twelve rigid frames: compression & buckling ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2019 lecture

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1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2019 lecture twelve rigid frames: compression & buckling Rigid Frames 1 nisee.berkeley.edu/godden

2 Rigid Frames rigid frames have no pins frame is all one body joints transfer moments and shear typically statically indeterminate types portal gable Rigid Frames 2

3 Rigid Frames behavior Rigid Frames 3

4 Rigid Frames moments get redistributed deflections are smaller effective column lengths are shorter very sensitive to settling Rigid Frames 4

5 Moment Redistribution continuous slabs & beams with uniform loading joints similar to fixed ends, but can rotate change in moment to center = wl M max for simply supported beam 8 2 Rigid Frames 5

6 Rigid Frames resists lateral loadings shape depends on stiffness of beams and columns 90 maintained Rigid Frames 6

7 Rigid Frames staggered truss rigidity clear stories Rigid Frames 7

8 Rigid Frames connections steel concrete nisee.berkeley.edu/godden Rigid Frames 8

9 Braced Frames pin connections bracing to prevent lateral movements Rigid Frames 9 nisee.berkeley.edu/godden

10 Braced Frames types of bracing knee-bracing diagonal X K or chevron shear walls diagonal X K (chevron) shear walls Rigid Frames 10

11 Shear Walls resist lateral load in plane with wall Rigid Frames 11

12 Compression Members designed for strength & stresses designed for serviceability & deflection need to design for stability ability to support a specified load without sudden or unacceptable deformations Rigid Frames 12

13 Column Buckling axially loaded columns long & slender unstable equilibrium = buckling sudden and not good Rigid Frames 13

14 Modeling can be modeled with a spring at mid-height when moment from deflection exceeds the spring capacity... boing critical load P Rigid Frames 14

15 Effect of Length long & slender short & stubby Rigid Frames 15

16 Buckling Load related to deflected shape (P) shape of sine wave Euler s Formula smallest I governs P critical 2 EI L 2 Rigid Frames 16

17 Critical Stress short columns f critical P actual A slenderness ratio = L e /r (L/d) F a f radius of gyration = critical Rigid Frames 17 P critical A 2 A EAr 2 r I A 2 2 L e L e 2 r E P critical weak axis 2 EA Le r 2

18 Critical Stresses when a column gets stubby, F y will limit the load real world has loads with eccentricity C c for steel and allowable stress L e r C c 2 2 E F y Rigid Frames 18

19 Effective Length end conditions affect shape effective length factor, K L e K L Rigid Frames 19

20 Bracing bracing affects shape of buckle in one direction both should be checked! Rigid Frames 20

21 Centric & Eccentric Loading centric allowable stress from strength or buckling eccentric combined stresses Rigid Frames 21

22 Combined Stresses axial + bending f max P Mc A I M P e design f max F cr f cr F. S. Rigid Frames 22

23 Stress Limit Conditions ASD interaction formula f F a a f F b b 1.0 with biaxial bending 1 f F a a f F a a f F bx bx f F by by f F interaction diagram b b Rigid Frames 23

24 Stress Limit Conditions in reality, as the column flexes, the moment increases P- effect f F a a f b ( Magnification F bx factor) 1.0 Rigid Frames 24

25 Rigid Frame Analysis members see shear axial force bending V & M diagrams plot on outside Rigid Frames 25

26 Rigid Frame Analysis need support reactions free body diagram each member end reactions are equal and opposite on next member turn member like beam draw V & M Rigid Frames 26

27 Rigid Frame Analysis FBD & M opposite end reactions at joints P M+ Rigid Frames 27

28 Rigid Frame Design loads and combinations usually uniformly distributed gravity loads worst case for largest moments... wind direction can increase moments Rigid Frames 28

29 Rigid Frame Design frames & floors rigid frame can have slab floors or slab with connecting beams other slabs or plates on columns Rigid Frames 29

30 Rigid Frame Design floors plates & slabs one-way behavior side ratio > 1.5 strip beam two-way behavior more complex Rigid Frames 30

31 Rigid Frame Design columns in frames ends can be flexible stiffness affected by beams and column = EI/L G for the joint EI EI l c is the column length of each column l b is the beam length of each beam measured center to center l l c b Rigid Frames 31

32 Rigid Frame Design column effective length, k A B Rigid Frames 32

33 Tools Visual Analysis (VA Edu) in open access labs and VOAL and Rigid Frames 33

34 Tools Visual Analysis (VA Edu) model view / structure tab grid and units define frame members or pre-defined frames (Create) columns up, beams left-right select points, assign supports select members, assign member shapes & any connection types Rigid Frames 34

35 Tools Visual Analysis (VA Edu) loading tab select points, add point load (edit load case with no self weight) results view status bar results filter member graph choose options report view - choose and drag options Rigid Frames 35