APPLIED ARCHITECTURAL STRUCTURES:
STRUCTURAL ANALYSIS AND SYSTEMS
Rigid Frames
ARCH 631
composed of linear elements
member geometry fixed at joints
DR. ANNE NICHOLS
FALL 2013
no relative rotation
lecture
seven
statically indeterminate
see
rigid frames:
analysis & design
Rigid Frames 1
Lecture 7
Applied Architectural Structures
ARCH 631
shear
axial forces
bending moments
http:// nisee.berkeley.edu/godden
F2009abn
Rigid Frames 2
Lecture 7
Rigid Frames
Rigid Frames
rigidity
end
constraints
smaller
horizontal
members
larger
vertical
members
behavior
Rigid Frames 3
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 4
Lecture 7
Architectural Structures III
ARCH 631
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Architectural Structures III
ARCH 631
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Rigid Frames
Rigid Frames
resists lateral
loadings
shape depends on
stiffness of beams
and columns
90 maintained
moments get redistributed
deflections are smaller
effective column lengths are shorter
Rigid Frames 5
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frame Analysis
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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
shear
axial force
bending
V & M diagrams
plot on outside
Architectural Structures III
ARCH 631
Architectural Structures III
ARCH 631
Rigid Frame Analysis
members see
Rigid Frames 7
Lecture 7
Rigid Frames 6
Lecture 7
F2008abn
Rigid Frames 8
Lecture 7
Architectural Structures III
ARCH 631
F2008abn
Analysis Methods
Rigid Frame Analysis
FBD & M
opposite end
reactions at joints
computer-based
matrix analysis or finite element analysis
equilibrium
support conditions
joint locations
relative stiffness of members
output
M+
deflections
member forces
http://eng.midasuser.com
Rigid Frames 9
Lecture 7
Architectural Structures III
ARCH 631
F2008abn
Rigid Frames 10
Lecture 7
Architectural Structures III
ARCH 631
Analysis Methods
Analysis Methods
RAM
approximate methods
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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 11
Lecture 7
Architectural Structures III
ARCH 631
F2008abn
Rigid Frames 12
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames
Sidesway
member sizes do affect behavior
location of inflection points critical
translation with vertical load
Rigid Frames 13
Lecture 7
Architectural Structures III
ARCH 631
F2008abn
Rigid Frames 14
Lecture 7
Architectural Structures III
ARCH 631
Support Settlements
Multistory Frame Analysis
moments induced
cantilever method (approximate)
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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 15
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 16
Lecture 7
Architectural Structures III
ARCH 631
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Multistory Frame Analysis
Rigid Frame Design - Types
cantilever method
(approximate)
Rigid Frames 17
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 18
Lecture 7
Architectural Structures III
ARCH 631
Rigid Frame Design
Rigid Frame Design
materials
forms
steel
monolithic
concrete
laminated
wood
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small
large
forms
small
Riola Parish Church, Alto Alvar
www.greatbuildings.com
single story, gabled frame, portal, hinged...
large - multistory
http:// nisee.berkeley.edu/godden
Rigid Frames 19
Lecture 7
Architectural Structures III
ARCH 631
F2009abn
Rigid Frames 20
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frame Design
Rigid Frame Design
staggered truss
connections
rigidity
clear stories
steel
concrete
http:// nisee.berkeley.edu/godden
Rigid Frames 21
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 22
Lecture 7
Architectural Structures III
ARCH 631
Rigid Frame Design
Rigid Frame Design
considerations
load combinations
need frame?
minimize moment (affects member size)
increasing stiffness
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worst case for largest moments...
wind direction can increase moments
redistributes moments
limits deflections
joint rigidity
support types
Rigid Frames 23
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 24
Lecture 7
Architectural Structures III
ARCH 631
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Combined Stresses & Design
Combined Stresses
axial + bending
beam-columns have moments at end
often due to eccentric load
P Mc
A I
M Pe
f max
design
f max Fcr
Rigid Frames 25
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 26
Lecture 7
Architectural Structures III
ARCH 631
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Biaxial Bending
Eccentric Loading
when there is moment in two directions
find e such that the minimum stress = 0
f min
f cr
F .S .
P Pe c
0
A
I
M 1 P e1
M 2 P e2
P M y M z
f max 1 2
A
I
I
area defined by e from centroid is the kern
biaxial bending
y
B
b
e1
e2
z
+
x
M 2 P e2
Rigid Frames 27
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 28
Lecture 7
P
z
result
M 1 P e1
Architectural Structures III
ARCH 631
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Stress Limit Conditions
Stress Limit Conditions
ASD interaction formula
f a fb
1.0
Fa Fb
in reality, as the column flexes,
the moment increases
fa
Fa
P- effect
with biaxial bending
f a f bx f by
1.0
Fa Fbx Fby
Rigid Frames 29
Lecture 7
Architectural Structures III
ARCH 631
fb
Fb
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f a f b ( Magnification factor )
1.0
Fa
Fb
Rigid Frames 30
Lecture 7
Architectural Structures III
ARCH 631
Design for Combined Stress
Tools Multiframe4D
satisfy
in computer lab
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strength
stability
pick
section
Rigid Frames 31
Lecture 7
Architectural Structures III
ARCH 631
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Rigid Frames 32
Lecture 7
Architectural Structures III
ARCH 631
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Tools Multiframe4D
Tools Multiframe4D
frame window
to run analysis choose
Analyze menu
define frame members
Linear
or pre-defined frame
plot
select points, assign supports
select members,
assign section
load window
select point or member,
add point or distributed
loads
Rigid Frames 33
Lecture 7
Architectural Structures III
ARCH 631
choose options
results
choose
options
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Rigid Frames 34
Lecture 7
Architectural Structures III
ARCH 631
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