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S2019abnSteel Columns 1
Lecture 18
Elements of Architectural Structures
ARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES:
FORM, BEHAVIOR, AND DESIGN
ARCH 614
DR. ANNE NICHOLS
SPRING 2019
lecture
eighteen
steel construction:
column designCor-Ten Steel Sculpture By Richard Serra
Museum of Modern Art Fort Worth, TX
(AISC - Steel Structures of the Everyday)
S2019abnSteel Columns 2
Lecture 18
Elements of Architectural Structures
ARCH 614
Structural Steel
• standard rolled shapes
(W, C, L, T)
• tubing
• pipe
• built-up
S2019abnSteel Columns 3
Lecture 18
Elements of Architectural Structures
ARCH 614
Design Methods (revisited)
• know
– loads or lengths
• select
– section or load
– adequate for
strength and
no buckling
S2019abnSteel Columns 4
Lecture 18
Elements of Architectural Structures
ARCH 614
Allowable Stress Design (ASD)
• AICS 9th ed
• slenderness ratio
– for kl/r Cc
22
23
12
..r
Kl
E
SF
fF critical
a
r
Kl
= 126.1 with Fy = 36 ksi
= 107.0 with Fy = 50 ksi
S2019abnSteel Columns 5
Lecture 18
Elements of Architectural Structures
ARCH 614
Cc and Euler’s Formula
• Kl/r < Cc
– short and stubby
– parabolic transition
• Kl/r > Cc
– Euler’s relationship
– < 200 preferred
y
cF
EC
22
S2019abnSteel Columns 6
Lecture 18
Elements of Architectural Structures
ARCH 614
Cc and Euler’s Formula
S2019abnSteel Columns 7
Lecture 18
Elements of Architectural Structures
ARCH 614
Short / Intermediate
• Le/r < Cc
– where
..2
12
2
SF
F
C
rKl
Fy
c
a
3
3
88
3
3
5..
cc C
rKl
C
rKl
SF
S2019abnSteel Columns 8
Lecture 18
Elements of Architectural Structures
ARCH 614
Unified Design
• limit states for failure
1. yielding
2. buckling
gcrnc AFP. 900
ye
y
F.ForF
E.
r
KL440714
n
a
PP
ncu PP
ye
y
F.ForF
E.
r
KL440714
Fe – elastic buckling stress (Euler)
S2019abnSteel Columns 9
Lecture 18
Elements of Architectural Structures
ARCH 614
Unified Design
• Pn = FcrAg
– for
– for
– where
ecr
y
F.FF
E.
r
KL8770714
y
F
F
cr
y
F.FF
E.
r
KLe
y
6580714
22
rKL
EFe
S2019abnSteel Columns 10
Lecture 18
Elements of Architectural Structures
ARCH 614
Procedure for Analysis
1. calculate KL/r• biggest of KL/r with respect to x axes and y axis
2. find Fcr (see Note) from appropriate equation
• tables are available
3. compute Pn = FcrAg
4. is Pa Pn/? or is Pu Pn?• yes: ok
• no: insufficient capacity and no good
Note: text uses Fc
and old = 0.85
S2019abnSteel Columns 11
Lecture 18
Elements of Architectural Structures
ARCH 614
Procedure for Design
1. guess a size (pick a section)
2. calculate KL/r• biggest of KL/r with respect to x axes and y axis
3. find Fa or Fcr (see Note) from appropriate
equations• or find a chart
4. compute Pn = FcrAg
Note: text uses Fc
and old = 0.85
S2019abnSteel Columns 12
Lecture 18
Elements of Architectural Structures
ARCH 614
Procedure for Design (cont’d)
5. is Pa Pn/? or is Pu Pn?• yes: ok
• no: pick a bigger section and go back to step 2.
6. check design efficiency
• percentage of stress =
• if between 90-100%: good
• if < 90%: pick a smaller section and
go back to step 2.
%P
P
c
r 100
S2019abnSteel Columns 13
Lecture 18
Elements of Architectural Structures
ARCH 614
Column Charts, Fcr
S2019abnSteel Columns 14
Lecture 18
Elements of Architectural Structures
ARCH 614
Column Charts
S2019abnSteel Columns 15
Lecture 18
Elements of Architectural Structures
ARCH 614
Beam-Column Design
• moment magnification (P-)
Cm – modification factor for end conditions
= 0.6 – 0.4(M1/M2 or
0.85 restrained, 1.00 unrestrained
Pe1 – Euler buckling strength
- 1.00 (LRFD), 1.60(ASD) 22
1
rKl
EAPe
factoredmaxu MBM 1m
1u e1
CB
1 ( P / P )
S2019abnSteel Columns 16
Lecture 18
Elements of Architectural Structures
ARCH 614
Beam-Column Design
• LRFD (Unified) Steel
– for
– for
Pr is required, Pc is capacity
c – resistance factor for compression = 0.9
c – resistance factor for bending = 0.9
019
820 .
M
M
M
M
P
P:.
P
P
nxb
ux
nxb
ux
nc
u
c
r
012
20 .M
M
M
M
P
P:.
P
P
nxb
ux
nxb
ux
nc
u
c
r
S2019abnSteel Columns 17
Lecture 18
Elements of Architectural Structures
ARCH 614
Design Steps Knowing Loads (revisited)
1. assume limiting stress
• buckling, axial stress,
combined stress
2. solve for r, A or S
3. pick trial section
4. analyze stresses
5. section ok?
6. stop when section is ok
S2019abnSteel Columns 18
Lecture 18
Elements of Architectural Structures
ARCH 614
Rigid Frame Design (revisited)
• columns in frames
– ends can be “flexible”
– stiffness affected by beamsand 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
S2019abnSteel Columns 19
Lecture 18
Elements of Architectural Structures
ARCH 614
Rigid Frame Design (revisited)
• column effective length, k
A
B
