Page 227 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.7

CRITERIA FOR BUILDING DESIGN

CRITERIA FOR BUILDING DESIGN 5.7

Moments and forces may be obtained from a general second-order elastic analysis that considers
both P–∆ and P–δ effects, where equilibrium is satisfied for the deformed geometry. Alternatively,
moments and forces may be obtained by amplification of a traditional first-order elastic analysis,
where equilibrium is satisfied for the original or undeformed structure. In low-rise moment frames,
the amplification of axial forces is often negligible, but it becomes more significant in high-rise struc-
tures. Amplified values of the required flexural strength and axial strength may be calculated from
the following equations:
(5.3)
M r = B 1 M nt + B 2 M lt
(5.4)
P r = P nt + B 2 P lt
where
B = C m ≥ 1 (5.5)
1
( 1− α PP / e1 )
r
B = 1 ≥ 1 (5.6)
1−∑ P ∑ / P e2
2
α
nt
α= 1.0 (LRFD) = 1.60 (ASD)
The following definitions apply:
M r = required second-order flexural strength, kip⋅in (N⋅mm)
M nt = first-order moment, assuming no lateral translation of frame, kip⋅in (N⋅mm)
M lt = first-order moment as a result of lateral translation of frame only, kip⋅in (N⋅mm)
P r = required second-order axial strength, kips (N)
P nt = first-order axial force, assuming no lateral translation of frame, kips (N)
∑P nt = total vertical load supported by a story, including gravity column loads, kips (N)
P lt = first-order axial force, as a result of lateral translation of frame only, kips (N)
C m = coefficient assuming no lateral translation of frame, the value of which is taken as follows:
• For beam-columns not subject to transverse loading between supports in the plane of bending,
 M 
−
.
C = 06 04 .  1  (5.7)
m
 M 
2
where M 1 and M 2 , calculated from a first-order analysis, are the smaller and larger moments,
respectively, at the ends of that portion of the member unbraced in the plane of bending under
consideration. M 1 /M 2 is positive when the member is bent in reverse curvature, negative when
it is bent in single curvature.
• For beam-columns subjected to transverse loading between supports, the value of C m may be
determined either by analysis or taken conservatively as 1.0.
P e1 = elastic critical buckling load of the member in the plane of bending, kips (N)
π 2 EI
P = (5.8)
e1
( KL) 2
1
ΣP e2 = elastic critical buckling resistance for the story determined by sidesway buckling analy-
sis, kips (N)
• For moment frames where sidesway buckling effective length K 2 factors are determined for the
columns, the following equation may be used:
e2 ∑
∑ P = π 2 EI
( KL) 2 (5.9a)
2

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