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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
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S2014abn 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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S2014abn Rigid Frames 3
Lecture 11
Elements of Architectural Structures
ARCH 614
Rigid Frames
• behavior
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S2014abn 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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S2014abn 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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S2014abn 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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S2014abn 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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S2014abn 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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S2014abn 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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Lecture 11
Elements of Architectural Structures
ARCH 614
Shear Walls
• resist lateral load in plane with wall
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S2014abn 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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S2014abn 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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S2014abn 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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Lecture 11
Elements of Architectural Structures
ARCH 614
Effect of Length
• long & slender • short & stubby
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S2014abn 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
22
L
EIPcritical
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S2014abn 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
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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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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Lecture 11
Elements of Architectural Structures
ARCH 614
Effective Length
• end conditions affect shape
• effective length factor, K LKLe
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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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S2014abn 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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S2014abn Rigid Frames 21
Lecture 11
Elements of Architectural Structures
ARCH 614
Combined Stresses
– axial + bending
– design
I
Mc
A
Pf max
..max
SF
fFf cr
cr
ePM
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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
0.1b
b
a
a
F
f
F
f
0.1by
by
bx
bx
a
a
F
f
F
f
F
f
interaction diagram
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Lecture 11
Elements of Architectural Structures
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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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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S2014abn 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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Lecture 11
Elements of Architectural Structures
ARCH 614
Rigid Frame Analysis
– FBD & M
• opposite end
reactions at joints
M+
P
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S2014abn 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
lEI
lEI
G
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Lecture 11
Elements of Architectural Structures
ARCH 614
Rigid Frame Design
• column effective length, k
A
B
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Lecture 11
Elements of Architectural Structures
ARCH 614
Tools – Multiframe
• in computer lab
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S2014abn Rigid Frames 30
Lecture 11
Elements of Architectural Structures
ARCH 614
Tools – Multiframe
• 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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Lecture 11
Elements of Architectural Structures
ARCH 614
Tools – Multiframe
• to run analysis choose
– Analyze menu
• Linear
• plot
– choose options
• results
– choose
options