Compression and Buckling - Architectural Structures - Lecture Slides, Slides of Structural Design and Architecture

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Rigid Frames 1 Lecture 12

ARCHITECTURAL STRUCTURES:

FORM, BEHAVIOR, AND DESIGN

lecture

twelve

rigid frames:

compression & buckling

http:// nisee.berkeley.edu/godden

Rigid Frames 2 Lecture 12 Architectural Structures

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 4 Lecture 12

Rigid Frames

• moments get redistributed
• deflections are smaller
• effective column lengths are shorter
• very sensitive to settling

Rigid Frames 5 Lecture 12

Moment Redistribution

• continuous slabs & beams with uniform

loading

• joints similar to fixed ends, but can rotate
• change in moment to center =
• Mmax for simply supported beam^8

wL^2

Rigid Frames 7 Lecture 12

Rigid Frames

• staggered truss
  • rigidity
  • clear stories

Rigid Frames 8 Lecture 12

Rigid Frames

• connections
  • steel
  • concrete

http:// nisee.berkeley.edu/godden

Rigid Frames 10 Lecture 12

Braced Frames

• types of bracing
  • knee-bracing
  • diagonal
  • X
  • K or chevron
  • shear walls

diagonal X

K (chevron) shear walls

Rigid Frames 11 Lecture 12

Shear Walls

• resist lateral load in plane with wall

Rigid Frames 13 Lecture 12

Column Buckling

• axially loaded columns
• long & slender
  • unstable equilibrium = buckling
  • sudden and not good

Rigid Frames 14 Lecture 12 Architectural Structures

Modeling

• • can be modeled with a spring at mid-height
• when moment from deflection exceeds the spring capacity ... “boing”
• critical load P

Rigid Frames 16 Lecture 12

Buckling Load

• related to deflected shape (P )
• shape of sine wave
• Euler’s Formula
• smallest I governs

 

2

2

L

EI Pcritical

 

Rigid Frames 17 Lecture 12

Critical Stress

• short columns
• slenderness ratio = Le/r (L/d)
• radius of gyration =

A

I

r 

a

actual critical F A

P f  

(^) weak axis

  2

2 2

2 2

r

L

E

A L

EAr

A

P

f

e e

critical critical

2 e

2 critical

r

L

EA

P

Rigid Frames 19 Lecture 12

Effective Length

• end conditions affect shape
• effective length factor, K Le  K  L

Rigid Frames 20 Lecture 12

Bracing

• bracing affects shape of buckle

in one direction

• both should be checked!