Behavior Factor of Flat double-layer Space Structures Behnam Shirkhanghah, Vahid Shahbaznejhad-Fard, Houshyar Eimani-Kalesar, Babak Pahlevan

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1 Abtract Flat double-laer grid i from categor of pace tructure that are formed from two flat laer connected together with diagonal member. Increaed tiffne and better eimic reitance in relation to other pace tructure are advantage of flat double laer pace tructure. The objective of thi tud i aement and calculation of Behavior factor of flat double laer pace tructure. With regarding that thee tructure are ued widel but Behavior factor ued to deign thee tructure againt eimic force i not determined and exact, the neceit of tud i obviou. Thi tud i theoretical. In thi tud we ued tructure with pan length of 16m and 20 m. All connection are pivotal. ANSYS oftware i ued to non-linear anali of tructure. World Academ of Science, Engineering and Technolog Behavior Factor of Flat double-laer Space Structure Behnam Shirkhanghah, Vahid Shahbaznejhad-Fard, Houhar Eimani-Kalear, Babak Pahlevan Over few lat decade method of calculating thi factor for different tructural tem wa not pecified and it value wa pecified baed on engineering realization and gue of committee member of code preparation from behavior of tructural tem. But over lat few ear ome reearcher propoed reaonable and reliable method to calculate behavior factor. Bai of all method of behavior factor calculation i force or energ level that a frame aborb from firt platic hinge formation to reaching full collapible mechanim [1]. International Science Index, ivil and Environmental Engineering waet.org/publication/9387 Keword Behavior factor, Double-laer, Intenified reitance, Non-linear anali I. INTRODUTION HERE i high rik of eimic occurrence in mot of Tworld countrie and trong earthquake caue human and financial loe in ome countrie earl, o it i necear to prepare code to deign earthquake reitant tructure with enough accurac and afet factor. Dicuing about variou method of tructural anali and electing variou factor of deign in thee code i inevitable.onl a nonlinear dnamic anali i repreentative of exact and real behavior of tructure during earthquake event but thi tpe of anali i ver time-conuming and expenive, o uing of thi method to analze and deign of tructural frame i not practical. Beide analze and deign of tructure onl baed on elatic behavior without conidering platic behavior and energ aborbing or repelling capacit of tructure during large earthquake that are non-permanent and hazardou force reult in non-economical deign with ver heav member. In order to conidering poitive effect of platic behavior of tructure to carr lateral force almot all of authorized world code ue pecial factor called behavior factor of tructure or reflection corrective factor to decreae calculated eimic force and allow deigner to perform elatic anali of tructure under reduced force and deign baed on that reult. Thi factor i function of variou factor for example ductilit of tructure, material propert, damping characteritic, non-tructural member participation, tructural degree of indeterminac, member extra reitance, member over deign. Behnam Shirkhanghah i Ph.D. tudent of Mohaghegh Ardabili univerit in tructural engineering, ( behnam.hir60@gmail.com) Vahid Shahbaznejhad-Fard i M.Sc. tudent of mohaghegh ardabili univerit in tructural engineering, ( v.h.fard@gmail.com) Houhar Eimani-Kalear i profeor of the technolog and engineering department of the mohaghegh ardabili univerit,ardabil, Iran, ( HEK@uma.ac.ir) Babak pahlevan i profeor of Mehkin Shar Ilamic Azad univerit, Ardabil, Iran, ( ba_pahlevan@ahoo.com) II. FINIT ELEMENT MODELING A. Determining required element There are different element with different pecification to perform variou anale. In thi tud we ued Beam189 that i beam element baed on Timohenko beam theor. Thi element i uitable for non-linear problem. B pecifing an cro- ection geometric propertie i calculated automaticall. B. Material propert It i cutomar to model teel behavior a tre-train curve approximated b two traight line. Firt line from origin with lope of E connect to point of ielding. To conider train hardening behavior of teel econd line i approximated b line with lope 5 % of initial tiffne. Modulu of elaticit and Poion ratio of teel i 2.1E6, 0.3 repectivel.. Modeling Geometr of model b uing FORMAIN oftware i created then i imported to ANSYS. After aigning element to geometr, model i read to anali, but firt tructure i analzed and deigned [2]. D. Loading Now we pecif upported node then contraint all tranlational degree of freedom. Load are impoed on top laer node. According to anali tpe, it i necear that value of load i greater than critical load of tructure, o during anali load will be impoed increaingl to reach to critical load that olution will be divergent. E. Solution control Nonlinear tatic anali i elected. Large diplacement and arc-length method with convergence control baed on limit point i ued. To obtain behavior factor we need olution up to limit point. III. MODEL SELETION In thi tud behavior factor i calculated for three model A, B, and with plan view hown in Fig. 1. Each model ha pan of 16m and 20m and height of 2m, 2.5m, and 3m. Totall 18 different model i analzed. Propertie of model are hown in table I. 740

