Page 250 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.30

CRITERIA FOR BUILDING DESIGN

5.30 CHAPTER FIVE

φ b = resistance factor for tension = 0.90 for yielding or 0.75 for rupture
φ b = resistance factor for flexure = 0.90
The following definitions apply for ASD design, using ASD load combinations:
f a = required compression, ksi (MPa)
F = F cr = F cr = allowable axial stress (compression or tension as appropriate), ksi (MPa)
Ω
Ω
a
c
t
f bw , f bz = required flexural stress at the specific location in the cross section, ksi (MPa)
F , F = Ω M n S = allowable flexural stress, ksi (MPa). Use the section modulus for the specific
bw
bz
b
location in the cross section and consider the sign of the stress.
Ω c = safety factor for compression = 1.67
Ω t = safety factor for tension = 1.67 for yielding or 2.00 for rupture
Ω b = safety factor for flexure = 1.67
5.7.4 Round and Rectangular HSS under Torsion
Closed sections are particularly advantageous where a member is required to resist torsion. The
design torsional strength φ T T n and the allowable torsional strength T n /Ω T for round and rectangular
HSS is determined as follows using φ T = 0.90 (LRFD) and Ω T = 1.67 (ASD). The nominal torsional
strength T n for the limit states of torsional yielding and torsional buckling is

T n = F cr C (5.106)
where C is the HSS torsional constant and F cr is the critical torsional shear stress.
For a round HSS,
−
2
)
C = π( Dt t (5.107)
2
For rectangular HSS,
C = 2(B − t)(H − t)t − 4.5(4 −π)t 3 (5.108)

For round HSS, F cr is the larger of the following:
.
F = 123 E ≤ 06 . F y (5.109)
cr
/
LD D t / ) 54
/(
and
.
F = 060 E ≤ 06 . F y (5.110)
cr
/
(/ 32
Dt)
For rectangular HSS, F cr depends on the h/t ratio, as follows.
/
/
For ht ≤ 245 E F ,
.
y
(5.111)
F cr = 0.6F y
For 2 45 EF < / h t ≤ 3 07 EF y
.
.
/ ,
/
y
/
 245. EF 
F = 06. F  y  (5.112)
y
cr
  (/  
ht)
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