Framework to Explore the Design Space for Design of Tall Buildings

Transcription

1 Framework to Explore the Deign Space or Deign o Tall uilding Yogeh Unde 1 Subramaniam Rajan 2 1 Graduate Student, 2 Proeor School o Sutainable Engineering & the uilt Environment, Arizona State Univerity, Tempe, AZ ASTRACT Deign o tall building i undergoing a reurgence that i driven by a variety o actor economical growth, carcity o l in urban area, high l cot, increaed population denity, technological advancement man deire to build taller tructure. Coniderable reearch work ha been done in the lat two decade to meet thi dem. Computer-baed tool that help deign engineer explore deign alternative are indipenable in tackling thi complex problem. In addition, a ramework that ind the near optimal deign, add value to thi exploratory work. In thi paper, we develop a general ramework or the deign optimization o building uing izing, hape, topology deign variable. Sizing optimization can be carried out uing dicrete deign variable (rom a databae o available ection) or continuou deign variable (cro-ectional dimenion o cutom wide lange ection). Similarly, hape optimization can be carried out uing either dicrete or continuou deign variable. And inally, topology optimization can be carried out uing boolean deign variable. Allowable tre deign guideline are ued a contraint along with diplacement, inter-tory drit, total tructural weight, requency contraint. The inite element model i made o three-dimenional beam element. A typical unction evaluation involve a linear, tatic analyi with multiple load cae, a linear, modal analyi to extract the lowet ew eigenpair, a linear, buckling analyi to ind the buckling capacity. An optimization toolbox that contain gradient-baed population-baed optimizer, i a part o the ramework. Numerical reult how that the ramework i capable o producing eicient deign eectively. KEYWORDS Tall building; inite element analyi; deign optimization; izing, hape topology optimization. INTRODUCTION The dem or tall building continue to grow ueled by economic growth, carcity o l in urban area, high l cot, technological advance in material, contruction technique deign principle, growing population in megacitie, above all, the ego to build the tallet building. From 2000 to 2013, the total number o 200-meter-plu building completion in exitence increaed rom 261 to 830 an atounding 318 percent (Saarik Wood, 2014). The challenge in building higher taller at a more economical level with due conideration to uability, aety utainability have kept alive the reearch interet in tall building deign. Ali Moon (2007) dicu the evolution o tall building ytem the technological driving orce behind tall building development. They categorize interior tructure a rigid rame, braced hinged rame, hear wall/hinged rame, hear wall-rame interaction ytem outrigger tructure, exterior tructure tube, diagrid, pace tru tructure, pacerame exo-keleton. Fawzia Fatima (2010) dicu the ue o belt tru outrigger ytem in controlling delection. A three-dimenional inite element model o a 60-torey compoite building i ued to invetigate the perormance (delection control) o the building ubjected to wind load. One, two three outrigger level are ued to how that igniicant reduction in lateral delection inter-tory drit can be obtained in comparion to a model without any outrigger ytem. A method or determination o preliminary member ize in the context o diagrid ytem i preented in Moon et al. (2007). The developed methodology i ued to ize the diagrid member in building ranging rom 20 to 60 torie. With an apect ratio o 7, or 60-tory diagrid tructure, the optimal range o diagrid angle i rom about 65 0 to With an apect ratio o 5, or 42-tory building, the range i lower by 10 0 indicating that the angle i a unction o the building dimenion. At the preliminary a well a the detailed deign tage, the ue o a deigner guided ytem i indipenable. Deign optimization tool provide uch a ytem helping take over the mundane tak o inding the bet poible deign once the problem ormulation i et the baic inite element deign model are etablihed. Several reearcher have addreed deign optimization o building ytem cotrevenue conceptual deign o high-rie building (Grieron Khajehpour, 2002), multiple deign criteria (Ng Lam, 2005), evolutionary method (Manickarajah et al., 2000; Kamehki Saka, 2001; Kicinger et al., 2005), optimality criteria (Chan Chui, 2005), optimum deign o teel tructure with opening uing izing, hape topology deign variable (Lagaro et al., 2006), numerical deign optimization tool (aker et al., 2008), preliminary 1142

