seven rigid frames: analysis & design Rigid Frames Rigid Frames Rigid Frames composed of linear elements member geometry fixed at joints

Transcription

1 APPLIED ARCHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS ALL 2018 lecture seven rigid rmes: nlysis & design nisee.erkeley.edu/godden Rigid rmes composed o liner elements memer geometry ixed t joints no reltive rottion stticlly indeterminte see sher xil orces ending moments Rigid rmes 1 Applied Architecturl Structures 2009n Rigid rmes 2 Rigid rmes rigidity end constrints smller horizontl memers lrger verticl memers Rigid rmes ehvior Rigid rmes 3 Rigid rmes 4 1

2 Rigid rmes moments get redistriuted delections re smller eective column lengths re shorter Rigid rmes resists lterl lodings shpe depends on stiness o ems nd columns 90 mintined Rigid rmes 5 Rigid rmes 6 Rigid rme Anlysis memers see sher xil orce ending V & M digrms plot on outside Rigid rme Anlysis 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 7 Rigid rmes 8 2

3 Rigid rme Anlysis BD & M M+ opposite end rections t joints P Anlysis Methods computer-sed mtrix nlysis or inite element nlysis equilirium support conditions joint loctions reltive stiness o memers output delections memer orces Rigid rmes 9 Rigid rmes 10 Anlysis Methods RAM Anlysis Methods pproximte methods presume where inlection points occur in deormed shpe these points hve zero moment portl method hinge is plced t the center o ech girder hinge is plced t the center o ech column sher t interior columns is twice tht o exterior columns Rigid rmes 11 Rigid rmes n 3

4 Rigid rmes memer sizes do ect ehvior loction o inlection points criticl Sideswy trnsltion with verticl lod Rigid rmes 13 Rigid rmes 14 Support Settlements moments induced Multistory rme Anlysis cntilever method (pproximte) point o inlection t midspn o ech em point o inlection t midheight o ech column xil orce in ech column proportionl to the horizontl distnce o tht column rom the centroid o ll columns in the story centroids re verge loctions Rigid rmes 15 Rigid rmes n 4

5 Multistory rme Anlysis cntilever method (pproximte) Rigid rme Design - Types Rigid rmes 17 Rigid rmes 18 Rigid rme Design mterils steel monolithic concrete lminted wood orms smll single story, gled rme, portl, hinged... lrge - multistory Riol Prish Church, Alto Alvr Rigid rme Design orms smll lrge nisee.erkeley.edu/godden Rigid rmes n Rigid rmes 20 5

6 Rigid rme Design stggered truss rigidity cler stories Rigid rme Design connections steel concrete nisee.erkeley.edu/godden Rigid rmes 21 Rigid rmes 22 Rigid rme Design considertions need rme? minimize moment (ects memer size) incresing stiness redistriutes moments limits delections joint rigidity support types Rigid rme Design lod comintions worst cse or lrgest moments... wind direction cn increse moments + = Rigid rmes 23 Rigid rmes 24 6

7 Comined Stresses em-columns hve moments t end oten due to eccentric lod Comined Stresses & Design xil + ending mx P A M P Mc I e design mx cr cr. S. Rigid rmes 25 Rigid rmes 26 Eccentric Loding ind e such tht the minimum stress = 0 P Pe c min 0 A I re deined y e rom centroid is the kern Bixil Bending when there is moment in two directions M P 1 e 1 M P 2 e 2 P M1y M 2z mx A I I ixil ending y B h z e 1 e 2 A P x + + = x y z result M 2 P e 2 M1 P e1 Rigid rmes 27 Rigid rmes 28 7

8 Stress Limit Conditions ASD interction ormul 1.0 with ixil ending 1 Stress Limit Conditions in relity, s the column lexes, the moment increses P- eect P x x y y ( Mgniiction ctor ) 1.0 Rigid rmes 29 Rigid rmes 30 Design or Comined Stress stisy strength stility pick section Tools Visul Anlysis (VA Edu) in open ccess ls nd VOAL nd Rigid rmes 31 Rigid rmes 32 Applied Architecturl Structures 8

9 Tools Visul Anlysis (VA Edu) model view / structure t grid nd units deine rme memers or pre-deined rmes (Crete) columns up, ems let-right select points, ssign supports select memers, ssign memer shpes & ny connection types Tools Visul Anlysis (VA Edu) loding t select points, dd point lod (edit lod cse with no sel weight) results view sttus r results ilter memer grph choose options report view - choose nd drg options Rigid rmes 33 Applied Architecturl Structures Rigid rmes 34 9