APPENDIX B DESIGN REQUIREMENTS
APPENDIX B DESIGN REQUIREMENTS
Appendix B5.1 provides an expanded definition of limiting width-thickness ratio for webs in combined flexure and axial compression. Appendix B5.3 applies to the design of members containing slender compression elements.
B5. LOCAL BUCKLING
1. Classification of Steel Sections
For members with unequal flanges and with webs in combined flexural and axial compression, l r for the limit state of web local buckling is
ú (A-B5-1)
èøè h
For members with unequal flanges with webs subjected to flexure only, l r for the limit state of web local buckling is
æö h ù
l r = 1.49 + 1 2.83
èø ç÷ h c ú û
(A-B5-2)
4 h c 2 where l r , h, and h c are as defined in Section B5.1.
These substitutions shall be made in Appendices F and G when applied to members with unequal flanges. If the compression flange is larger than the tension flange, l r shall be determined using Equation A-B5-1, A-B5-2, or Table B5.1.
3. Slender-Element Compression Sections
Axially loaded members containing elements subject to compression which have a width-thickness ratio in excess of the applicable l r as stipulated in Section B5.1 shall be proportioned according to this Appendix. Flexural members with slender compression elements shall be designed in accordance with Appendices F and G. Flexural members with proportions not covered by Appendix F1 shall be designed in accordance with this Appendix.
90 LOCAL BUCKLING [App. B5.
3a. Unstiffened Compression Elements
The design strength of unstiffened compression elements whose width-thickness ratio exceeds the applicable limit l r as stipulated in Section B5.1 shall be subject to
a reduction factor Q s . The value of Q s shall be determined by Equations A-B5-3 through A-B5-10, as applicable. When such elements comprise the compression flange of a flexural member, the design flexural strength, in ksi, shall be computed
using f b F y Q s , where f b = 0.90. The design strength of axially loaded compression members shall be modified by the appropriate reduction factor Q, as provided in Appendix B5.3d.
(a) For single angles:
when 0.45 EF / y < bt / < 0.91 EF / y :
Q s = 1.340 - 0.76( / ) bt F y / E (A-B5-3)
when bt EF / > 0.91 / y :
Errata 9/4/01
E 0.53 / é Fbt
ë y () / ù û
(A-B5-4)
(b) For flanges, angles, and plates projecting from rolled beams or columns or other compression members:
when 0.56 EF / y < bt / < 1.03 EF / y :
Q s = 1.415 0.74( / ) - bt F y / E (A-B5-5)
when bt / ³ 1.03 EF / y :
E 0.69 / é Fbt / ù
ë y () û
(A-B5-6) (c) For flanges, angles and plates projecting from built-up columns or other com-
pression members:
when 0.64 EF /( y / k c ) < bt / < 1.17 EF /( y / k c ):
Q s = 1.415 0.65( / ) ( - bt F y / kE c )
(A-B5-7)
when bt / ³ 1.17 EF /( y / k c ): Q 2
s = 0.90 Ek c / é Fbt () / ù ë y û
(A-B5-8)
The coefficient, k c , shall be computed as follows:
(a) For I-shaped sections:
App. B5.] LOCAL BUCKLING 91
, 0 35 0 763 . £ k c £ .
ht / w where
h = depth of web, in. (mm) t w = thickness of web, in. (mm)
(b) For other sections: k c = 0.763 (d) For stems of tees:
when 0.75 EF d t EF / y < / < 1.03 / y :
Q s = 1.908 1.22( / ) - dt F y / E (A-B5-9) Errata
when dt EF / ³ 1.03 / y :
(A-B5-10) where
Fdt 0.69 / é ë y (/) û ù
d = width of unstiffened compression element as defined in Section B5.1, in. (mm) t = thickness of unstiffened element, in. (mm)
3b. Stiffened Compression Elements
When the width-thickness ratio of uniformly compressed stiffened elements (except perforated cover plates) exceeds the limit l r stipulated in Section B5.1, a
reduced effective width b e shall be used in computing the design properties of the section containing the element.
(a) For flanges of square and rectangular sections of uniform thickness:
when ³ 1.40 :
0.38 E ù
b e = 1.91 t
f ë ú ê (/) bt f ú û
(A-B5-11)
otherwise b e = b. (b) For other uniformly compressed elements:
when b ³ E 1.49 :
0.34 E ù
b e = 1.91 t
(A-B5-12)
f ê ë (/) bt f û ú
otherwise b e = b. where
92 LOCAL BUCKLING
[App. B5.
b = actual width of a stiffened compression element, as defined in Section B5.1, in. (mm)
b e = reduced effective width, in. (mm) t = element thickness, in. (mm)
f = computed elastic compressive stress in the stiffened elements, based on the design properties as specified in Appendix B5.3c, ksi (MPa). If un- stiffened elements are included in the total cross section, f for the stiff- ened element must be such that the maximum compressive stress in the
unstiffened element does not exceed f c F cr as defined in Appendix B5.3d with Q = Q s and f c = 0.85, or f b F y Q s with f b = 0.90, as applicable.
(c) For axially loaded circular sections with diameter-to-thickness ratio D / t greater than 0.11E/F y but less than 0.45E / F y
0.038 E 2
(A-B5-13)
FDt y (/) 3
where
D = outside diameter, in. (mm) t = wall thickness, in. (mm)
3c. Design Properties
Properties of sections shall be determined using the full cross section, except as fol- lows:
In computing the moment of inertia and elastic section modulus of flexural mem- bers, the effective width of uniformly compressed stiffened elements b e , as deter- mined in Appendix B5.3b, shall be used in determining effective cross-sectional properties.
For unstiffened elements of the cross section, Q s is determined from Appendix B5.3a. For stiffened elements of the cross section
effective area
(A-B5-14)
actual area
where the effective area is equal to the summation of the effective areas of the cross section.
3d. Design Strength
For axially loaded compression members the gross cross-sectional area and the radius of gyration r shall be computed on the basis of the actual cross section. The critical stress F cr shall be determined as follows:
(a) For l c Q £ 1.5:
(A-B5-15) (b) For l c Q > 1.5:
cr = Q (0.658 ) F y
93
App. B5.]
LOCAL BUCKLING
é 0.877 ù
F cr =ê 2
(A-B5-16)
where Q = QQ s a (A-B5-17) Cross sections comprised of only unstiffened elements, Q = Q s , (Q a = 1.0) Cross sections comprised of only stiffened elements, Q = Q a , (Q s = 1.0) Cross sections comprised of both stiffened and unstiffened elements, Q = Q s Q a
App. E App. E