2 deign optimization (Jayachran, 2009), topology optimization (Liang et al., 2000; Stromberg et al., 2012). Through the ue o principal tre trajectorie, evolutionary tructural optimization gradient-baed population-baed technique, conceptual development o innovative tructural architectural topologie can take place [aker et al., 2008]. Principal tre trajectorie are decribed in term o partial dierential equation then olved to yield diagrid ytem. In another approach, gradient-baed method i ued to ind the optimal hape o a tall building by minimizing the diplacement at the top o the building when ubjected to contant wind preure. The tructural element are aumed to be located only on the exterior ace o the tower when height, encloed volume bae are contrained. For veriication, a imilar problem i alo olved uing genetic algorithm where the bet olution i imilar to that obtained by the gradient-baed technique. Topology optimization provide another mean o inding a better deign. Liang et al. (2000) developed a methodology or inding the optimal layout o member in a bracing ytem ubjected to multiple lateral loading condition. The objective unction i the weight the perormance contraint place an upper limit on the mean compliance o the tructure. The unbraced (keletal) tructure i modeled with beam element the continuum between the beam column are modeled with plane tre element. The inal continuum topology i ued a a guide or placing the bracing element. Similarly, Stromberg et al. (2012) addre the tak o inding an eicient planar lateral bracing ytem via topology optimization that i baed on combining beam continuum inite element where, though untated, the inal topology i a reaonable gue or the exploration o a diagrid ytem. The main objective o thi paper i to develop a ramework or the optimal deign o tall building. The ramework allow or invetigating the deign eiciencie o dierent building ytem, e.g. rigid rame, belt tru outrigger ytem, diagrid ytem etc. The deign ramework tart with a general deign problem ormulation that allow or inding the izing variable (eentially cro-ectional dimenion propertie), hape variable (location o tructural member joint), topology variable (preence, abence location o member). The perormance erviceability contraint include normal tre, hear tre, diplacement, inter-tory drit, buckling, natural requencie. An optimization toolbox i tightly integrated with a unction gradient evaluation ytem that include a inite element analyi ytem computer code to compute the unction gradient value. The problem ormulation the evaluation o unction gradient value are dicued in the next ection. Thi i ollowed by everal deign example that how how the ramework i ued to invetigate the deign pace. OPTIMAL DESIGN PROLEM FORMULATION Deign problem involving building can be poed everal dierent way. The ormulation are motivated by the need to ind optimal olution at the preliminary deign tage o that an exhautive earch o the deign poibilitie can take place accurately eiciently. The objective i to deign building with m torie having n tructural teel member, aigned to p cro-ection property group p n. The keletal ramework i aumed to be made o teel. Deign Problem Formulation Minimum Weight Deign (MWD) Thi i a minimum weight deign problem the problem i poed a ollow. Find x x b Minimize Subject to W x c, n AL i i i i1 tc, tc, max, i a ( i 1,2,... n) (3) max, i a ( i 1,2,... n) (4) D D j i T max D h j D (5) j1 a D ( j 1,2,..., m) (6) ij a (1) (2a) 1143

3 2 EI kl a P 2 cr a L U xc xc x c c1, 2,.., p (9a) b 0,1 ( l 1,2,..., r) (9b) l where W i the total weight o all the tructural element, i i the weight denity o material, A i i the cro-ectional area o member i. Eqn. (3-4) are ued to impoe tre contraint where max,i L i (7) (8) i the length are the maximum tenile, compreive hear tre, the ubcript a denote the allowable value. Eqn. (5) deine the contraint impoed on the maximum lateral drit max the building. Eqn. (6) deine the inter-tory drit contraint or the tructure where th j ( j 1) th tory repectively h j i the height o th j D i T t max, i, c max, i in longitudinal tranvere direction o D j D j 1 are the drit o tory. uckling contraint are impoed via Eqn. (7) in the orm o Euler buckling via Eqn. (8) in the orm o overall buckling o the tructure where allowable buckling capacity o the member a P cr a, i the i the lowet eigenvalue rom the buckling eigenvalue problem i the allowable value. Eqn. (9a) i ued to denote either dicrete deign variable (elected rom a predetermined table o cro-ectional hape) or continuou deign variable a explained later. Eqn. (9b) denote boolean deign variable that are ued to elect