CSI Analysis Reference Manual

1 CSI Analysis Reference Manual CSI Anal y sis Reference ManualFor SAP2000 , ETABS , SAFE and CSiBridge ISO# GEN062708M1 ley, Cal i for nia, USAJuly 2016 COPYRIGHTCopy right Com put ers & Struc tures, Inc., 1978-2016 All rights re CSI Logo , SAP2000 , ETABS , SAFE , CSiBridge , and SAPFire arereg is tered trade marks of Com put ers & Struc tures, Inc. Model-AliveTM and Watch& LearnTM are trade marks of Com put ers & Struc tures, Inc. Win dows is a reg is -tered trade mark of the Microsoft Cor po ra tion. Adobe and Ac ro bat are reg is -tered trade marks of Adobe Sys tems In cor po com puter pro grams SAP2000 , ETABS , SAFE , and CSiBridge and allas so ci ated doc u men ta tion are pro pri etary and copy righted prod ucts. World widerights of own er ship rest with Com put ers & Struc tures, Inc. Unlicensed use of thesepro grams or re pro duc tion of doc u men ta tion in any form, with out prior writ ten au -tho ri za tion from Com put ers & Struc tures, Inc.

2 , is ex plic itly pro hib ited. No part ofthis pub li ca tion may be re pro duced or dis trib uted in any form or by any means, orstored in a da ta base or re trieval sys tem, with out the prior ex plicit writ ten per mis -sion of the pub ther in for ma tion and cop ies of this doc u men ta tion may be ob tained from:Com put ers & Struc tures, (for gen eral in for ma tion)sup (for tech ni cal sup port)DISCLAIMER CON SID ER ABLE TIME, EF FORT AND EX PENSE HAVE GONEINTO THE DE VEL OP MENT AND TEST ING OF THIS SOFT EVER, THE USER AC CEPTS AND UN DER STANDS THATNO WAR RANTY IS EX PRESSED OR IM PLIED BY THE DE VEL -OP ERS OR THE DIS TRIBU TORS ON THE AC CU RACY OR THERE LI ABIL ITY OF THE PRO GRAMS THESE PRODUCTS. THESE PROD UCTS ARE PRAC TI CAL AND POW ER FUL TOOLSFOR STRUC TURAL DE SIGN. HOWEVER, THE USER MUST EX -PLIC ITLY UN DER STAND THE BA SIC AS SUMP TIONS OF THESOFT WARE MOD EL ING, ANAL Y SIS, AND DE SIGN AL GO -RITHMS AND COM PEN SATE FOR THE AS PECTS THAT ARENOT IN FOR MA TION PRO DUCED BY THE SOFT WARE MUST BECHECKED BY A QUAL I FIED AND EX PE RI ENCED EN GI EN GI NEER MUST IN DE PEND ENTLY VER IFY THE RE -SULTS AND TAKE PROFESSIONAL RE SPON SI BIL ITY FOR THEIN FOR MA TION THAT IS Thanks are due to all of the nu mer ous struc tural en gi neers, who over theyears have given valu able feed back that has con trib uted to ward the en -hance ment of this prod uct to its cur rent cial rec og ni tion is due Dr.

3 Ed ward L. Wil son, Pro fes sor Emeri tus,Uni ver sity of Cali for nia at Ber keley, who was re spon si ble for the con -cep tion and de vel op ment of the origi nal SAP se ries of pro grams andwhose con tin ued origi nal ity has pro duced many unique con cepts thathave been im ple mented in this ver sion. Ta ble of Con tentsChap ter IIn tro duc tion1 Anal y sis Fea tural Anal y sis and De This Man po graph i cal Con ven for Def i ni for Vari able ics for Math e mat i cal Vari ics for Em pha i tal ized lio graphic Ref er ter IIOb jects and El e ments7Ob jects and El e ter IIICo or di nate Sys tems11 Over Co or di nate Sys ward and Hor i zon tal Di rec fin ing Co or di nate Sys tor Cross Prod fin ing the Three Axes Us ing Two Vec iLo cal Co or di nate Sys ter nate Co or di nate Sys lin dri cal and Spher i cal Co or di ter IVJoints and De grees of Free dom21 Over el ing Con sid er cal Co or di nate Sys vanced Lo cal Co or di nate Sys er ence Vec fin ing the Axis Ref er ence Vec fin ing the Plane Ref er ence Vec ter min ing the Lo cal Axes from the Ref er ence Vec Co or di nate An grees of Free able and Un avail able De grees of Free strained De grees of Free strained De

