PE Exam Sample Question, Structural

How to Calculate the Compression Capacity of a Steel Column 

... the easy way.

Examinees lose the most points in the structural questions. Here is a tip for answering structural questions. Many questions can be answered using tables in AISC 360, the "Steel Construction Manual."
For example, look at Table 4-22. For any section, convert to KL/r (L in inches) and then use the table to find the maximum axial compressive load (Fcr in ksi). Multiply Fcr by the cross sectional area of the column and that is the capacity.
Problem:
Given:
Column = HSS 6x6x1/4
Material = A500 Grade B, Fy = 46 ksi
Column Height = 18 feet, no bracing
K = 0.8
Find:
Maximum axial capacity in compression

Solution:
1.) Look up the r value in Table 1-12 of AISC. r = 2.34 inches. Also note the area of the cross section for later. A = 5.24 square inches. (page 1-93 of the steel manual)
2.) Calculate KL/r = (0.8)(18ft x 12"/ft) / (2.34) = 73.8
3.) Use Table 4-22 (page 4-323). Find the column for F_y = 46 ksi. Within that column, find the sub-column for KL/r on the left. Follow the KL/r column down to the value closest to 73.8, which is 74. Now, follow the row to the right. You will see two values. The ASD value is 19.1 ksi (highlighted green in the 14th edition) and the LRFD value is 28.6 ksi.
4.) Multiply F_cr x A = 19.1 x 5.24 = 100,100 pounds maximum capacity in axial compression.

Notes:
* Linear interpolation within the table is permitted. (But, the precision of the answer choices on the exam will not likely require it.)
* If you use Euler's equation, there are several checks you would have to calculate rather than the two simple ones in this procedure.
* This example uses a bi-symmetric section. The X-X and Y-Y axes have the same r value. If you had a Wide Flange or other section, you must check both axes and use the lower r value.
* L is the least braced length and can differ from one axis to the other.
* 35 ksi: railing (A53, Grade B carbon steel)
* 36 ksi: pipe, angles, channels (A36)
* 42 ksi: round HSS (A500 Grade B)
* 46 ksi: square and rectangular HSS (A500 Grade C)
* 50 ksi: W shapes, WT shapes (A572, A992)
* Notice that omega-o and phi-sub-c are already applied to the values for F_cr. Do not apply these reductions a second time. 
* Tables 4-1 to 4-12 can be used for specific sections of plain steel. 
* Tables 4-13 to 4-15 can be used for axial compression capacity of concrete-filled hollow sections. 
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