or deelect bracing member r n. Finite Element Analyi Finite element analyi i ued during unction evaluation neceary to compute the objective unction contraint. Three et o linear algebraic eigenproblem are olved a ollow. where Κ K D F dd dlc dlc K Φ Λ M Φ (11) dd dd dd dd dd K K (12) dd d1 dd d1 dd, Md d Κ qq qq qq qq qq dd (10) are the tructure tine matrix, ma matrix geometric tine matrix repectively. In addition, d i the total number o degree-o-reedom in the inite element model, lc i the number o load cae, i the buckling load actor or the lowet mode. Eqn. (11) i typically olved in a maller pace a ˆ ˆ q d. Further explanation K Φ Λ M Φ ince only the lowet ew q eigenpair are o interet involving the problem ormulation are preented next. Perormance Contraint Perormance-baed deign include trength erviceability requirement a dicued below. Stre Contraint: Allowable Stre Deign (ASD) requirement are impoed where the requirement i that the allowable trength o each tructural component equal or exceed the required trength. A per AISC Speciication (2005), the allowable tenile/compreive tre or gro teel cro ection i 0.6 y the allowable hear tre or gro teel cro ection i 0.4 y where y i the yield trength o the teel material. In the inite element analyi, the magnitude o the maximum beam element tree are computed conervatively a ollow (x-y-z denote the longitudinal axi the two tranvere direction, repectively) at the two end at the quarter-point o each beam inite element. 1144

4 Normal tre: t N M y M x z max max,0 A Sy S z c N M y M x z max min,0 A Sy S z Shear tre: V y y Qy z Vz Qz It It y y z y T T T x J y T z T max max, (16) where AS, y, Sz, Qy, Qz, ty, tz, Iy, Iz, TJ are the cro-ectional propertie dimenion, i.e. area, ection moduli, irt moment o the area, width reiting hear, moment o inertia torional contant, repectively, Nx, Vy, Vz are the normal hear orce in the element local x, y, z direction, Tx, M y, M z are the torional bending moment in the element local x, y, z direction. Diplacement Contraint: Two type o diplacement contraint are impoed Eqn. (5) (6). Firt, the diplacement in the two tranvere direction are limited to 1/600 to 1/400 o the total building height [ASCE, 1998]. Second, the inter-tory drit i another erviceability criterion or deign requirement i taken to be le than 1/500 o the tory height [Ng Lam, 2005]. uckling Contraint: In addition o the trength requirement impoed via tre contraint, in perormance baed deign, tructural intability mut be prevented. Member buckling i controlled via the impoition o Euler buckling contraint (Eqn. (7)). uckling behavior o the tructure i determined by olving the eigenproblem hown in Eqn. (12) where i the buckling load actor that need to be much greater than 1 to prevent buckling under the action o the applied load, i.e. all load cae. Other intabilitie uch a buckling o lange, torional buckling etc. are not conidered. Deign Variable Selection o the deign variable help deine the problem a izing, hape /or topology deign optimization problem [Rajan, 1995]. Sizing Variable: To meet the high trength requirement o the beam, brace column, we aume that cutom ection are needed. Uing continuou deign variable, each element cro ection i taken a a cutom wide lange ection the web height o the ection i ued a the primary deign variable. A group o heavy 130 wide lange ection rom the AISC databae wa examined or generating relationhip among the our dimenion o a typical wide lange ection - web height,, lange width, w, web thickne,, lange thickne, t. A ample relationhip i hown in Fig. 1. h w Figure 1. Flange width veru web height relationhip t w (13) (14) (15) The linear relationhip obtained rom thi exercie are a ollow (the R 2 value or the three it are 0.924, 0.956, 0.553) [Sirigiri et al., 2015] w 0.235h 7.12 (17) t t w 0.492t (18) w w (19) where the implied unit are inche. The low R 2 value or the lange thickne lange width relationhip i due to the wide range o available lange thicknee ( ) or a given lange width ( ). It hould be noted that other commonly ued cro-ectional hape can be 1145

