five trusses & columns APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2017 lecture STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631

Transcription

1 APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2017 lecture five trusses & columns Columns & Trusses 1

2 Calibrated Peer Review / Turnitin Cables & Arches 2 Lecture 6

3 Trusses ancient (?) wood 1800 s analysis efficient long spans Columns & Trusses 3

4 Trusses comprised of straight members geometry with triangles is stable loads applied only at joints Columns & Trusses 4

5 Trusses 2 force members compression tension 3 members connected by 3 joints 2 more members need 1 more joint b 2 n 3 ( n 2 j 3) Columns & Trusses 5

6 Truss Analysis visualize compression and tension from deformed shape Columns & Trusses 6

7 Truss Analysis Method of Joints F 0 Method of Sections F 0 M 0 Graphical Methods all rely on equilibrium of bodies internal equilibrium nisee.berkeley.edu/godden Columns & Trusses 7

8 Truss Connections pins can t resist rotation nisee.berkeley.edu/godden Columns & Trusses 8

9 Trusses 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 nisee.berkeley.edu/godden Columns & Trusses 9

10 Space Trusses pyramid tetrahedron nisee.berkeley.edu/godden Columns & Trusses 10

11 Space Trusses connections supports Columns & Trusses 11

12 Crystal Cathedral, Johnson 1980 Columns & Trusses 12 nisee.berkeley.edu/godden

13 Expo 70 Festival Plaza Tange & Kamiya 1970 Columns & Trusses 13

14 Jacob K. Javits Convention Center I.M. Pei 1980 Columns & Trusses 14

15 Jacob K. Javits Convention Center Columns & Trusses 15

16 Louvre Museum Addition, Pei 1989 Columns & Trusses 16

17 Louvre Museum Addition, Pei 1989 Columns & Trusses 17

18 Truss Design variables spans depths length of members spacing transverse beam spacing pattern materials; size & strength efficiency Columns & Trusses 18

19 Trusses common designs Columns & Trusses 19

20 Trusses common designs Columns & Trusses 20

21 Truss Configurations external factors roof form openings basic forms symmetrical loading maximum bending cables in tension only Columns & Trusses 21

22 Truss Configurations parallel chords verticals common longer members in tension often cross members - indeterminate funicular shapes efficient similar sized forces some zero force Columns & Trusses 22

23 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 nisee.berkeley.edu/godden Columns & Trusses 23

24 Tools Multiframe in classrooms and open access labs Columns & Trusses 24

25 Tools Multiframe 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 & Trusses 25

26 Tools Multiframe to run analysis choose Analyze menu plot Linear choose options results choose options Columns & Trusses 26

27 Columns compression members column behavior is length dependent short: crush long: buckle (sudden) in slender direction end restraints bearing walls continuous in one direction can resist lateral forces Columns & Trusses 27

28 Columns column buckling crushing Columns & Trusses 28

29 Columns stability stable equilibrium P < P cr neutral equilibrium P = P cr unstable equilibrium P > P cr Columns & Trusses 29

30 Buckling Load related to deflected shape (P ) shape of sine wave Euler s Formula I minimum P critical 2 EI L 2 min stiffness related to E, I, & L Columns & Trusses 30

31 Critical Stress short columns f critical actual slenderness ratio = L e /r (L/d) P A F a f radius of gyration = critical P Columns & Trusses 31 critical A 2 A EAr 2 r I A 2 2 L e L e 2 r E P critical weak axis 2 EA L e r 2

32 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 KL r E F y Columns & Trusses 32

33 Columns end conditions affect shape effective length factor, k Columns & Trusses 33

34 Bracing bracing affects shape of buckle in one direction both directions should be checked! Columns & Trusses 34

35 Columns and Walls bearing & shear Columns & Trusses 35

36 Columns typical cross sections Columns & Trusses 36

37 Centric & Eccentric Loading centric allowable stress from strength or buckling eccentric combined stresses Columns & Trusses 37

38 Combined Stresses axial + bending f max design P A M P e Mc I f max F cr f cr F. S. Columns & Trusses 38 Foundations Structures ARCH 331

39 Column Materials wood steel W sections can buckle about both axes concrete & masonry compression primarily in concrete reinforcement for bending Columns & Trusses 39