Page 248 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.28

CRITERIA FOR BUILDING DESIGN

5.28 CHAPTER FIVE

5.7.1 Doubly and Singly Symmetric Members under
Axial Force and Flexure

Doubly and singly symmetric members subjected to axial force and flexure may be treated as fol-
lows. (See Arts. 5.7.2 and 5.7.3 for alternatives.) The interaction of compression and flexure in
members for which 0.1 ≤ (I yc /I y ) ≤ 0.9, constrained to bend about a geometric axis (x and/or y), is
limited by the following equations, where I yc is the moment of inertia about the y axis referred to the
4
4
compression flange, in (mm ).
/
For PP ≥ 02
. ,
r
c
P r + 8   M rx + M   ≤10. (5.102)
ry
P c 9  M cx M 
cy
/
. ,
For PP < 02
c
r
P r +  M rx + M  ≤ 10 . (5.103)
ry
2 P c   M cx M  
cy
The following definitions apply when the axial force causes compression:
For LRFD design, using LRFD load combinations,
P r = P u = required compression strength, kips (N)
P c =φ c P n = design compression strength, kips (N)
M r = required flexural strength, kip⋅in (N⋅mm)
M c =φ b M n = design flexural strength, kip⋅in (N⋅mm)
φ c = resistance factor for compression = 0.90
φ b = resistance factor for flexure = 0.90
For ASD design, using ASD load combinations,
P r = P a = required compression strength, kips (N)
P c = P n /Ω c = allowable compression 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 c = safety factor for compression = 1.67
Ω b = safety factor for flexure = 1.67
Doubly and singly symmetric members subjected to tension and flexure are also subject to Eqs.
(5.102) and (5.103), but the definitions of terms differ. Also, when determining M n for doubly sym-
metric members, the C b term (see Art. 5.5) may be increased by (1 + P u /P ey ) 1/2 for LRFD and (1 +
1/2
1.5 P a /P ey ) for ASD, where the tension acts concurrently with flexure. The elastic critical buckling
2
2
load is given by P ey =π EI y /L b .
The following definitions apply when the axial force causes tension:
For LRFD design, using LRFD load combinations,
P r = P u = required tensile strength, kips (N)
P c =φ t P n = design tensile strength, kips (N)
M r = required flexural strength, kip⋅in (N⋅mm)
M c =φ b M n = design flexural strength, kip⋅in (N⋅mm)
φ t = resistance factor for tension
= 0.90 for gross section yielding = 0.75 for net section rupture
φ b = resistance factor for flexure = 0.90

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