5 eaily incorporated in the problem ormulation, that the wide-lange ection are ued in thi tudy to readily illutrate the deign concept. Topology Variable: Diagonal bracing member are oten ued to brace teel ramework to maintain lateral drit within acceptable limit. The optimal layout deign o bracing ytem i a challenging tak or tructural deigner becaue it involve a large number o poibilitie or the arrangement o the member. In the abence o an eicient optimization technique, the election o lateral bracing ytem or multi-tory teel ramework i undertaken by a deigner baed on a trial--error proce or previou deign experience. In topology optimization o a tructure, boolean deign variable are aigned to tructural element. The value o 1 or the variable implie that the element exit in the tructure 0 implie that element i removed rom the tructure [Rajan, 1995]. Finite Element Analyi The FE analyi neceary to compute the unction gradient value in the problem ormulation are carried out uing the GS-USA Frame3D program [Sirigiri Rajan, 2013]. A mall train, mall diplacement, linear elatic inite element analyi i carried out by the computer program. The repone rom the FE analyi that can be ued in the problem ormulation include nodal diplacement, beam element nodal orce, beam element maximum tenile, compreive hear tree, thin plate/hell tree tructural lowet requencie. The requency analyi i carried out uing the tine ma o the tructural element plu the ma o the nontructural element a raction (25%) o the live load. Numerical Optimization Technique The deign optimization toolbox ued or optimal deign ha everal optimization technique that can be invoked depending on the problem type. Gradient-baed Technique: Gradient-baed technique are particularly ueul when deigning with continuou deign variable continuou dierentiable objective contraint value. In particular, the Method o Feaible Direction (MFD) [Rajan et al., 2006] i ued in thi tudy. Typical problem with about deign variable can be olved in about iteration involving le than a hundred unction evaluation about gradient evaluation. The active et trategy i ued in order to make the torage pace computation eicient. Population-aed Global Optimization Technique: When the deign variable are not continuou (e.g. dicrete, boolean), or the objective contraint unction are not dierentiable, or i there i a need to ind everal ditinct local optima poibly, the global optimum, population-baed technique are deirable. In particular, the Genetic Algorithm i ued in thi tudy [Rajan, 1995; Rajan Nguyen, 2004]. Typical problem involving deign variable require everal hundred unction evaluation to yield high quality olution. In the next ection, detail o a cae tudy are preented howing how the developed deign optimization methodology i ued or the deign o tall building. NUMERICAL RESULTS The numerical reult are obtained by executing the developed program, GS-USA Frame3D, on a Dell Preciion Worktation T5400 with Intel Xeon E GHz proceor, 8 G RAM running Window 7-64 bit operating ytem. Deign Optimization with Planar Frame Model The developed deign methodology i teted uing a 40-tory building that ha a t by t rectangular loor layout (Fig. 2) where i the pacing between the rame i the number o rame in the (trong) y-direction. The height o the irt loor containing the lobby i 16 t. All the other loor height are 13 t. The total height o the building i 523 t. The loor ytem conit o a compoite metal deck lab (3 cellular teel deck with 2.5 concrete lab), upported on the teel joit. All the degree-o-reedom at the bottom o the column are retrained. All the model with bracing element conidered in thi tudy are aumed to be ymmetrical. 1146

6 y y A C D E F G A C D E F G x 3 6 x 3 (a) (b) (c) Figure 2. (a) Initial 40-loor planar rame layout (b) Typical loor plan (x-y plane; z: gravity direction) howing interior rame (c) End rame In the ret o thi ection, the rame hown in Fig. 2(a) correponding to the interior rame with the haded area in Fig. 2(b), i ued during deign optimization. Three dierent rame are conidered with 20', 25',30' are labeled 120-WF, 150-WF 180-WF rame. There are 287 node, 1000 beam inite element 840 eective degree-o-reedom in the initial planar inite element model. Material Propertie Load The teel column, beam bracing o the building are aumed to be o grade A992/A992M. The loor lab elevator hat wall are aumed to be o high trength reinorced concrete. Table 1 ummarize the material propertie. Table 1. Material Propertie Material Structural element Ma Denity Elatic Modulu 3 Steel, Grade 992/A992M Column, beam, bracing lug t ki Concrete Slab, curtain wall & elevator hat wall lug t 4600 ki The dead load are due to the teel deck loor inihe. Auming that the building i or oice ue, the live load on the loor roo are a per the peciication in Table 4-1, ASCE-7-10 [ASCE, 2010]. Wind preure load are computed a per Chicago City Code Table 16 ( ). Tributary area concept i ued to compute the loading on the planar rame. Table 2 ummarize the key loading value. Table 2. Load Value Location Item Load x Floor Dead load 144 p Floor Live load 100 p Column (ground level-top loor) Wind load p Allowable Stre Deign (ASD) Load Combination In ASD, the combination o ervice load are evaluated or maximum tree compared to allowable tree. ASCE combination o load are hown below. 