eleven rigid frames: compression & buckling Rigid Frames 1 - - PowerPoint PPT Presentation

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eleven rigid frames: compression & buckling Rigid Frames 1 - - PowerPoint PPT Presentation

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E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS S PRING 2019 lecture eleven rigid frames: compression & buckling Rigid Frames 1 Elements of Architectural Structures S2019abn http://

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SLIDE 1

S2019abn Rigid Frames 1 Lecture 11 Elements of Architectural Structures ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 614

  • DR. ANNE NICHOLS

SPRING 2019 lecture

eleven

rigid frames: compression & buckling

http:// nisee.berkeley.edu/godden

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SLIDE 2

S2019abn Rigid Frames 2 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frames

  • rigid frames have no

pins

  • frame is all one body
  • joints transfer

moments and shear

  • typically statically

indeterminate

  • types

– portal – gable

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SLIDE 3

S2019abn Rigid Frames 3 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frames

  • behavior
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SLIDE 4

S2019abn Rigid Frames 4 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frames

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

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SLIDE 5

S2019abn Rigid Frames 5 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frames

  • resists lateral

loadings

  • shape depends on

stiffness of beams and columns

  • 90° maintained
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SLIDE 6

S2019abn Rigid Frames 6 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frames

  • staggered truss

– rigidity – clear stories

www.arcchicago.blogspot.com

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SLIDE 7

S2019abn Rigid Frames 7 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frames

  • connections

– steel – concrete

http:// nisee.berkeley.edu/godden

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SLIDE 8

S2019abn Rigid Frames 8 Lecture 11 Elements of Architectural Structures ARCH 614

Braced Frames

  • pin connections
  • bracing to prevent lateral movements

http:// nisee.berkeley.edu/godden

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SLIDE 9

S2019abn Rigid Frames 9 Lecture 11 Elements of Architectural Structures ARCH 614

Braced Frames

  • types of bracing

– knee-bracing – diagonal – X – K or chevron – shear walls

diagonal X K (chevron) shear walls

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SLIDE 10

S2019abn Rigid Frames 10 Lecture 11 Elements of Architectural Structures ARCH 614

Shear Walls

  • resist lateral load in plane with wall
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SLIDE 11

S2019abn Rigid Frames 11 Lecture 11 Elements of Architectural Structures ARCH 614

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

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SLIDE 12

S2019abn Rigid Frames 12 Lecture 11 Elements of Architectural Structures ARCH 614

Column Buckling

  • axially loaded columns
  • long & slender

– unstable equilibrium = buckling – sudden and not good

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SLIDE 13

S2019abn Rigid Frames 13 Lecture 11 Elements of Architectural Structures ARCH 614

Modeling

  • can be modeled with a spring at mid-height
  • when moment

from deflection exceeds the spring capacity ... “boing”

  • critical load P
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SLIDE 14

S2019abn Rigid Frames 14 Lecture 11 Elements of Architectural Structures ARCH 614

Effect of Length

  • long & slender
  • short & stubby
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SLIDE 15

S2019abn Rigid Frames 15 Lecture 11 Elements of Architectural Structures ARCH 614

Buckling Load

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

 

2 2

L EI P

critical

 

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SLIDE 16

S2019abn Rigid Frames 16 Lecture 11 Elements of Architectural Structures ARCH 614

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 L A EAr A P f

e e critical critical

 

2 e 2 critical

r L EA P        

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SLIDE 17

S2019abn Rigid Frames 17 Lecture 11 Elements of Architectural Structures ARCH 614

Critical Stresses

  • when a column gets stubby, Fy will limit the

load for steel

  • real world has loads with eccentricity
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SLIDE 18

S2019abn Rigid Frames 18 Lecture 11 Elements of Architectural Structures ARCH 614

Effective Length

  • end conditions affect shape
  • effective length factor, K

L K Le  

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SLIDE 19

S2019abn Rigid Frames 19 Lecture 11 Elements of Architectural Structures ARCH 614

Bracing

  • bracing affects shape of buckle

in one direction

  • both should be checked!
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SLIDE 20

S2019abn Rigid Frames 20 Lecture 11 Elements of Architectural Structures ARCH 614

Centric & Eccentric Loading

  • centric

– allowable stress from strength or buckling

  • eccentric

– combined stresses

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SLIDE 21

S2019abn Rigid Frames 21 Lecture 11 Elements of Architectural Structures ARCH 614

Combined Stresses

– axial + bending – design

I Mc A P f  

max

. .

max

S F f F f

cr cr 

 e P M  

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SLIDE 22

S2019abn Rigid Frames 22 Lecture 11 Elements of Architectural Structures ARCH 614

Stress Limit Conditions

– ASD interaction formula – with biaxial bending

1 1

a a

F f

b b

F f

. 1  

b b a a

F f F f . 1   

by by bx bx a a

F f F f F f

interaction diagram

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SLIDE 23

S2019abn Rigid Frames 23 Lecture 11 Elements of Architectural Structures ARCH 614

Stress Limit Conditions

– in reality, as the column flexes, the moment increases – P- effect

. 1 ) (   

bx b a a

F factor ion Magnificat f F f

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SLIDE 24

S2019abn Rigid Frames 24 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frame Analysis

  • members see

– shear – axial force – bending

  • V & M diagrams

– plot on “outside”

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SLIDE 25

S2019abn Rigid Frames 25 Lecture 11 Elements of Architectural Structures ARCH 614

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

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SLIDE 26

S2019abn Rigid Frames 26 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frame Analysis

– FBD & M

  • opposite end

reactions at joints

M+

P

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SLIDE 27

S2019abn Rigid Frames 27 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frame Design

  • columns in frames

– ends can be “flexible” – stiffness affected by beams and column = EI/L – for the joint

  • lc is the column length of each column
  • lb is the beam length of each beam
  • measured center to center

b c

l EI l EI G     

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SLIDE 28

S2019abn Rigid Frames 28 Lecture 11 Elements of Architectural Structures ARCH 614

Rigid Frame Design

  • column effective length, k

A B

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SLIDE 29

S2019abn Rigid Frames 29 Lecture 11 Elements of Architectural Structures ARCH 614

Tools – Visual Analysis (VA Edu)

  • in open access labs and VOAL and

https://www.iesweb.com/edu/index.htm

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SLIDE 30

S2019abn Rigid Frames 30 Lecture 11 Elements of Architectural Structures ARCH 614

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

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SLIDE 31

S2019abn Rigid Frames 31 Lecture 11

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