ten rigid frames: compression & buckling Rigid Frames Rigid Frames Rigid Frames

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1 RCHITECTURL STRUCTURES: ORM, BEHVIOR, ND DESIGN DR. NNE NICHOLS SUMMER 017 lecture ten rigid rmes: compression & uckling Rigid rmes rigid rmes hve no pins rme is ll one ody joints trnser moments nd sher typiclly stticlly indeterminte types portl gle Rigid rmes 1 Lecture 10 rchitecturl Structures nisee.erkeley.edu/godden 009n Rigid rmes Rigid rmes Rigid rmes ehvior moments get redistriuted delections re smller eective column lengths re shorter very sensitive to settling Rigid rmes 3 Rigid rmes 4 1

2 Moment Redistriution continuous sls & ems with uniorm loding joints similr to ixed ends, ut cn rotte wl chnge in moment to center = M mx or simply supported em 8 Rigid rmes resists lterl lodings shpe depends on stiness o ems nd columns 90 mintined Rigid rmes 5 Rigid rmes 6 Rigid rmes stggered truss rigidity cler stories Rigid rmes connections steel concrete nisee.erkeley.edu/godden Rigid rmes 7 Rigid rmes 8

3 Brced rmes pin connections rcing to prevent lterl movements Brced rmes types o rcing knee-rcing digonl X K or chevron sher wlls digonl X K (chevron) sher wlls Rigid rmes 9 nisee.erkeley.edu/godden Rigid rmes 10 Sher Wlls resist lterl lod in plne with wll Compression Memers designed or strength & stresses designed or serviceility & delection need to design or stility ility to support speciied lod without sudden or uncceptle deormtions Rigid rmes 11 Rigid rmes 1 3

4 Column Buckling xilly loded columns long & slender unstle equilirium = uckling sudden nd not good Modeling cn e modeled with spring t mid-height when moment rom delection exceeds the spring cpcity... oing criticl lod P Rigid rmes 13 Rigid rmes 14 Eect o Length long & slender short & stuy Buckling Lod relted to delected shpe (P) shpe o sine wve Euler s ormul smllest I governs P criticl EI L Rigid rmes 15 Rigid rmes 16 4

5 Criticl Stress short columns slenderness rtio = L e /r (L/d) rdius o gyrtion = criticl Rigid rmes 17 P criticl criticl Er P ctul r I E Le r L e P criticl wek xis E Le r Criticl Stresses when column gets stuy, y will limit the lod rel world hs lods with eccentricity C c or steel nd llowle stress L e r Rigid rmes 18 C c E y Eective Length end conditions ect shpe eective length ctor, K L e K L Brcing rcing ects shpe o uckle in one direction oth should e checked! Rigid rmes 19 Rigid rmes 0 5

6 Centric & Eccentric Loding centric llowle stress rom strength or uckling eccentric comined stresses Comined Stresses xil + ending mx P Mc I M P e design mx cr cr. S. Rigid rmes 1 Rigid rmes Stress Limit Conditions SD interction ormul 1.0 with ixil ending x x y y interction digrm Stress Limit Conditions in relity, s the column lexes, the moment increses P- eect ( Mgniiction x ctor) 1.0 Rigid rmes 3 Rigid rmes 4 6

7 Rigid rme nlysis memers see sher xil orce ending V & M digrms plot on outside Rigid rme nlysis need support rections ree ody digrm ech memer end rections re equl nd opposite on next memer turn memer like em drw V & M Rigid rmes 5 Rigid rmes 6 Rigid rme nlysis BD & M opposite end rections t joints P Rigid rme Design lods nd comintions usully uniormly distriuted grvity lods worst cse or lrgest moments... wind direction cn increse moments M+ Rigid rmes 7 Rigid rmes 8 7

8 Rigid rme Design rmes & loors rigid rme cn hve sl loors or sl with connecting ems other sls or pltes on columns Rigid rme Design loors pltes & sls one-wy ehvior side rtio > 1.5 strip em two-wy ehvior more complex Rigid rmes 9 Rigid rmes 30 Rigid rme Design columns in rmes ends cn e lexile stiness ected y ems nd column = EI/L EI lc G EI or the joint l c is the column length o ech column l is the em length o ech em mesured center to center l Rigid rme Design column eective length, k B Rigid rmes 31 Rigid rmes 3 8

9 Tools Multirme in clssrooms nd OL Tools Multirme rme window deine rme memers or pre-deined rme select points, ssign supports select memers, ssign section lod window select point or memer, dd point or distriuted lods Rigid rmes 33 Rigid rmes 34 Tools Multirme to run nlysis choose nlyze menu Liner plot choose options results choose options Rigid rmes 35 9