1. LC 1: Dead load 2. LC 2: Dead load + Live load 3. LC 3: Dead load Wind Load 4. LC 4: Dead load Live Load (0.6 Wind Load) Deign Variable The loor were grouped together into 20 group, 2 loor per group. The cro ection propertie o column, beam bracing member are varied along the height o that the propertie are the ame in any group. In thi tudy, the two end column the interior column are not treated dierently are aumed to have the ame propertie in a particular loor group. The web height o the wide lange ection aigned or each o thee group i deined a a continuou izing deign variable with an upper limit a a unction o the tory height. Twenty belt true were created x 3 6 x x 1147

7 along the height o the planar rame by grouping the bracing o two loor together. A boolean value o 1 or L 1 indicate that the bracing exit along the entire loor o the building. The location o the interior column (along C) are allowed to vary. Equality contraint are ued to impoe ymmetry o that column E, C F are ymmetrically placed about D. Thu, there are 62 continuou deign variable 20 boolean deign variable in each deign model a hown in Table 3. Table 3. Decription o Deign Variable in Planar Frame Model Variable Variable type Number Decription C 1 to C 10 Continuou Web height o column cro-ection or the 20 group 20 (Sizing) o loor L 1 to L 10 Continuou Web height o longitudinal beam cro-ection or the 20 (Sizing) 20 group o loor T 1 to T 10 Continuou Web height or belt tru bracing member croection or the 20 group o loor 20 (Sizing) L 1 to L 10 oolean racing pattern or belt true or the 20 group o 20 (Topology) loor Continuou Location o the two interior column. The end 2 (Shape) column the center column remain ixed. For problem involving only continuou deign variable, MFD wa ued or a maximum o 50 iteration with a relative abolute convergence tolerance o Otherwie, GA wa ued with a population ize o 500 or 50 generation. Deign Optimization Solution Initially, model were created with no bracing element. Thee model were executed to ind a baeline optimal deign or comparative purpoe. However, no eaible olution could be ound or two o the three model - the 150 wide the 180 wide rame. The addition o bracing element via belt true produced acceptable deign in thoe two cae. It hould be noted that the weight o each member wa calculated center-to-center without accounting or connection. The value o ome o the key tructural parameter are hown in Table 4 (ton denote 2000 pound). Table 4. Key Structural Parameter 120-2D 120-2D-T 150-2D-T 180-2D-T Total weight o all beam, column bracing member, ton Initial location o the interior column x, x, x (ee Fig. 2), in Final location o the interior column x, x, x (ee Fig. 2), in (240, 480, 720) (205, 449, 720) (240, 480, 720) (204, 448, 720) (300, 600, 900) (287, 587, 900) (360, 720, 1080) (344, 700, 1080) Lowet requencie, Hz (0.18, 0.45, (0.18, 0.45, (0.15, 0.64, (0.17, 0.72, 0.80) 0.80) 0.96) 1.03) Smallet uckling Load Factor, The optimal deign are ummarized in Table 5-6. Table 5 how the weight ditribution o the tructural element. The ummary o the tructural repone i hown in Table 6. The normalized weight (weight per deigned unit area) i computed by auming a quare building with 49 rame a 7W 42W 3WX 7W 42W 3WX WN (20) 2 Total covered area where W i the total weight on one rame (ee Table 4), W i the weight o all the remaining beam W X i the weight o all the remaining bracing element. The inal hape topologie o the optimal deign are hown in Fig. 3 along with the plot o the highet compreive tre (blue denote highet value red the lowet value) or LC 4, the governing load cae. Dicuion: A expected, increaing the pan rom =20 to =30 make it much more challenging diicult to obtain a eaible deign. A imple moment-connected rame appear to be the optimal deign when the pan i relatively mall (=20 ) both 120-2D model (olved via MFD) 120-2D-T model (olved via GA) lead to very 1148

