V. AISC N690 1984 Pipe Section With SLC

Slenderness Ratio

The slenderness ratio is the same about either local z or y axes: KL/r = 120 in / 1.888 in = 63.56 < 300, OK

Axial Tension

From section Q1.5.1.1, the allowable tensile stress:

The actual tensile stress from load case 1:

Stress ratio = 2.49 / 21.6 = 0.115, hence OK.

Axial Compression

Allowable compressive stress per Cl Q1.9.2.3:

Since Kl/r < C_c , per eq. Q1.5-1, the allowable axial compressive stress:

The actual compressive stress from load case 2:

Stress ratio = 2.49 / 17.08 = 0.146, hence OK.

Bending

Section is compact per Cl Q1.5.1.4.1:

Allowable bending stress about both axes: F_b = 0.66×F_y = 23.76 ksi

Moment due to load case 3 or 4 on a propped cantilever (ref. AISC Steel Construction Manual):

Actual bending stress about the major axis:

Actual bending stress about the minor axis:

Stress ratio: 9.17 / 23.76 = 0.386, hence OK.

Combined Bending and Axial Tension

Interaction per Cl Q1.6.2 in load case 3 (tension + bending):

(Eq. Q1.6-1b)

Combined Bending and Axial Compression

Interaction per Cl Q1.6 in load case 4 (compression + bending):

(Eq. Q1.6-2)

Shear

Actual shear (at supports):

Shear area (calculated as per Gere & Timoshenko reference):

where

=

the inner radius of the pipe = 5.56 / 2 - 0.24 = 2.54 in

=

the outer radius of the pipe = 5.56 / 2 = 2.78 in

Thus, the shear area along both axes = 2.008 in² .

The allowable shear stress:

Stress ratio in Y (minor axis): 0.98/14.4 = 0.068, hence OK.

Stress ratio in Z (major axis): 0.94/14.4 = 0.065, hence OK.