where 1c = (KL/rn)v/(Fy/E) is the slenderness parameter, Ag is the gross cross-sectional area, Fy is the specified minimum yield stress, E is the modulus of elasticity, K is the effective length factor, l is the unbraced member length in the plane of buckling, and r is the radius of gyration of the cross-section about the axis of buckling.

The first part of Equation 4.17 is the design strength for inelastic buckling and the second part is the design strength for elastic buckling. The slenderness parameter 1c = 1.5 is the slenderness parameter that demarcates between inelastic behavior from elastic behavior.

Torsional buckling (with width-thickness ratio < 1r): f cPn is to be calculated from Equation 4.17, but with 1c replaced by 1e and given by

1e VFe where p2ECW

in which Cw is the warping constant, G is the shear modulus = 11,200 ksi (77,200 MPa), Ix, Iy are the moments of inertia about the major and minor principal axes, respectively, J is the torsional constant, and Kz is the effective length factor for torsional buckling.

The warping constant Cw and the torsional constant J are tabulated for various steel shapes in the AISC-LRFD Manual (AISC 2001). Equations for calculating approximate values for these constants for some commonly used steel shapes are shown in Table 4.5.

Flexural-torsional buckling (with width-thickness ratio < 1r): Same as for torsional buckling except Fe is now given by For singly symmetric sections:

Fes H Fez

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