Drift Design Method for High-rise Buildings using Dynamic Resizing Algorithm

Transcription

1 ctbuh.org/papers Tte: Authors: Subject: Keywords: Drft Desgn Method for Hgh-rse Budngs usng Dynac Reszng Agorth Hyo Seon Park, Ph.D Canddate, Yonse Unversty Seo J Hyun, Assocate Professor, Yonse Unversty Structura Engneerng Stee Structure Pubcaton Date: Orgna Pubcaton: Paper Type: CTBUH Seou Conference. Book chapter/part chapter. Journa paper. Conference proceedng. Unpubshed conference paper. Magazne artce. Unpubshed Counc on Ta Budngs and Urban Habtat / Hyo Seon Park; Seo J Hyun

2 Drft Desgn Method for Hgh-rse Budngs usng Dynac Reszng Agorth Seo J Hyun, Hyo Seon Park Ph. D. Canddate, Dept. of Archtectura Eng., Yonse Unversty Assocate Professor, Yonse Unversty Abstract Structura optzaton agorths based on senstvty coeffcents n drft desgn of hgh-rse budngs are far fro beng practca because of coputatona requreents. In recent years, varous drft desgn ethod based on eber dspaceent partcpaton factors have been deveoped for szng ebers to satsfy stffness crtera. However, there s no practca reszng agorth for drft desgn of structures subjected to dynac atera forces. Therefore, n ths paper, a reszng agorth based on dynac dspaceent partcpaton factor obtaned fro response spectru anayss s presented for drft desgn of stee structures subjected to sesc atera forces. The perforance of the agorth s evauated usng a braced frae structure. Keywords: Drft Desgn, Stee Structure, Dynac Dspaceent Partcpaton Factors, Reszng Technques. Introducton The structura desgn of hgh-rse budngs ncudes the process of scheatc desgns, structura anayss, strength desgns, and stffness desgns. Unt now the effectveness of a structura desgn has depended on a desgner s heurstcs based on experence but recenty any researches have been carred out usng optzaton technques to prove the effectveness and autoaton of the structura desgn. As budngs ncrease n heght, the aount of atera requred s deterned by the structura stffness crtera wth respect to nter-story drfts, the axu dspaceent on the top of budng, and natura perods rather than eber strength crtera. Athough any drft contro ethods have been deveoped wth the bass on exstng optzaton agorths, the appcaton to practca affars s excessvey restrcted. Reszng technque whch uses the unt oad ethod had been deveoped for structures subjected to statc oad by Baker (), Forrest-Brown and Saa (), Charney (), and Park and Park (), and then the part s apped to practca affars. On the other hand, a ot of dffcutes st rean n appyng the drft desgn of the structures subjected to dynac forces to practca affars, even f the researches regardng the dynac senstvty anayss and optzaton technques are actvey advanced. In ths paper, a practca dynac reszng agorth w be deveoped to contro the atera dspaceent of a stee frae structure subjected to a sesc force. Foruaton of reszng agorth Dynac dspaceent partcpaton factors The drft desgn ethod whch uses reszng technque s based on the prncpe of vrtua work and deternes the redstrbuted quantty by the stran whch s accuuated n each eber. Fro the unt oad ethod, the dspaceent of structure can be found by sung dynac dspaceent partcpaton factors (DDPFs) for a ebers n a structure: Contact Author: Hyo Seon Park, Professor, Dept. of Archtectura Engneerng, Yonse Unversty, Shnchon-dong, Seodaeun-gu, Seou, -, Korea Te:(-)- Fax:(-)- e-a: hspark@yonse.ac.kr N N M M δ = = + S U S U δ dx = = EA EI V V T T dx S U S U + a dx+ dx GA GI p () CTBUH October ~, Seou, Korea