2 World Academ of Science, Engineering and Technolog International Science Index, ivil and Environmental Engineering waet.org/publication/9387 ( ( (c) Fig. 1 Selected model (model A, (model B, (c)model model A B thick (mm) 4,5 4,5 6,4 TABLE I SPEIFIATION OF MODELS dia (mm) 8,10 8,10 12,8 height long wide IV. ALULATION OF BEHAVIOR FATOR Reditribution of lateral force caue increae in tructural reitance. Extra tree tranfer from ielded member to not ielded member and load-bearing capacit of tructure increae. According to mechanim tpe in deigning baed on demand and ductilit capacit, the objective of deign i to create enough reitance and tiffne for tructure o that ductilit demand of deign earthquake exceed from ductilit demand of tructure. Deign i baed on evaluation of exited ductilit demand and capacit b conidering nonlinear behavior of tructure. Intenified reitance i important factor in determining behavior factor. Behavior factor i equal to ratio of bae hear related to overall ielding of tructure to bae hear related to creation of firt platic hinge and how value of reitance tored in tructure becaue of variou factor and dela collape of tructure. In multi-degree of freedom tructure, with increae in earthquake force tiffne of tructure due to creation of platic hinge and reduced degree of indeterminac decreae and input energ i aborbed b inelatic deformation o that tructure become intable and collape. Intenified reitance of tructure depend on variou factor uch a material tpe, tructure geometr, deign code, tructural detail, and tor number. Practical wa to determine intenified reitance factor of pace tructure i performing nonlinear anali that can be repreentative of pecification of tructure that ubjected to eimic motion and can be ued to determine ductilit and collape mechanim of tructure. Firt, we appl lateral force along with bae hear and record them continuoul. Thi trend continue o that firt tructural element ield a platic hinge, after thi tage reditribution of force caue aborbing of more lateral force. Lateral force increae again o that platic hinge create in other member. When anali top that tructure i mechanim or it diplacement exceed allowable limit or one of element buckle. In thi point we obtain intenified factor b dividing maximum force impoed on frame to force value correponding to firt ielding of frame. Fig. 2 how overall behavior and elatic and inelatic repone of ordinar tructure baed on nonlinear anali. Baed on Fig. 2, we define eimic force reduction factor a: eu (1) (2) eu (3) Where R i behavior factor, R i ductilit factor and R i intenified reitance factor, i ielding reitance or econdar reitance, i elatic reitance, and eu i maximum elatic reitance. According to (1)-(3) below definition of behavior factor i obviou [3]: R R R = (4) Method ued here i developed b Paule and Pritle that aume ielding force of frame V i known. Elatic curve obtain baed on ecant tiffne from force-diplacement curve in force correponding to 0.75V [4]. 741

3 World Academ of Science, Engineering and Technolog Fig. 2 Repone of tructure International Science Index, ivil and Environmental Engineering waet.org/publication/9387 V. NONLINEAR ANALYSIS ANSYS oftware in 1971 i created b American corporation Swanon a pioneering finite element oftware and ued here to perform nonlinear anali. In thi anali material and geometric nonlinearit i conidered. Loaddeflection curve obtained from anali for different model i hown in Fig. 3-5 Fig. 4 Load-deflection curve of model B (pan=16m(pan=20m Fig. 3 Load-deflection curve of model A (pan=16m (pan=20m Fig. 5 Load-deflection curve of model B (pan=16m (pan=20m VI. NUMERIAL RESULTS B uing method mentioned in ection ΙV and nonlinear anali reult, we can obtain behavior factor. 742

4 World Academ of Science, Engineering and Technolog A an example behavior factor of model A with pan of 20m and height of 2m i calculated. Behavior factor of all model i introduced in table ΙΙ, ΙΙΙ, and ΙV. Alo, variation of behavior factor with h/d ratio are hown in Fig. 7. h=3m,d=20m TABLE IV BEHAVIOR FATOR OF MODEL model geometr intenified ductilit behavior reitance factor factor h=2m,d=16m h=2m,d=20m h=2.5m,d=16m h=2.5m,d=20m h=3m,d=16m International Science Index, ivil and Environmental Engineering waet.org/publication/9387 Fig. 6 alculation of behavior factor for model A Intenified reitance i: = / = Ductilit behavior i: eu = / = Finall, behavior factor equal to: R R = = S TABLE II BEHAVIOR FATOR OF MODEL A intenified ductilit model geometr reitance factor behavior factor h=2m,d=16m h=2m,d=20m h=2.5m,d=16m h=2.5m,d=20m h=3m,d=16m h=3m,d=20m TABLE III BEHAVIOR FATOR OF MODEL B intenified ductilit model geometr reitance factor behavior factor h=2m,d=16m h=3m,d=20m ( ( h=2m,d=20m h=2.5m,d=16m h=2.5m,d=20m h=3m,d=16m Fig. 7 Variation of behavior factor with h/d ratio ( model A ( model B (c) model (c) 743

5 World Academ of Science, Engineering and Technolog VII. ONLUSIONS Average value of behavior factor in 18 model i 3.37 o it i poible introduce value of 3.5 obtained from thi tud for flat double laer grid. In pecific interval, tructure have maximum aborption of energ. In thi tud for thee model i from h/d=0.125 to h/d= With regard to curve, increae in height-to-pan ratio caue increae in behavior factor. AKNOWLEDGMENT Author would like to thank to univerit of Mohaghegh Ardabili. International Science Index, ivil and Environmental Engineering waet.org/publication/9387 REFERENES [1] G., S., Ramawam, M., Eekhout, G., R., Sureh, Anali, Deign and ontruction of Steel Space Frame, BHR Publication, No. B-382, [2] H., Noohin, P., Dine, Formex onfiguration Proceing II, International Journal of Space Structure, Vol.16, No.1, [3] S., Amirhekari, alculation of Behavior Factor for Single-Laer Barrel Vault, M.Sc. thei, Ilamic Azad Univerit of Kerman, Iran, September [4] T.,Paula, M.J.N.,Prietle, Seimic Deign of Reinforced oncrete and Maonr Building, Wile, pp. 744,