eleven rigid frames: compression & buckling Rigid Frames Rigid Frames Rigid Frames ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

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1 ELEMENTS O RCHITECTURL STRUCTURES: ORM, BEHVIOR, ND DESIGN DR. NNE NICHOLS SRING 018 lecture eleven rigid rmes: compression & uckling Rigid rmes 1 Lecture 11 S009n nisee.erkeley.edu/godden Rigid rmes 8 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 ehvior Rigid rmes moments get redistriuted delections re smller eective column lengths re shorter very sensitive to settling Rigid rmes 9 Rigid rmes 10 1

2 Rigid rmes resists lterl lodings shpe depends on stiness o ems nd columns 90 mintined Rigid rmes stggered truss rigidity cler stories Rigid rmes 11 Rigid rmes 1 Rigid rmes connections steel concrete Brced rmes pin connections rcing to prevent lterl movements nisee.erkeley.edu/godden Rigid rmes 13 Rigid rmes 14 nisee.erkeley.edu/godden

3 Brced rmes Sher Wlls types o rcing resist lterl lod in plne with wll knee-rcing digonl X K or chevron digonl X sher wlls K (chevron) sher wlls Rigid rmes 15 Rigid rmes 16 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 Column Buckling xilly loded columns long & slender unstle equilirium = uckling sudden nd not good Stility nd Columns 9 Lecture Stility nd Columns 14 Lecture 3

4 Modeling cn e modeled with spring t mid-height when moment rom delection exceeds the spring cpcity... oing criticl lod Eect o Length long & slender short & stuy Stility nd Columns 15 Lecture Stility nd Columns 16 Lecture Buckling Lod relted to delected shpe () shpe o sine wve Euler s ormul smllest I governs Criticl Stress short columns criticl ctul slenderness rtio = L e /r (L/d) Stility nd Columns 17 Lecture criticl EI L rdius o gyrtion = criticl criticl Stility nd Columns 18 Lecture Er r I E Le r L e criticl wek xis E Le r 4

5 Criticl Stresses Eective Length when column gets stuy, y will limit the lod or steel rel world hs lods with eccentricity end conditions ect shpe eective length ctor, K L e K L Stility nd Columns 19 Lecture Stility nd Columns 0 Lecture Brcing rcing ects shpe o uckle in one direction oth should e checked! Centric & Eccentric Loding centric llowle stress rom strength or uckling eccentric comined stresses Stility nd Columns 1 Lecture Column Eccentricity 18 Lecture 3 5

6 Comined Stresses xil + ending mx design mx M cr Mc I e cr. S. Stress Limit Conditions SD interction ormul 1.0 with ixil ending x x y y interction digrm Column Eccentricity 19 Lecture 3 Column Eccentricity Lecture 3 Stress Limit Conditions in relity, s the column lexes, the moment increses - eect ( Mgniiction x ctor) 1.0 Rigid rme nlysis memers see sher xil orce ending V & M digrms plot on outside Column Eccentricity 3 Lecture 3 Rigid rmes 17 6

7 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 rme nlysis BD & M opposite end rections t joints M+ Rigid rmes 18 Rigid rmes 19 Rigid rme Design columns in rmes ends cn e lexile stiness ected y ems nd column = EI/L or the joint G EI l EI l l c is the column length o ech column l is the em length o ech em mesured center to center c Rigid rme Design column eective length, k B Rigid rmes 4 Rigid rmes 19 Lecture 6 S006n 7

8 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 9 Lecture 11 S008n Rigid rmes 30 Lecture 11 S008n Tools Multirme to run nlysis choose nlyze menu Liner plot choose options results choose options Rigid rmes 31 Lecture 11 S008n 8

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