Example E.9 rectangular HSS compression member without slender elements

The results are generated with SDC Verifier 3.6 and calculated with FEMAP v11.0.0

Task:

Select an ASTM A500 Grade B rectangular HSS compression member, with a length of 20 ft, to support a dead load of 85 kips and live load of 255 kips in axial compression. The base is fixed and the top is pinned.

Solution:

From AISC Manual Table 2-4, the material properties are as follows:

ASTM A500 Grade B

F_y = 46 ksi

F_u = 58 ksi

From Chapter 2 of ASCE/SEI 7, the required compressive strength is:

Table Solution

From AISC Specification Commentary Figure C-A-7.1, for a fixed-pinned condition, k = 0.8.

(KL)_x = (KL)_y = 0.8(20.0 ft) = 16.0 ft.

Enter AISC Manual Table 4-3 for rectangular sections or AISC Manual Table 4-4 for square sections.

Try an HSS12×10×?.

From AISC Manual Table 4-3, the available strength in axial compression is:

The available strength can be easily determined by using the tables of the AISC Manual. Available strength values can be verified by hand calculations, as follows

Calculation Solution

From AISC Manual Table 1-11, the geometric properties are as follows:

HSS12×10×?

A_g = 14.6 in².

r_x = 4.61 in.

r_y = 4.01 in.

t_des = 0.349 in.

Slenderness Check

Note: According to AISC Specification Section B4.1b, if the corner radius is not known, b and h shall be taken as the outside dimension minus three times the design wall thickness. This is generally a conservative assumption.

Calculate b/t of the most slender wall.

Determine the wall limiting slenderness ratio, Λ_r, from AISC Specification Table B4.1a Case 6.

Λ < Λ_r; therefore, the section does not contain slender elements.

Because r_y < r_x and (KL)_x = (KL)_y, r_y will govern the available strength.

Determine the applicable equation.

Example from AISC Design Examples

Material summary

Properties Summary

1..HSS×12×10×?

Geometry Property	Value
Height	12.00
Width	10.00
h	12.00
b	10.00
d	0.349

FEM Loads and Constraint

1..Dead load 85 kips

2..Live load 255 kips

Constraint

1.. Pinned

Check 1..ANSI / AISC LRFD 360-10

Axial check

All (LS1, All Entities)

From AISC Specification Section E1, the available compressive strength is:

Comparing results of calculation in SDC Verifier and in Example E.9 we can see that values completely match. The available compressive strength is 518 kips.

Download SDC Verifier project file, model and report of  Example E.9