steel construction: column designfaculty.arch.tamu.edu/media/cms_page_media/4211/lect18... ·...
TRANSCRIPT
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 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