## Asd

LRFD and LSD

Shapes having single unreinforced webs

Shapes having multiple unreinforced webs such as I-sections

Support point of two nested Z-shapes

Mno Pn" Q

0 ■ 821 ——] + ( —I < 1 ■ 32 (6 ■ 68)

VfwPj VfbMnxJ - V 7

MP P , / x --h 0 ■ 85— < 1 ■ 65f (6 ■ 70)

Mno Pn

Note: The AISI Specification includes some exception clauses, under which the effect of combined bending and web crippling need not be checked. P is the concentrated load or reaction in presence of bending moment, Pn is the nominal web crippling strength for concentrated load or reaction in the absence of bending moment (for Equations 6.65, 6.66, 6.67, and 6.68), Pn is the nominal web crippling strength assuming single web interior one-flange loading for the nested Z-sections, that is, the sum of the two webs evaluated individually (for Equations 6.69 and 6.70), P is the required strength for concentrated load or reaction in the presence of bending moment (Pu for LRFD and Pf for LSD), M is the applied bending moment at, or immediately adjacent to, the point of application of the concentrated load or reaction, Mno is the nominal yield moment for nested Z-sections, that is, the sum of two sections evaluated individually, Mnxo is the nominal flexural strength about the centroidal x-axis determined in accordance with the specification excluding the consideration of lateral-torsional buckling, M is the required flexural strength at, or immediately adjacent to, the point of application of the concentrated load or reaction p (Mu for LRFD and Mf for LSD), O is the factor of safety = 1.75, Ob and Ow are the factors of safety for bending and web crippling, respectively, f is the resistance factor (0.9 for LRFD and 0.80 for LSD), fb is the resistance factor for bending, and fw is the resistance factor for web crippling.

6.6.5.1 Yielding

A very short, compact column under axial load may fail by yielding. For this case, the nominal axial strength is the yield load, that is,

where Ag is the gross area of the column and Fy is the yield point of steel.

6.6.5.2 Overall Column Buckling

Overall column buckling may be one of the following three types:

1. Flexural bucking — bending about a principal axis. The elastic flexural buckling stress is p2E

where E is the modulus of elasticity, K is the effective length factor for flexural buckling (Figure 6.28), L is the unbraced length of member for flexural buckling, and r is the radius of gyration of the full-section. 2. Torsional buckling — twisting about shear center. The elastic torsional buckling stress is p2ECw

where A is the full cross-sectional area, Cw is the torsional warping constant of cross-section, G is the shear modulus, J is the St. Venant torsion constant of cross-section, Kt is the effective length factor for twisting, Lt is the unbraced length of member for twisting, and r0 is the polar radius of gyration of cross-section about shear center.

3. Torsional-flexural buckling — bending and twisting simultaneously. The elastic torsional-flexural buckling stress is

Buckled shape of column is shown by dashed line |

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