## Asd

LRFD and LSD

When

OCP ObMx ObMy

OCP ObCmxMx ObCmyMy OcP/Pn > 0.15, -C- + x + bCmy y < 1.0

Pn Mnx a-x Mnyay

When

When p cm C MA

fcPno fbMnx fbMn

Note: Mx and My are the required moments with respect to the centroidal axes of the effective section determined for the required axial strength alone, Mnx and Mny are the nominal flexural strengths about the centroidal axes, Mx and My are the required flexural strengths with respect to the centroidal axes of the effective section determined for the required axial strength alone (Mux and Muy for LRFD, Mfx and Mfy for LSD), P is the required axial load, Pn is the nominal axial strength determined in accordance with Equation 6.75, Pno is the nominal axial strength determined in accordance with Equation 6.75, for Fn = Fy, T is the required compressive axial strength (Pu for LRFD and Pf for LSD), ax = 1 — OcP/Pex (for Equation 6.85), ay = 1 — OcP/PEY (for Equation 6.85), ax = 1 — T/PEX (for Equation 6.86), ay = 1 — T/PEY (for Equation 6.86), PEX = p2EIx/(KxLx)2, PEY = n2EIy/(KyLy)2, Ob is the factor of safety for bending, Oc is the factor of safety for concentrically loaded compression, and Cmx and Cmy are the coefficients whose value is taken as follows:

1. For compression members in frames subject to joint translation (side sway), Cm = 0.85.

2. For restrained compression members in frames braced against joint translation and not subjected to transverse loading between their supports in the plane of bending, Cm = 0.6 — 0.4(M1/M2), where M1/M2 is the ratio of the smaller to the larger moment at the ends of that portion of the member under consideration which is unbraced in the plane of bending. M1/M2 is positive when the member is bent in reverse curvature and negative when it is bent in single curvature.

3. For compression members in frames braced against joint translation in the plane of loading and subjected to transverse loading between their supports, the value of Cm may be determined by rational analysis. However, in lieu of such analysis, the following values maybe used: (1) for members whose ends are restrained, Cm = 0.85 and (2) for members whose ends are unrestrained, Cm = 1.0.

Ix, Iy, Lx, Ly, Kx, and Ky have been defined previously.

### 6.6.7 Closed Cylindrical Tubular Members

Thin-walled closed cylindrical tubular members are economical sections for compression and torsional members because of their large ratio of radius of gyration to area, the same radius of gyration in all directions, and the large torsional rigidity. The AISI design provisions are limited to the ratio of outside diameter to wall thickness, D/t, not being greater than 0.441E/Fy.

6.6.7.1 Bending Strength

For cylindrical tubular members subjected to bending, the nominal flexural strengths are as follows according to the D/t ratio:

where D is the outside diameter of the cylindrical tube, t is the wall thickness, Fc is the critical buckling stress, and Sf is the elastic section modulus of full, unreduced cross-section. Other symbols have been defined previously.

### 6.6.7.2 Compressive Strength

When cylindrical tubes are used as concentrically loaded compression members, the nominal axial strength is determined by Equation 6.75, except that (1) the elastic buckling stress, Fe, is determined for flexural buckling by using Equation 6.72 and (2) the effective area, Ae, is calculated by Equation 6.92 given below:

where

A0 = {0.037/[(DFy)/(tE)] + 0.667}A < A for D/t < 0.441E/ Fy (6.93)

A = area of unreduced cross-section In the above equations, the value A0 is the reduced area due to the effect of local buckling [1,7].

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