Page 249 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.29

CRITERIA FOR BUILDING DESIGN

CRITERIA FOR BUILDING DESIGN 5.29

For ASD design, using ASD load combinations,
P r = P a = required tensile strength, kips (N)
P c = P n /Ω t = allowable tensile strength, kips (N)
M r = required flexural strength, kip⋅in (N⋅mm)
M c = M n /Ω b = allowable flexural strength, kip⋅in (N⋅mm)
Ω t = safety factor for tension
= 1.67 for gross section yielding = 2.00 for net section rupture
Ω b = safety factor for flexure = 1.67

5.7.2 Doubly Symmetric Members under Axial Compression
and Single-Axis Flexure
For doubly symmetric members in flexure and compression with moments primarily in one plane,
the AISC Specification permits one to consider two separate independent limit states, in-plane insta-
bility and out-of-plane buckling or flexural-torsional buckling, as an alternative to the combined
approach provided in Art. 5.7.1. For the limit state of in-plane instability, use Eqs. (5.105) and
(5.106) with P c , M r , and M c determined in the plane of bending. For the limit state of out-of-plane
buckling, use the following:

P r +   M  2 (5.104)
r
P co  M   ≤10.
cx
where P co = available compressive strength out of the plane of bending, kips (N)
M cx = available flexural-torsional strength for strong axis flexure, kip⋅in (N⋅mm)
If bending occurs only about the weak axis, the moment ratio in Eq. (5.104) may be neglected.
For members with significant biaxial moments, M r /M c ≥ 0.05 in both directions, use Eqs. (5.102) and
(5.103).

5.7.3 Unsymmetric and Other Members under Axial Force and Flexure
The method presented here is for unsymmetric shapes, but may be used as an alternative for shapes
discussed in Art. 5.7.1. Equation (5.105), absolute value, must be satisfied using the principal bend-
ing axes, either by the addition of all the maximum axial and flexural terms, or by considering the
sense of the flexural stresses at the critical points of the cross section. The flexural terms are either
added or subtracted from the axial term as appropriate. Second-order effects must be included, as
discussed in Art. 5.2.
f a + f bw + f bz (5.105)
.
F a F bw F bz ≤10
The subscripts w and z indicate the major and minor axes of bending, respectively.
The following definitions apply for LRFD design, using LRFD load combinations:

f a = required axial stress, ksi (MPa)
F a =φ c F cr or φ t F cr = design axial stress (compression or tension as appropriate), ksi (MPa)
f bw , f bz = required flexural stress at the specific location in the cross section, ksi (MPa)
F bw , F bz =φ b M n /S = design flexural stress, ksi (MPa). Use the section modulus for the specific
location in the cross section and consider the sign of the stress.
φ c = resistance factor for compression = 0.90

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