five trusses & columns Trusses Trusses Trusses ancient (?) wood 1800 s analysis efficient long spans

Transcription

1 APPLIED ARCHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 017 lecture five ancient (?) wood 1800 s analysis efficient long spans trusses & columns Columns & 1 Lecture 5 Applied Architectural Structures F010abn Columns & comprised of straight members geometry with triangles is stable loads applied only at joints force members compression tension Columns & members connected by 3 joints more members need 1 more joint Columns & 4 b n 3 ( n j 3) 1

2 Truss Analysis visualize compression and tension from deformed shape Columns & 5 F 0 F 0 M 0 Truss Analysis Method of Joints F 0 Method of Sections F 0 M 0 Graphical Methods all rely on equilibrium of bodies internal equilibrium Columns & 6 Truss Connections pins can t resist rotation require lateral bracing consider buckling indeterminate trusses extra members solvable with statics cables can t hold compression displacement methods elastic elongation too few members, unstable One Maritime Plaza, SOM 1964 Columns & 7 Columns & 8

3 Space pyramid tetrahedron Space connections supports Columns & 9 Columns & 10 Crystal Cathedral, Johnson 1980 Expo 70 Festival Plaza Tange & Kamiya 1970 Columns & 11 Columns & 1 3

4 Jacob K. Javits Convention Center I.M. Pei 1980 Jacob K. Javits Convention Center Columns & 13 Columns & 14 Louvre Museum Addition, Pei 1989 Louvre Museum Addition, Pei 1989 Columns & 15 Columns & 16 4

5 Truss Design variables spans depths length of members spacing transverse beam spacing pattern materials; size & strength efficiency common designs Columns & 17 Columns & 18 common designs Truss Configurations external factors roof form openings basic forms symmetrical loading maximum bending cables in tension only Columns & 19 Columns & 0 5

6 Truss Configurations parallel chords verticals common longer members in tension often cross members - indeterminate funicular shapes efficient similar sized forces some zero force Truss Configurations special shapes Vierendeel frame depth depends on loads, span rules of thumb, charts structurally tension members can have holes! compression members can buckle 3D trusses stable Columns & 1 Columns & Tools Multiframe Tools Multiframe in classrooms and open access labs frame window define truss members or pre-defined truss select points, assign supports select members, assign section & assign pin ends load window select points, add point load Columns & 3 Columns & 4 6

7 Tools Multiframe to run analysis choose Analyze menu Linear plot choose options results choose options Columns compression members column behavior is length dependant short: crush long: buckle (sudden) in slender direction end restraints bearing walls continuous in one direction can resist lateral forces Columns & 5 Columns & 6 Columns column buckling crushing Columns stability stable equilibrium P < P cr neutral equilibrium P = P cr unstable equilibrium P > P cr Columns & 7 Columns & 8 7

8 Buckling Load related to deflected shape (P) shape of sine wave Euler s Formula I minimum Critical Stress short columns f critical P A actual slenderness ratio = L e /r (L/d) F a stiffness related to E, I, & L Columns & 9 P critical EI L min f radius of gyration = critical P A Columns & 30 critical EAr A r I A E Le r L e P critical weak axis EA Le r Critical Stresses when a column gets stubby, F y will limit the load real world has loads with eccentricity buckling for steel when F e < 0.44F y Columns end conditions affect shape effective length factor, k KL r E F y Columns & 31 Lecture 5 F011abn Columns & 3 8

9 Bracing bracing affects shape of buckle in one direction both directions should be checked! Columns and Walls bearing & shear Columns & 33 Columns & 34 Columns typical cross sections Centric & Eccentric Loading centric allowable stress from strength or buckling eccentric combined stresses Columns & 35 Columns & 36 Lecture 5 F010abn 9

10 Combined Stresses axial + bending design f f max max P Mc A I M P e F cr fcr F. S. Column Materials wood steel W sections can buckle about both axes concrete & masonry compression primarily in concrete reinforcement for bending Columns & 37 Lecture 5 F010abn Columns & 36 10