eleven rigid frames: compression & buckling ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture

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1 ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture eleven 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 Rigid Frames resists lateral loadings shape depends on stiffness of beams and columns 90 maintained Rigid Frames 5

6 Rigid Frames staggered truss rigidity clear stories Rigid Frames 6

7 Rigid Frames connections steel concrete nisee.berkeley.edu/godden Rigid Frames 7

8 Braced Frames pin connections bracing to prevent lateral movements Rigid Frames 8 nisee.berkeley.edu/godden

9 Braced Frames types of bracing knee-bracing diagonal X K or chevron shear walls diagonal X K (chevron) shear walls Rigid Frames 9

10 Shear Walls resist lateral load in plane with wall Rigid Frames 10

11 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 11

12 Column Buckling axially loaded columns long & slender unstable equilibrium = buckling sudden and not good Rigid Frames 12

13 Modeling can be modeled with a spring at mid-height when moment from deflection exceeds the spring capacity... boing critical load P Rigid Frames 13

14 Effect of Length long & slender short & stubby Rigid Frames 14

15 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 15

16 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 16 P critical A 2 A EAr 2 r I A 2 2 L e L 2 r E e P critical weak axis 2 EA Le r 2

17 Critical Stresses when a column gets stubby, F y will limit the load for steel real world has loads with eccentricity Rigid Frames 17

18 Effective Length end conditions affect shape effective length factor, K L e K L Rigid Frames 18

19 Bracing bracing affects shape of buckle in one direction both should be checked! Rigid Frames 19

20 Centric & Eccentric Loading centric allowable stress from strength or buckling eccentric combined stresses Rigid Frames 20

21 Combined Stresses axial + bending f max P Mc A I M P e design f max F cr f cr F. S. Rigid Frames 21

22 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 22

23 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 23

24 Rigid Frame Analysis members see shear axial force bending V & M diagrams plot on outside Rigid Frames 24

25 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 25

26 Rigid Frame Analysis FBD & M opposite end reactions at joints P M+ Rigid Frames 26

27 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 27

28 Rigid Frame Design column effective length, k A B Rigid Frames 28

29 Tools Multiframe in computer lab Rigid Frames 29

30 Tools Multiframe frame window define frame members or pre-defined frame select points, assign supports select members, assign section load window select point or member, add point or distributed loads Rigid Frames 30

31 Tools Multiframe to run analysis choose Analyze menu plot Linear choose options results choose options Rigid Frames 31