steel construction: columns & tension...
Transcript of steel construction: columns & tension...
Su2014abn Steel Columns & Tension 1
Lecture 17
Architectural Structures
ARCH 331
ARCHITECTURAL STRUCTURES:
FORM, BEHAVIOR, AND DESIGN
ARCH 331
DR. ANNE NICHOLS
SUMMER 2014
lecture
seventeen
steel construction:
columns & tension members
Cor-Ten Steel Sculpture By Richard Serra
Museum of Modern Art Fort Worth, TX
(AISC - Steel Structures of the Everyday)
Su2014abn Steel Columns & Tension 2
Lecture 17
Architectural Structures
ARCH 331
Structural Steel
• standard rolled shapes
(W, C, L, T)
• tubing
• pipe
• built-up
Su2014abn Steel Columns & Tension 3
Lecture 17
Architectural Structures
ARCH 331
Design Methods (revisited)
• know
– loads or lengths
• select
– section or load
– adequate for
strength and
no buckling
Su2014abn Steel Columns & Tension 4
Lecture 17
Architectural Structures
ARCH 331
Allowable Stress Design (ASD)
• AICS 9th ed
• slenderness ratio
– for kl/r Cc
22
23
12
..r
Kl
E
SF
fF criticala
r
Kl
= 126.1 with Fy = 36 ksi
= 107.0 with Fy = 50 ksi
Su2014abn Steel Columns & Tension 5
Lecture 17
Architectural Structures
ARCH 331
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
Su2014abn Steel Columns & Tension 6
Lecture 17
Architectural Structures
ARCH 331
Cc and Euler’s Formula
Su2014abn Steel Columns & Tension 7
Lecture 17
Architectural Structures
ARCH 331
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
Su2014abn
Unified Design
• limit states for failure
1.yielding
2.buckling
Fe – elastic buckling stress (Euler)
Steel Columns & Tension 8
Lecture 17
Architectural Structures
ARCH 331
ye
y
F.ForF
E.
r
Kl440714
ye
y
F.ForF
E.
r
Kl440714
gcrnc AFP. 900 ncu PP
na
PP
Su2014abn
Unified Design
• Pn = FcrAg
– for
– for
– where
Steel Columns & Tension 9
Lecture 17
Architectural Structures
ARCH 331
yF
E.
r
Kl714
yF
E.
r
Kl714
y
F
F
cr F.F e
y
6580
22
rKL
EFe
ecr F.F 8770
Su2014abn Steel Columns & Tension 10
Lecture 17
Architectural Structures
ARCH 331
Procedure for Analysis
1. calculate KL/r • biggest of KL/r with respect to x axes and y axis
2. find Fa or Fcr from appropriate equation • tables are available
3. compute Pallowable = FaA or Pn = FcrAg • or find factual = P/A
4. is P Pallowable (Pa Pn/)? or is Pu Pn? • yes: ok
• no: insufficient capacity and no good
Su2014abn
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 from appropriate equations • or find a chart
4. compute Pallowable = FaA (or Pn/ = FcrA)
or Pn = FcrAg • or find factual = P/A
Steel Columns & Tension 11
Lecture 17
Architectural Structures
ARCH 331
Procedure for Design
Su2014abn Steel Columns & Tension 12
Lecture 17
Architectural Structures
ARCH 331
Procedure for Design (cont’d)
5. is P Pallowable (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
Su2014abn Steel Columns & Tension 13
Lecture 17
Architectural Structures
ARCH 331
Column Charts, Fa (pg. 361-364)
Su2014abn Steel Columns & Tension 14
Lecture 17
Architectural Structures
ARCH 331
Column Charts, Fcr
Su2014abn Steel Columns & Tension 16
Lecture 17
Architectural Structures
ARCH 331
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
)P/P(
CB
eu
m
1
11
f a c t o r e dm a xu MBM 1
22
1
rKl
EAPe
Su2014abn Steel Columns & Tension 17
Lecture 17
Architectural Structures
ARCH 331
Beam-Column Design
• LRFD Steel
– for
– for
Pr is required load, Pc is capacity
c - resistance factor for compression = 0.9
b - resistance factor for bending = 0.9
:.P
P
c
r 20
:.P
P
c
r 20
019
8.
M
M
M
M
P
P
nyb
uy
nxb
ux
nc
u
012
.M
M
M
M
P
P
nyb
uy
nxb
ux
nc
u
Su2014abn Steel Columns & Tension 18
Lecture 17
Architectural Structures
ARCH 331
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
Su2014abn Steel Columns & Tension 19
Lecture 17
Architectural Structures
ARCH 331
Rigid Frame Design (revisited)
• 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
Su2014abn Steel Columns & Tension 20
Lecture 17
Architectural Structures
ARCH 331
Rigid Frame Design (revisited)
• column effective length, k
A
B
Su2014abn Steel Columns & Tension 21
Lecture 17
Architectural Structures
ARCH 331
Tension Members
• steel members can
have holes
• reduced area
• increased stress (AISC - Steel Structures of the Everyday) g
stAAA holesallofgn4
Su2014abn Steel Columns & Tension 22
Lecture 17
Architectural Structures
ARCH 331
Effective Net Area
• likely path to “rip” across
• bolts divide transferred force too
• shear lag UAA ne
Su2014abn Steel Columns & Tension 23
Lecture 17
Architectural Structures
ARCH 331
LRFD - Tension Members
• limit states
for failure
1. yielding
2. rupture*
Ag - gross area
Ae - effective net area
(holes 1/8” + d)
Fu = the tensile strength
of the steel (ultimate)
ntu PP
eunt AFP 75.0
gynt AFP. 900
n
u
PP