3 where N, M, V, and T are the stress resutants of the th eber due to the actua oad or the unt oad respectvey. A, I and I p are the cross-sectona area, the oent of nerta, and the poar oent of nerta of the th eber. The stress resutants due to the actua oad and the unt oad are dentfed by the superscrpts S and U, respectvey. In equaton (), s the tota nuber of structura ebers n a structure and E and G are the oduus of eastcty and the shear oduus of eastcty, respectvey. δ s the dspaceent to be controed and δ s the DDPF defned by each eber s contrbuton to the dspaceent, whch conssts of four coponents: axa, bendng, shear and torsona dspaceent coponents for a ebers n a structure. In ths paper, DDPF s cacuated by usng response spectru anayss (RSA). In RSA, the axu response (Δ nax ) of the nth story s gven n the foowng for. =Φ Y = L S Φ () nax n nax n dn n where Φ n, L n, and S dn are the ode shape, the ode partcpaton factor and the spectra dspaceent of the nth ode. The atera dspaceent (Δ srss ) can be presented by the square root of the su of the squares (SRSS) of the responses n each ode. N = ( ) srss n= n ax () Modfcaton factor In ths paper, the drft contro technque based on DDPF s deveoped fro ntroducng cross-sectona odfcaton factor (β ) as a desgn varabe. The optzaton probe consdered n ths research s presented n the foowng for. Mnze δ = = δ β () proportona to the change of the weght of the eber. The constraned optzaton probe n equatons () and () can be transfored nto an unconstraned optzaton probe by ntroducng the Lagrange utper. δ δ λ β ρ ρ = + L AL AL = β = = () where λ L s the Lagrange utper. In ths optzaton probe, the dspaceent s nzed wthout changng the weght of a structure at the fna stage of the desgn process. Takng dervatves of the transfored objectve functon wth respect to β and λ L, et the equatons equa to zero. δ δ = + λρ, L AL = = β β δ = = βρ AL ρal λ L = = () () Accordng to equaton () and (), the odfcaton factor (β ) s cacuated n the foowng for. ρal j = δ ρal = δ β = =, ρ AL () where s the tota nuber of structura ebers n a structure. The nta dspaceent to be controed s reduced to δ by equaton () and the weght of each eber s redstrbuted wthout the change n the tota weght of the structure. For over a structura desgn ode for hgh-rse budngs, the proposed drft desgn ethod usng the reszng agorth s cobned wth usua strength desgn odue as shown n Fg. Subject to = = βρal = ρal () where δ s the odfed dspaceent to be controed and δ s the nta DDPF of each eber. A, ρ, and L are the cross-sectona area, the densty and the ength of the th eber. In ths foruaton, t s assued that the DDPF of each eber s nversey. Exape Ths exape s a -story braced stee frae structure. The ode wth the heght of. has unt story heght as., except the frst story equa to.. The base densons of the ode n the x- and y-drectons are and respectvey. CTBUH October ~, Seou, Korea

4 A X - Braced frae. Y X. Fg. -story braced stee structure Fg. Drft desgn ode of hgh-rse budngs The oads consst of a dead oad. kn/, a ve oad. kn/, and an earthquake oad. The sesc oad s presented wth the response spectru scaed proportonay down the northern and southern drecton coponent of the earthquake, whch occurs at E Centro n Unted States n, wth the axu ground acceeraton equa to. G and % dapng rato. A unt oad s apped at pont A where the axu dspaceent occurs. Before appyng the drft desgn ethod, RSA s used for dynac anayss and the coony used desgn specfcaton, aowabe stress desgn (ASD), s used for prenary structura eber desgn (AIK, ). Tabe Dspaceent partcpaton factors Meber Prenary reszng Drft Desgn Re-anayss Coun.... Grders.... Brace.... Tota.... Tabe Structura weght Meber Prenary reszng drft desgn Re-anayss Coun.... Grders.... Brace.... Tota.... Fro the dynac anayss wth the prenary desgn, the atera dspaceent of. c at the top of the structure s estated by addng up the eber dspaceent partcpaton factors of a ebers as gven n Eq. (). By appyng the drft desgn ode, the atera dspaceent of.c at the top of the structure s estated. The atera dspaceent s reduced by.% of the nta drft wthout changng the structura weght. Meber dspaceent partcpaton factors and structura weght are shown n Tabes and, respectvey. Fro these resuts, t s cear that the atera of grders shoud be redstrbuted to couns and brace ebers. CTBUH October ~, Seou, Korea