8 imilar inal deign. However, when the pan i increaed, it become neceary to combine a rigidly-connected rame with belt true. Even with the ue o thee tructural element, the column dictate the deign requiring a relaxed upper bound on the web height. Interetingly enough, the column with the highet tree are the interior column at the bae o the belt true (Fig. 3(c)-(d)). However, a large number o member have their max. compreive (column beam) tenile tre (beam) cloe to the limit o 30,000 pi or both LC 2 LC 4 indicating that the deign i near optimal eicient. Diplacement, hear tre, buckling (Euler buckling load actor) the lowet requencie o the tructure are not cloe to controlling the deign. The lowet three requencie are well paced. The larget diplacement value occur on the top loor o the tructure i about 4% o the typical loor height. In every model, the interior column move outward thereby reducing the outermot pan increaing the interior pan. From an oice pace uage viewpoint, thi may be deirable ince larger uninterrupted pan are available or ue a conerence or meeting room. The normalized weight how a wide range between p. It i poible that the 150-2D-T 180-2D-T model can be improved (are not the global optimum olution) that with a better olution, a lower normalized weight can be ound. We will dicu the diiculty o inding olution in the oolean-continuou deign variable pace later in the paper. The wall clock time (WCT) or one unction evaluation i about 0.11 o that the total WCT or a GA-run (the belt tru model) i about 2800 about 250 or the MFD-olved model (120-2D). Table 5. Summary o the Weight or Variou et Deign (Number in parenthei denote % o total weight) Model Weight o Column, W C Weight o eam, W Weight o racing, (ton) W X Total Weight, W (ton) Normalized Weight, (lb/t 2 ) (ton) (ton) 120-2D 485 (56) 380 (44) 0 (0) D-T 485 (56) 375 (44) 0 (0) D-T 690 (49) 380 (27) 335 (24) D-T 1040 (53) 440 (23) 455 (24) Table 6. Summary o the Maximum Structural Repone (Number in parenthei denote % o allowable value) Model X-Dip. (in) Tenile Stre (pi) Comp. Stre (pi) Shear Stre (pi) 120-2D 6.1 (51) (74) (100) 7540 (38) 120-2D-T 6.1 (51) (75) (100) 7540 (38) 150-2D-T 5.9 (49) (100) (99) 9850 (49) 180-2D-T 3.8 (32) (100) (99) (52) W N 120-2D 120-2D-T 150-2D-T 180-2D-T Figure 3. Final topology o the bet deign compreive tre plot (LC 4) Deign Uing raced Tube - Diagrid The building deign problem rom Section 3.1 i ued in the context o braced tube-diagrid building orm. To acilitate the automatic election o the two end node or the bracing element, a lit o potential node wa ued or each 1149

9 element thee dicrete deign variable were added to the lit o deign variable (Eqn. (1)) a,, x x b x. The new problem ormulation ha a total o 38 deign variable. The C 1 to C 10 deign variable were applied to column, C, E, F. The L 1 to L 10 deign variable were applied to all beam not connected to the primary braced tubediagrid ytem, Figure 4. Two o the everal poible bracing coniguration deign variable were ued a beore. Uing inormation rom a preliminary deign tudy o thi coniguration, new deign variable were introduced to hle the diagrid ytem - 4 continuou deign variable were introduced or column A, D G, 4 continuou deign variable or the longitudinal beam, 4 deign variable or the bracing member, 4 dicrete deign variable were introduced to take care o the end node o the bracing member. Poible bracing coniguration are hown in Fig. 4 where the thick line denote column, beam bracing member that are part o the diagrid ytem. Symmetry o the tructure i enorced with the node o the bracing element being placed on column A, D G a hown in Fig. 4. Thi approach i perhap preerable to the ue o continuum element-beam element model a thoe hown in previou reearch work [Liang et al., 2000; Stromberg et al., 2012] ince the modeling deign approach it in with the optimal deign problem with no additional aumption or limitation. The problem data are the ame a thoe ued in Section 3.1 The optimal deign reult are hown in Table 7-9. The inal hape topology o the building i hown in Fig. 5. Table 7. Key Structural Parameter 180-2D-D Total weight o all beam, column bracing member, ton 2800 Initial location o the interior column Final location o the interior column x, x, x (ee Fig. 2), in (360, 720, 1080) x1, x2, x (ee Fig. 2), in (289, 650, 1080) 3 Lowet requencie, Hz (0.40, 1.04, 1.69) Smallet uckling Load Factor, Table 8. Summary o the Weight or Variou et Deign (Number in parenthei denote % o total weight) Model Weight o Column, Weight o eam, Weight o racing, Total Weight, W Normalized Weight, (ton) (ton) (ton) (lb/t 2 ) 180-2D-D 1130 (40.3) 655 (23.4) 1015 (36.3) W C (ton) W W X 45.5 Table 9. Summary o the Maximum Structural Repone (Number in parenthei denote % o allowable value) Model X-Dip. (in) Tenile Stre (pi) Comp. Stre (pi) Shear Stre (pi) 180-2D-D 0.92 (8) (99) (99) 9980 (50) Dicuion: oth the compreive/tenile tre buckling load actor control the deign. The reaon why the latter control the deign i becaue o the extremely long bracing member. In practice one would attach the intermediate point in the bracing member to appropriate point in the