, Analysis of steel plate sear alls, No Edmonton Department of Civil Engineering, University of Alberta, Edmonton, Canada, 198. [] Sabouri-Gomi S, Ventura C W, Karrazi M H K, Sear analysis and design of dutile steel plate alls, Journal of Strutural Engineering, ASCE, vol. 11, No. 06, pp , 005. [4] Trompos E W, Kulak G L, Cyli and Stati Beaviour of Tin Panel Steel Plate Sear Walls, Strutural Engineering Rep. No.145, University of Alberta, Alberta, Canada, [5] Cem Topkaya, Memet Atasoy, Lateral stiffness of plate sear all systems, tin-alled strutures, vol. 47, pp , 009. [6] Karrazi M H K, Rational metod for analysis and design of steel plate alls, Vanouver University of Britis Columbia, 005. [7] GUO Yanlin, ZHOU Ming,DONG Quanli, Hystereti beavior of bukling-restrained steel plate sear all, Engineering Meanis, vol. 6, No. 0, pp , 009. [8] GUO Yanlin, DONG Quanli, ZHOU Ming, Tests and analysis on ystereti beavior ofbukling-restrained steelplate searall, Journal ofbuilding Strutures, vol. 0, No. 0, pp. 1-9, 009. [9] ZHOU Ming, Studies on Design Metod of Unstiffened or Bukling-Restrained Steel Plate Sear Wall Strutures, LI Ran,GUO Lande,ZHANG Sumei, Hystereti analysis and simplified model of steel plate sear all, Journal of Tianjin University, vol. 4, No. 10, pp , 010. DOI /IJSSST.a ISSN: x online, print