4 Grees of Free ing Re straints and Con straints Not Rec om tive De grees of Free De grees of Free straint Sup Sup lin ear Sup trib uted Sup Re ac Re ac Dis place ment straint Dis place Dis place port Dis place er al ized Dis place gree of Free dom Out sem bled Joint Mass Out place ment Out Out e ment Joint Force Out CSI Analysis Reference ManualChap ter VCon straints and Welds49 Over Con Con nec tiv cal Co or di nate Sys straint Equa Def i ni a phragm Con Con nec tiv cal Co or di nate Sys straint Equa Con Con nec tiv cal Co or di nate Sys straint Equa Def i ni Con Con nec tiv cal Co or di nate Sys straint Equa Con Con nec tiv cal Co or di nate Sys straint Equa Con Con nec tiv cal Co or di nate Sys lected De grees of Free straint Equa cal Con Con nec tiv Lo cal Co or di nate Sys lected De grees of Free straint Equa to matic Mas ter ness, Mass, and cal Co or di nate Sys straint Out iiiTable of ContentsChap ter VIMa te rial Prop er ties69 Over cal Co or di nate Sys and tro pic Ma te ri ax ial Ma te ri Ma te ri Ma te ri per a ture-De pend ent Prop er e ment Ma te rial Tem per a Den Den te rial Damp Damp cous Pro por tional Damp Pro por tional Damp lin ear Ma te rial Be hav sion and Com pres ter pli ca tion and Dilitational An ter esis Mod bone Curve (Ac tion vs.)

5 De for ma tion)..86Cy clic Be hav tic Hys ter esis ne matic Hys ter esis grad ing Hys ter esis Hys ter esis Hys ter esis crete Hys ter esis Hard en ing Hys ter esis tro pic Hys ter esis i fied Dar win-Pecknold Con crete pend ent Prop er er te gra tion Con CSI Analysis Reference ManualChap ter VIIThe Frame El e ment105 Over Con nec tiv ser tion grees of Free cal Co or di nate Sys gi tu di nal Axis fault Ori en ta or di nate An vanced Lo cal Co or di nate Sys er ence Vec ter min ing Trans verse Axes 2 and tion Prop er cal Co or di nate Sys te rial Prop er met ric Prop er ties and Sec tion to matic Sec tion Prop erty Cal cu la tion Prop erty Da ta base tion-De signer Sec di tional Mass and matic Sec erty Mod i fi Prop erty ser tion cal Off Fac fect upon Non-pris matic El e fect upon In ter nal Force Out fect upon End Re Re sta ble End Re fect of End Off Prop

6 Erty lin ear Prop er sion/Com pres sion Lim tic vTable of ContentsGrav ity cen trated Span trib uted Span In ten jected per a ture for ma tion get-Force ter nal Force Out fect of End Off Out ter VIIIH inge Prop er ties147 Over Prop er tic De for ma tion ing the of P-M2-M3 tro pic P-M2-M3 met ric P-M2-M3 ber P-M2-M3 ter esis Mod to matic, User-De fined, and Gen er ated Prop er to matic Hinge Prop er y sis Mod el pu ta tional Con sid er y sis Re ter IXThe Ca ble El e ment165 Over Con nec tiv Cal cu la ble vs. Frame El e ber of Seg grees of Free CSI Analysis Reference ManualLo cal Co or di nate Sys tion Prop er te rial Prop er met ric Prop er ties and Sec tion ity trib uted Span per a ture and De for ma tion get-Force lin ear Anal y e ment Out ter XThe Shell El e ment177 Over mo ge Con nec tiv Guide Con grees of Free cal Co or di nate Sys mal Axis fault Ori en ta e ment Co or di nate An vanced Lo cal Co or di nate Sys er ence Vec ter min ing Tan gen tial Axes 1 and tion Prop er Sec tion Sec tion mo ge neous Sec tion Prop er ered Sec tion Prop erty Mod i fi Prop erty Off sets and Thick ness Off fect of Joint Off sets on the Lo cal ness viiTable of ity form face Pres sure per a ture ter nal Force and Stress Out ter XIThe Plane El e ment215 Over Con nec tiv grees of Free cal Co or di nate Sys and tion Prop er tion te rial Prop

7 Er te rial An com pat i ble Bend ing ity face Pres sure Pres sure per a ture Out ter XIIThe Asolid El e ment225 Over Con nec tiv grees of Free cal Co or di nate Sys and tion Prop er tion te rial Prop er te rial An CSI Analysis Reference ManualAxis of Sym me and Thick com pat i ble Bend ing ity face Pres sure Pres sure per a ture tate Out ter XIIIThe Solid El e ment237 Over Con nec tiv gen er ate Sol grees of Free cal Co or di nate Sys vanced Lo cal Co or di nate Sys er ence Vec fin ing the Axis Ref er ence Vec fin ing the Plane Ref er ence Vec ter min ing the Lo cal Axes from the Ref er ence Vec e ment Co or di nate An and Prop er te rial Prop er te rial An com pat i ble Bend ing ity face Pres sure Pres sure per a ture Out ter XIVThe Link/Sup port El e ment Ba sic251 Over ixTable of ContentsJoint Con nec tiv ver sion from One-Joint Ob jects to Two-Joint El e El e grees of Free cal Co or di nate Sys gi tu di nal Axis fault Ori en ta or di nate An vanced Lo cal Co or di nate Sys Ref er ence Vec Ref er ence Vec ter min ing Trans verse Axes 2 and ter nal De for ma port Prop er cal Co or di nate Sys ter nal Spring Force-De for ma tion Re la tion e ment In ter nal cou pled Lin ear Force-De for ma tion Re la tion of Lin ear/Non lin ear Prop er pled Lin ear Prop De grees of Free ity ter nal Force and De for ma tion Out ter XVThe Link/Sup port El e ment Ad vanced275 Over lin ear Link/Sup port Prop er ear Ef fec tive Stiff cial Con sid er ations for Modal Anal y ear Ef fec tive Damp po nen tial Maxwell Damper Prop Maxwell Damper Prop tion-Spring Damper Prop Prop Prop Plas tic ity Prop ear Elas tic Prop CSI Analysis Reference ManualMulti-Lin ear Plas tic Prop (Rub ber)

