ACHITECTURAL STRUCTURES: S ANALYSIS AND SYSTEMS ARCH …faculty.arch.tamu.edu/anichols/Courses/Arch 631/Lectures/Files/lect… · ARCH 631 Analysis Methods • approximate methods

S2019abnRigid Frames 1

Lecture 7

Applied Architectural Structures

ARCH 631

seven

rigid frames:

analysis & design

lecture

http://nisee.berkeley.edu/godden

APPLIED ACHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS

ARCH 631

DR. ANNE NICHOLS

SPRING 2019


Lecture 7


ARCH 631

Rigid Frames

• composed of linear elements

• member geometry fixed at joints

– no relative rotation

• statically indeterminate

• see

– shear

– axial forces

– bending moments


Lecture 7


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Rigid Frames

• rigidity

• end

constraints

• smaller

horizontal

members

• larger

vertical

members


Lecture 7


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Rigid Frames

• behavior


Lecture 7


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Rigid Frames

– moments get redistributed

– deflections are smaller

– effective column lengths are shorter


Lecture 7


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Rigid Frames

• resists lateral

loadings

• shape depends on

stiffness of beams

and columns

• 90° maintained

../animations/rigid_connection2.mov

../animations/rigid_connection2.mov


Lecture 7


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Rigid Frame Analysis

• members see

– shear

– axial force

– bending

• V & M diagrams

– plot on “outside”


Lecture 7


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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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– FBD & M

• opposite end

reactions at joints

M+

P


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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 forces

http://eng.midasuser.com


Lecture 7


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Analysis Methods

• RAM


Lecture 7


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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


Lecture 7


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Rigid Frames

• member sizes do affect behavior

• location of inflection points critical


Lecture 7


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Sidesway

• translation with vertical load


Lecture 7


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Support Settlements

• moments induced


Lecture 7


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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


Lecture 7


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Multistory Frame Analysis

• cantilever method

(approximate)


Lecture 7


ARCH 631

Rigid Frame Design - Types


Lecture 7


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Rigid Frame Design

• materials

– steel

– monolithic concrete

– laminated wood

• forms

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

– large - multistory

Riola Parish Church, Alto Alvarwww.greatbuildings.com


Lecture 7


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Rigid Frame Design

• forms

– small

– large

http:// nisee.berkeley.edu/godden


Lecture 7


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Rigid Frame Design

• staggered truss

– rigidity

– clear stories

www.arcchicago.blogspot.com


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Rigid Frame Design

• connections

– steel

– concrete

http:// nisee.berkeley.edu/godden


Lecture 7


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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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– axial + bending

– design

Rigid Frames 26

Lecture 7


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Combined Stresses & Design

I

Mc

A

Pf max

ePM

..max

SF

fFf cr

cr

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– find e such that the minimum stress = 0

– area defined by e from centroid is the kern

Rigid Frames 27

Lecture 7


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Eccentric Loading

0min

I

cPe

A

Pf

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11 ePM 22 ePM

I

zM

I

yM

A

Pf 21

max

– when there is moment in two directions

– biaxial bending

Rigid Frames 28

Lecture 7


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P

y

x

z x y z

+ + =

result

22 ePM 11 ePM

e2

e1

b

h

A

B

Biaxial Bending

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0.1b

b

a

a

F

f

F

f

0.1by

by

bx

bx

a

a

F

f

F

f

F

f

– ASD interaction formula

– with biaxial bending

Rigid Frames 29

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Stress Limit Conditions

1

1

a

a

F

f

b

b

F

f

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01.F

)factorionMagnificat(f

F

f

bx

b

a

a

– in reality, as the column flexes,

the moment increases

– P- effect

Rigid Frames 30

Lecture 7


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Stress Limit Conditions

P


Lecture 7


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Design for Combined Stress

• satisfy

– strength

– stability

• pick

– section


Lecture 7


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Tools – Visual Analysis (VA Edu)

• in open access labs and VOAL and

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

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


Lecture 7


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• 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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• 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 optionsRigid Frames 34

Lecture 7


ARCH 631


Documents

ACHITECTURAL STRUCTURES: S ANALYSIS AND SYSTEMS ARCH …faculty.arch.tamu.edu/anichols/Courses/Arch 631/Lectures/Files/lect… · ARCH 631 Analysis Methods • approximate methods