interecting column beam. Such connection are not generated in the model in the current reearch ince thi would involve inding the interection o the beam column during the optimization run, thereby requiring new node element to be generated. Finally, it hould be noted that the bracing member help reduce the lateral diplacement rom 3.8 to jut CONCLUSIONS A imultaneou izing, hape topology optimization methodology i developed ued or the optimal deign o tall building modeled a planar rame. The developed ramework allow or invetigating the deign eiciencie o dierent building ytem uing planar inite element model. Continuou, dicrete oolean deign variable are ued in the context o izing, hape topology optimization. The computed reult yield important building W N c d 1150

10 parameter uch a cro-ectional dimenion propertie, location o tructural joint, member layout via preence, abence location o member. The perormance erviceability contraint include normal tre, hear tre, diplacement, inter-tory drit, buckling, natural requencie. (a) (b) Figure 5. (a) Final deign (b) Compreive tre plot (LC 4) Reult how that eicient planar model can be obtained that atiy perormance requirement in a reaonable amount o time. Finally, it hould be noted that the reult rom a geometrically nonlinear analyi yielded almot the ame reult a that obtained rom linear analyi jutiying the ue o linear analyi. While planar rame provide a wealth o knowledge, the underting i limited by the limitation o the model. uilding are three-dimenional planar rame typically do not contain ome o the important tructural element loor, wall, pecialized ytem uch a tube or core etc. A tributary area approach in computing equivalent planar model load i approximate. In addition, planar model do not account or behavior ound only in three-dimenional ytem uch a member bending hear about two axe, torional moment, torional eigenmode. A logical extenion o the ramework dicued in thi paper i to build ue a three-dimenional inite element model or deign optimization. One o the numerical optimization challenge i the diiculty in inding olution in the oolean-continuou deign variable pace encountered when izing hape continuou deign variable are mixed with topology deign variable that are either oolean or dicrete or both. The computational challenge i to reduce the overall compute time o a obtain olution in a reaonable amount o time. One o the eaily implementable trategie to improve the computational throughput i through parallel computation. In the gradient-baed olution, the computation o numerical derivative thoe during line earch can be parallelized [Rajan et al., 2006]. The reduction in the objective unction i typically much greater in the initial ew iteration ater which the reduction are relatively much maller. Hence uing a coare convergence criteria can cut down on the computational cot without an unacceptable lo o accuracy. In population-baed olution, the parallelization i an embarraingly parallel problem [Rajan Nguyen, 2004]. The GA olution required involving topology optimization required a larger probability o mutation. In thi reearch, repeating chromoome [Chen Rajan, 2000] were not detected o a to avoid carrying out a previou unction evaluation. Implementing thi option would cut down the computational cot ince later generation typically contain a large number o identical member. REFERENCES American Society o Civil Engineer (2010), ASCE: Minimum Deign Load or uilding Other Structure, 7 10, ASCE/SEI, Reton, VA. ASCE (1988), Wind Drit Deign o Steel-Framed uilding: State-o-the-Art Report, ASCE J o Structural Engineering, 114:9, M.M. Ali K. Moon (2007), Structural development in tall building: current trend uture propect, Architect. Sci. Rev., 50.3, W. aker, A. eghini, J. Carrion, A. Mazeika A. Mazurek (2008). Numerical tool in tructural optimization, Proc. IASS-IACM 2008, Ithaca, NY. C.M. Chan J.K.L. Chui (2006). Wind-induced repone erviceability deign optimization o tall teel building. Engineering Structure, 28, C.M. Chan K.M. Wong (2008). Structural topology element izing deign optimization o tall teel ramework uing a hybrid OC GA method. Structural Multi-diciplinary Optimization, 35, S.Y. Chen S.D. Rajan (2000). A Robut Genetic Algorithm or Structural Optimization. Struct Eng Mech, 10-4, S. Fawzia T. Fatima (2010). Delection control in compoite building by uing belt tru outrigger ytem, World Academy o Science, Engineering Technology, 48, D.E. Grieron S. Khajehpour (2002). Method or conceptual deign applied to oice building, J o Computing in Civil Engineering, 16,

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