E ARCHITECTURAL STRUCTURES B DESIGN ARCH 614...

S2014abn 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 2014

lecture

eleven

rigid frames:

compression & buckling http:// nisee.berkeley.edu/godden


Lecture 11


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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ARCH 614

Rigid Frames

• behavior


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Rigid Frames

– moments get redistributed

– deflections are smaller

– effective column lengths are shorter

– very sensitive to settling


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Rigid Frames

• resists lateral

loadings

• shape depends on

stiffness of beams

and columns

• 90° maintained


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Rigid Frames

• staggered truss

– rigidity

– clear stories

www.arcchicago.blogspot.com


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Rigid Frames

• connections

– steel

– concrete

http:// nisee.berkeley.edu/godden


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Braced Frames

• pin connections

• bracing to prevent lateral movements

http:// nisee.berkeley.edu/godden


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Braced Frames

• types of bracing

– knee-bracing

– diagonal

– X

– K or chevron

– shear walls

diagonal X

K (chevron) shear walls


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Shear Walls

• resist lateral load in plane with wall


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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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Column Buckling

• axially loaded columns

• long & slender

– unstable equilibrium =

buckling

– sudden and not good


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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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Effect of Length

• long & slender • short & stubby


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Buckling Load

• related to deflected shape (P)

• shape of sine wave

• Euler’s Formula

• smallest I governs

22

L

EIPcritical


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Critical Stress

• short columns

• slenderness ratio = Le/r (L/d)

• radius of gyration = A

Ir

aactual

critical FA

Pf

weak axis

2

2

2

22

rL

E

LA

EAr

A

Pf

ee

criticalcritical

2

e

2

critical

rL

EAP


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Critical Stresses

• when a column gets stubby, Fy will limit the

load for steel

• real world has loads with eccentricity


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ARCH 614

Effective Length

• end conditions affect shape

• effective length factor, K LKLe


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Bracing

• bracing affects shape of buckle

in one direction

• both should be checked!


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Centric & Eccentric Loading

• centric

– allowable stress from strength or buckling

• eccentric

– combined stresses


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Combined Stresses

– axial + bending

– design

I

Mc

A

Pf max

..max

SF

fFf cr

cr

ePM


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Stress Limit Conditions

– ASD interaction formula

– with biaxial bending

1

1

a

a

F

f

b

b

F

f

0.1b

b

a

a

F

f

F

f

0.1by

by

bx

bx

a

a

F

f

F

f

F

f

interaction diagram


Lecture 11


ARCH 614

Stress Limit Conditions

– in reality, as the column flexes,

the moment increases

– P- effect

0.1)(

bx

b

a

a

F

factorionMagnificatf

F

f


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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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– FBD & M

• opposite end

reactions at joints

M+

P


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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

lEI

lEI

G


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Rigid Frame Design

• column effective length, k

A

B


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Tools – Multiframe

• 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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ARCH 614


• to run analysis choose

– Analyze menu

• Linear

• plot

– choose options

• results

– choose

options

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