8 Iso la tor Prop tion-Pen du lum Iso la tor Prop ial Be hav Be hav ear Be hav ble-Act ing Fric tion-Pen du lum Iso la tor Prop ial Be hav Be hav ear Be hav ple-Pen du lum Iso la tor Prop ial Be hav Be hav ear Be hav lin ear De for ma tion quency-De pend ent Link/Sup port Prop er ter XVIThe Ten don Ob ject309 Over om e dons Mod eled as Loads or El e nec tiv grees of Free cal Co or di nate Sys Lo cal Co or di nate Sys u ral Lo cal Co or di nate Sys tion Prop er te rial Prop er met ric Prop er ties and Sec tion sion/Com pres sion Lim stress ity per a ture for ma tion get-Force ter nal Force Out xiTable of ContentsChap ter XVIILoad Pat terns321 Over Pat terns, Load Cases, and Load Com bi na fin ing Load Pat or di nate Sys tems and Load Com po fect upon Large-Dis place ments Anal y Dis place ment ity cen trated Span trib uted Span don Pre stress form face Pres sure Pres sure per a ture for ma tion get-Force tate Pat from Spec i fied Load Pat a tive ti ple Mass to mated Lat eral cel er a tion ter XVIIILoad Cases341 Over of Anal y quence of Anal y ning Load ear and Non lin ear Load ear Static Anal y Static Anal y CSI Analysis Reference ManualLin ear Buck ling Anal y Com bi na tions (Com bos).

9 351 Con trib ut ing of Com am re spon di tional Con sid er En ergy Re tion Solv vi ron ment Vari ables to Con trol Anal y cess ing the As sem bled Stiff ness and Mass Ma tri ter XIXM odal Anal y sis365 Over Anal y ber of quency to matic Shift ver gence Tol er rec tion tor Anal y ber of ing Load Vec ber of Gen er a tion Cy Anal y sis Out ri ods and Fre quen tic i pa tion Fac tic i pat ing Mass Ra and Dy namic Load Par tic i pa tion Ra ter XXRe sponse-Spec trum Anal y sis383 Over cal Co or di nate Sys sponse-Spec trum Func Damp Com bi na xiiiTable of ContentsPe ri odic and Rigid Re so lute Sum Ten-Per cent Dou ble-Sum rec tional Com bi na so lute Sum sponse-Spec trum Anal y sis Out ing and Ac cel er a Am pli Re ac ter XXILin ear Time-His tory Anal y sis397 Over fin ing the Spa tial Load Vec fin ing the Time Func tial Con di Time-His tory Anal y Damp rect-In te gra tion Time-His tory Anal y In te gra tion Pa ram e ter XXIIGeo met ric Nonlinearity409 Over lin ear Load P-Delta Ef Forces in the Frame El e Forces in the Link/Sup port El e El e tial P-Delta Anal y ing Struc ble Struc Tow Dis place CSI Analysis Reference ManualAp pli ca tial Large-Dis place ment Anal y ter XXIIINon lin ear Static Anal y sis425 Over por tant Con sid er Ap pli ca tion Con Con place ment Con tial Con di put ing Mul ti ple lin ear So lu tion Con i mum To tal i mum Null (Zero) Step ping Con lin ear It er a Search Op Push over Anal y Con struc ing Sec tion Prop er put am get-Force It er a ter XXIVNon lin ear Time-His tory Anal y sis447 Over tial Con di lin ear Modal Time-His tory Anal y sis (FNA).

10 451 Ini tial Con di port Ef fec tive Stiff Su per po si Damp er a tive So lu xvTable of ContentsStatic Pe lin ear Di rect-In te gra tion Time-His tory Anal y In te gra tion Pa ram e tial Con di lin ear So lu tion Con ter XXVFre quency-Do main Anal y ses465 Over monic Mo quency Do of Damp fin ing the Spa tial Load Vec quency Anal y am tral-Den sity Anal y am ter XXVIMov ing-Load Anal y sis477 Over view for ing-Load Anal y sis in Mod ing-Load Anal y sis Pro ce ter line and Di rec cen tric trif u gal Ra te rior and Ex te rior flu ence Lines and Sur hi cle Live tri bu tion of form i mum Edge Dis CSI Analysis Reference ManualDi rec tions of Load strict ing a Ve hi cle to the Lane pli ca tion of Loads to the In flu ence Sur Ef pli ca tion of Loads in Multi-Step Anal y eral Ve hi i fi ca ing the Ve hi hi cle Re sponse Com po per struc ture (Span) Mo ment.