Section 7.7
Compression Member Summary
Last Revised:
11/04/2014
Compressive strength is limited by:
 Material Strength
 General Buckling
 Local Buckling
Strength Limit States:
All strength limit states take the form:
LRFD 
ASD 
P_{u} <
f_{c}P_{n} 
P_{a} < P_{n}/W_{c} 
Req'd P_{n} = P_{u}/f_{c}
< P_{n} 
Req'd P_{n} =
P_{a} W_{c}
< P_{n} 
P_{u} / (f_{c}P_{n})
< 1.00 
P_{a} / (P_{n}/W_{c})
< 1.00 
f_{c} = 0.90 
W_{c} = 1.67 
Which is:
FORCE on a column < STRENGTH of a column
The STRENGTH of a Column is computed by:
The nominal capacity of the column, P_{n} = F_{cr}
A_{g}
Limit State 
Specification 
Critical Stress, F_{cr} 
Typical Design Variables 
Flexural Buckling 
E3 (Q=1), E7 
If (KL/r) < 4.71
sqrt(E/QF_{y})
or
QF_{y}/F_{e} < 2.25
Then: F_{cr} = [.658^{(QFy/Fe)}] QF_{y}
Else: F_{cr} = .877 F_{e} 
Member selection (A_{g}
and slenderness parameters), KL, support conditions 

F_{e} = p^{2}
E / (KL/r)^{2} = Euler Critical Buckling Stress

Q =1 for compact and noncompact sections

Q = Q_{s} Q_{a }for slender sections
 Q_{s}: Slenderness factor for unstiffened elements
(SCM E7.1). A function of the slenderness (b/t) of the
unstiffened element.
 Q_{a}: Slenderness factor for stiffened elements (SCM
E7.2). Different equations for flanges of square and
rectangular sections, circular sections, and other uniformly
compressed elements.
 KL = Effective Length. The choice of K will depend on how
the demand side of the inequality was computed.
Slenderness Limit State (SCM E2)
This serviceability limit state is not binding, but a good suggestion:
(KL/r) < 200
Computing Effective Length (SCM
Commentary 7.2)
Principles of Mechanics are used to determine the effective length of
columns. The effective length is a function of the overall member length,
length between lateral braces, end support condition, and the arrangement of
these factors relative to each principle axis.
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