5 For the drft desgn, no addtona structura weghts are requred to satsfy the dspaceent constrants (H/) at the top of structure. In the fna stress check stage n Fg., the structura weght of couns s ncreased and the dspaceent s decreased by.c. The structura anayss usng coerca soft-ware wth the odfed cross- sectona propertes gves a dspaceent of.c. The error n the dspaceents fro the exact anayss and the reszng agorth for ths exape s found to be approxatey %. In addton to the axu atera dspaceent, nter-story drft ust not exceed a certan t. Fro the response spectru anayss wth the prenary desgn, the axu nter-story drft of.c.% of the heght of a typca story s found at th story eve. Based on the drft desgn ode, the axu nter-story of.c of.% of the heght of a typca story s found at the th story eve. The dstrbutons of atera dspaceent and nter-story drft through the heght of the structure before and after appcaton of the drft desgn ode are shown n Fgs. and. The change of natura perods and ass partcpaton factor by appyng drft desgn ode shown n Fgs. and. Natura perods are decreased at st ~th odes, and ass partcpaton factors are decreased at st ode, but ncreased at nd~th odes. Prenary drft desgn Dspaceent (c) Fg. Dstrbuton of Latera Dspaceents aong the Heght of the Budng (Sec)... Prenary drft desgn st nd rd th th Prenary drft desgn Fg. Natura Perods Prenary drft desgn (%)... Inter-story drft (c) st nd rd th th Fg. Inter-story drft Fg. Mass partcpaton factors CTBUH October ~, Seou, Korea

6 Fg. (a) st ode shape Prenary drft desgn... st ode Fg. (b) nd ode shape Prenary drft desgn -... nd ode Fg. (c) rd ode shape Prenary drft desgn -... rd ode Fro these resuts, t s cear that the decrease of dspaceent s argey dependent on the decrease of natura perods. The change of ode shape by appyng drft desgn ode shown Fg..(a),(b),(c). Mode shapes are sar before and after appyng the drft desgn ode.. Concuson In ths paper, the reszng agorth based on the unt oad ethod and dynac anayss s deveoped and apped to drft desgn of ta stee structures subjected to dynac atera forces. Durng the drft desgn process, the actve ebers were dentfed by DDPF nstead of cacuatng coputatonay ntensve senstvty nforaton. As deonstrated n the exapes, the dynac reszng agorth shortens the frst perod and thus effectvey contros the dspaceent. Acknowedgeent Ths atera s based on work sponsored by Mnstry of Constructon & Transportaton of Korea under grant CA-A-, whch s gratefuy acknowedged. References AIK.. Standard Desgn Loads for Budngs, Archtectura Insttute of Korea, Seou, Korea. Baker, W. F. () Szng Technques for Latera Systes n Mut-story Stee Budngs, Proceedngs fro the conference: Ta Budngs and and Beyond, - Chareny, F. A. () The Use of Dspaceent Partcpaton Factors n the Optzaton of Drft Controed Budngs, Proceedngs of the conference on Ta Budngs n Sesc Regons, Los Angees, CA, - Forrest-Brown, G. and Saa, B. () Practca Optzaton of Fraed Structures Usng Vrtua Work Prncpas, th Word Congress, Ta budngs: and Beyond, Hong Kong Conventon and Exhbton Center, CTBUH, - Park Hyo Seon, and Park Ch L. () Drft Contro of Hgh-rse Budngs wth Unt Load Method, The Structura Desgn of Ta Budngs, Vo., No., - Park Hyo Seon, and Seo J Hyun. () Drft Desgn of Stee-frae Shear-wa Systes for Ta Budngs, The Structura Desgn of Ta Budngs, Vo., No., - CTBUH October ~, Seou, Korea