## Na

3.76p(E/Fy) for nonseismic application 3.05p(E/Fy) for seismic application

For Pu/fbPy < 0.125: 3.76(1 - 2.75Pu/fbPy)P(E/Fy) for nonseismic application 3.05(1 - 1.54Pu/fbPy)P(E/Fy) for seismic application

For Pu/fbPy > 0.125: 1.12(2.33 - Pu/fbPy)P(E/Fy) > 1.49P(E/Fy) f b = 0.90

Pu factored axial force

C.C7E/Fy

D = outside dl-meter t wall thickness

Fyf = flange yield strength Fyw = web yield strength Fr = flange compressive residual stress (10 ksi for rolled shapes, 16.5 ksi for welded shapes) 0.95p[E/(FL/kc)c Fl = as defined above kc = as defined in the footnote of Table 4.4

C.31E/Fy a See Figure 4.5 for definition of b, hc, and t. b For ASD, this limit is 0.56P(E/Fy).

c For ASD, this limit is 0.56p[E/(Fyf/kc)], where kc = 4.05/(h/t)046 if h/t> 70, otherwise kc = 1.0. d For ASD, this limit is 4.46^/(E/Fb), where Fb = allowable bending stress.

Note: In all the equations, E is the modulus of elasticity and is Fy is the minimum specified yield strength.

4.5.1 Flexural Member Design

4.5.1.1 Allowable Stress Design 4.5.1.1.1 Flexural Strength Criterion

The computed flexural stress, fb, shall not exceed the allowable flexural stress, Fb, as given below (in all equations, the minimum specified yield stress, Fy, can not exceed 65 ksi).

4.5.1.1.1.1 Compact Section Members Bent about Their Major Axes — For Lb < Lc

where

Lc = smaller of {76bf^Fy,20,000/(d/Af)Fy}, for I and Channel shapes

= [1,950 + 1,200(Mi/M2)](b/Fy) > 1,200(b/Fy),for box sections,rectangular and circular tubes in which bf is the flange width (in.), d is the overall depth of the section (ksi), Af is the area of the compression flange (in.2), b is the width of the cross-section (in.), and M1/M2 is the ratio of the smaller to larger moment at the ends of the unbraced length of the beam; M1/M2 is positive for reverse curvature bending and negative for single curvature bending.

For the above sections to be considered as compact, in addition to having the width-thickness ratios of their component elements falling within the limiting value of 1p shown in Table 4.8, the flanges of the sections must be continuously connected to the webs. For box-shaped sections, the following requirements must also be satisfied: the depth-to-width ratio should not exceed six, and the flange-to-web thickness ratio should not exceed two. For Lb > Lc, the allowable flexural stress in tension is given by

and the allowable flexural stress in compression is given by the larger value calculated from Equations 4.30 and 4.31. While Equation 4.30 normally controls for deep, thin-flanged sections where warping restraint torsional resistance dominates, Equation 4.31 normally controls for shallow, thick-flanged sections where St Venant torsional resistance dominates:

2 Fya/rT)2

3 1,530 x 103Cb

Fy rT y Fy

170,000 Cb I 510,000Cb

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