Rigid frame

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seven

r ig id f rames:

analys is & design Rigid Frames 1 Lecture 7 Applied Architectural Structures ARCH 631

lecture

http:// n isee.berkeley.edu/godden

A PPLIED ARCHITECTURAL S TRUCTURES:

S TRUCTURAL A NALYSIS AND S YSTEMSARCH 631

D R. ANNE N ICHOLS

F ALL 2013

Rigid Frames 2

Lecture 7

Architectural Structures III

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Rigid Frames

• composed of linear elements

• member geometry fixed at joints

– no relative rotation

• statically indeterminate

• see

– shear

– axial forces

– bending moments

Rigid Frames 3Lecture 7

Architectural Structures III ARCH 631

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Rigid Frames

• rigidity

• end

constraints• smaller

horizontal

members

• larger

vertical

members



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Rigid Frames

• behavior


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Lecture 7


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Rigid Frames

– moments get redistributed

– deflections are smaller

– effective column lengths are shorter

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Lecture 7


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Rigid Frames

• resists lateral

loadings

•

shape depends onstiffness of beams

and columns

• 90° maintained

Rigid Frames 7 Lecture 7


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Rigid Frame Analysis

• members see

– shear

–

axial force – bending

• V & M diagrams

– plot on “ outside”



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– 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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Lecture 7


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– FBD & M

• opposite end

reactions at joints

M+

P

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Lecture 7


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Analysis Methods

• computer-based

– matrix analysis or finite element analysis

– equilibrium – support conditions

– joint locations

– relative stiffness of members

– output

• deflections

• member forceshttp://eng.midasuser.com

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Lecture 7


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Analysis Methods

• RAM

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Analysis Methods

• approximate methods

– presume where inflection points occur in

deformed shape

– these points have zero moment

– “portal method”

• hinge is placed at the center of each girder

• hinge is placed at the center of each column

• shear at interior columns

is twice that of exterior

columns

Rigid Frames 12

Lec ture 7

Architectu ral Structures III

ARCH 631


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Lecture 7


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Rigid Frames

• member sizes do affect behavior

• location of inflection points critical

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Sidesway

• translation with vertical load



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Support Settlements

• moments induced

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Multistory Frame Analysis

• cantilever method (approximate)

– point of inflection at midspan of each beam

– point of inflection at midheight

of each column

– axial force in each column

proportional to the horizontal

distance of that column from the

centroid of all columns in the story

– centroids are “average” locations

Rigid Frames 16 Lec ture 7

Architectu ral Structures III ARCH 631


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Lecture 7


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Multistory Frame Analysis

• cantilever method

(approximate)

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Lecture 7


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Rigid Frame Design - Types

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Rigid Frame Design

• materials

– steel

– monolithic

concrete – laminated

wood

• forms

– small

• single story, gabled frame, portal, hinged...

– large - multistory

Rigid Frames 19 Lec ture 7

Architectu ral Structures III ARCH 631

Riola Parish Church, Alto Alvar www.greatbui ld ings .com

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Rigid Frame Design

• forms

– small

–

large

http:// nisee.berkeley.edu/godden


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Rigid Frame Design

• staggered truss

– rigidity

– clear stories


Lecture 7


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Rigid Frame Design

• connections

– steel

– concrete

http:// nisee.berkeley.edu/godden



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Rigid Frame Design

• considerations

– need frame?

–

minimize moment (affects member size) – increasing stiffness

• redistributes moments

• limits deflections

– joint rigidity

– support types



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Rigid Frame Design

• load combinations

– worst case for largest moments...

–

wind direction can increase moments

+ =


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Combined Stresses

• beam-columns have moments at end

• often due to eccentric load

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Combined Stresses & Design

– axial + bending

– design

I

Mc

A

P

f

max

..max

S F

f F f cr cr

e P M

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Eccentric Loading

– find e such that the minimum stress = 0

– area defined by e from centroid is the kern

0

min

I

c Pe

A

P f

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P

y

x

zx y z

+ + =

result

22 e P M

11 e P M

e2

e1

b

h

A

B

Biaxial Bending

– when there is moment in two directions

– biaxial bending

I z M

I y M

A P f 21max

22 e P M

11 e P M


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Stress Limit Conditions

– ASD interaction formula

– with biaxial bending

1

1

a

a

F

b

b

F

0.1

b

b

a

a

F

f

F

f

0.1

by

by

bx

bx

a

a

F

f

F

f

F

f


Lecture 7


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Stress Limit Conditions

– in reality, as the column flexes,

the moment increases

– P- effect

01. F

) factor ion Magnificat ( f

F

f

b

b

a

a

P

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Design for Combined Stress

• satisfy

– strength

– stability

• pick

– section

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Tools – Multiframe4D

• in computer lab


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• 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


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• to run analysis choose

– Analyze menu

• Linear

• plot

– choose options

• results

– choose

options

Rigid frame

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