Structural Dynamcs and Earthuake Engneerng Course 9 Sesmc-resstant desgn of structures (1) Sesmc acton Methods of elastc analyss Course notes are avalable for download at http://www.ct.upt.ro/users/aurelstratan/ Sesmc-resstant desgn of structures P100-1/013 "Cod de proectare sesmcă P100 Partea I - Preveder de proectare pentru clădr" Eurocode 8 "Desgn of structures for earthuake resstance - Part 1: General rules, sesmc actons and rules for buldngs" Fundamental reurements: Lfe safety: suffcent safety margn over local or global collapse of the structure P100-1/013: assocated earthuake: 5 years return perod Eurocode 8: assocated earthuake: 475 years return perod Damage lmtaton. O occurrence of damage and the assocated lmtatons of use, wth dsproportonately hgh cost n comparson wth the costs of the structure tself P100-1/013: assocated earthuake: 40 years return perod Eurocode 8: assocated earthuake: 95 years return perod 1
Ultmate lmt states Fundamental reurements (lfe safety and damage lmtaton) are verfed by checkng the structure for two lmt states: Ultmate Lmt State (ULS) assocated to collapse and other forms of structural degradaton that may endanger human lves verfcaton of ULS mples a balance between strength and ductlty Servceablty Lmt State (SLS) assocated to degradatons, that lead to lmtaton of use lmtaton of structural and non-structural damage generally, check for SLS nvolves lmtaton of nterstorey drfts, n order to protect non-structural elements, eupments, etc. Sesmc acton: elastc response spectrum atonal terrtory: dvded n zones of constant sesmc hazard Sesmc hazard for desgn s expressed by horzontal peak ground acceleraton a g (determned for the return perod assocated to ULS)
Elastc response spectrum Sesmc acton on the ground surface expressed by pseudo-acceleraton response spectra horzontal components 1 vertcal component Local ste condtons affect: amplfcaton of acceleraton freuency content of the ground moton Control perods T C, s 0.7 1.0 1.6 T B, s 0.14 0.0 0.3 T D, s 3.0 3.0.0 Elastc spectrum: control perod T C P100-1/006: T C specfed at a macrosesmc scale 3
Elastc spectrum: normalzed form (T) Elastc response spectrum: S (T ) a ormalzed form of the response spectrum: e g T Elastc spectrum: normalzed form (T) 4
Local ste condtons: Eurocode 8 Behavour factor Most structures are able to survve a major earthuake wthout collapse, but wth mportant structural degradatons due to: ductlty of the structure (capacty to deform n the nelastc range) overstrength desgn of structures for a fracton of the strength necessary for an elastc response (behavour factor - ) Desgn codes: a sngle force reducton factor dependng on materal and structural typology F D F Fe R R y F y 1 R y Dy De=Dm D 1 5
Force reducton factors V F V e raspunsul nfnt elastc raspunsul real V y V 1 V d raspunsul dealzat R Sd S V y e u Force reducton factors u - ultmate dsplacement of the system y - dsplacement at global yeld V e - base shear force correspondng to an nfntely elastc response V y - yeld base shear force V 1 base shear force at frst yeld n the structure V d - desgn base shear force Global ductlty of the structure u y 6
Force reducton factors Ductlty-related force reducton factor Ve Vy Overstrength: redundancy V V S y d V V R y 1 S R Sd desgn governed by non-sesmc loads lmtaton of the number of dfferent cross-sectons use to smplfy fabrcaton and erecton a real strength larger than the nomnal one Sd 1 V V d Total reducton factor (behavour factor): S Sd R Force reducton factors Force reducton factors: perod dependent 1 S To smplfy, can be consdered constant In realty, depends on: propertes of the ground moton (T C ), n relaton wth perod of vbraton of the structure 7
Desgn response spectrum for elastc analyss 0T T B : 0 1 Sd ( T ) a g 1 T TB T> T B : ( T ) Sd ( T ) ag pseudo-accelerate, g 0.8 0.6 0.4 0. P100-1/013, T C =1.6 s, a g =0.30g S e S d, =6 0 0 1 3 4 T, s In desgn: elastc analyss Elastc desgn methods Alternatves: lateral force method (euvalent statc force method) modal response spectrum analyss (spectral analyss) 8
The euvalent statc force method Can be used for structures that: can be modeled usng two planar models for each prncpal drecton and whose sesmc response s not nfluenced sgnfcantly by hgher modes of vbraton (structures wth T 1 1.5 sec, regular n elevaton, and wth heght less than 30 m) A smplfed spectral analyss, that consders the contrbuton of the fundamental mode only V * M A F S T m bn n n b I, e d 1 (V b1 F b ; A 1 I,e S d (T 1 ); M 1* m ) The euvalent statc force method Base shear force (P100-1/013): F S T m b I, e d 1 S d (T 1 ) - ordnate of the desgn response spectrum correspondng to fundamental perod T 1 m - total mass of the structure I,e mportance factor of the buldng - correcton factor (contrbuton of the fundamental mode of vbraton usng the concept of effectve modal mass): = 0.85 f T 1 T C and the structure s hgher than two levels, and = 1.0 n all other cases 9
The euvalent statc force method Euvalent statc force at storey n mode n: mn where 1 fn nmn An n m 1 n M * n 1 1 mn m n usng the expresson A V M * n bn n mn mn 1 1 mn n n n n n bn bn n m n m m n n 1 1 1 f m A m V V The euvalent statc force method Euvalent statc forces f Lateral force at storey (P100-1/013): F V n bn F b m 1 1 m s n m n m s F b - base shear force n the fundamental mode of vbraton s - dsplacement of the mass n the fundamental mode shape n - number of storeys n the structure m - storey mass 10
The euvalent statc force method Fundamental mode shape can be approxmated by a horzontal dsplacements ncreasng lnearly wth heght F F b 1 m z m z F m z Prelmnary desgn of structures wth heght <40m 3 4 1 Ct H C t = 0.085 moment-resstng steel frames, C t = 0.075 moment resstng renforced concrete frames or steel eccentrcally braced frames, C t = 0.05 all other structures. T F b Modal response spectrum analyss Procedure: see course 8 Spectral analyss s used for structures for whch the lateral force method cannot be appled umber of modes that need to be consdered n analyss: the sum of effectve modal masses for the consdered modes should amount to at least 90% of the total mass of the structure, all modes wth effectve modal mass larger than 5% of the total mass of the structure were consdered n analyss Combnaton of modal response: Sum of absolute values (ABS) Suare root of sum of suares (SRSS) response n two modes k and k+1 can be consdered ndependent f T k and T k+1 check the followng relatonshp: Tk 1 0.9Tk Complete uadratc combnaton (CQC) 11