Last Updated on September 17, 2026 by Maged kamel
Solved Problem 13-28 For Compression Members-FE Exam.
This is a summary of the content of the post-8 introduction to solved problem 13-28: how to use Table 4-1 from NCEES Reference Handbook 10.4?
Detailed illustration for the Solved problem13-28 from Prof. Iqbal’s handbook.
We are going to have to look for a solved problem from Prof. Iqbal’s book, and the main title is How to use the AISC Table 4-1 from the Table; we can estimate the Φ*Pn available strength.
This is a solved problem from M. Iqbal. A W12 x50 is used as a column, as shown. Fy = 50 ksi, and the bottom support is fixed.
With a guided roller at the top, it is required to estimate the available strength in axial compression in kips; select the correct answer from the following options: 1) 90 kips, 2) 270 kips, 3) 360 kips, and 4) 660 kips.
For the solution, the roller allows movement in a delta, but the slope is zero. And provides Moment. As if fixed at the top, it contains both movement and fixation in both directions, x and y. We will choose type C. The Euler buckling Value,,Pcr = pi^2 EI/k*L)^2,, is shown in the next slide image.
Table C-A-7-1 lists six support-condition cases and the corresponding recommended effective K values.
What is the selected K Value?
The K Value for Type C is 1.2, as recommended in Table C-A-7-1 for both the X and y direYYtions.
For solved problem 13-28. Lex equals Ley and is 18 feet. Next, use Table 1-1 for the W12x50 data.
How to use Table 1-1-FE-Handbook 10.4?
This Table is quoted from the FE Reference Handbook and lists W sections with Area, depth, Flange width & thickness, and inertias about axes x and y for E = 29000 ksi and yield stress = 50 ksi. The next slide shows the first part of Table 1-1, which contains data for W sections from W24 to W16.
The required W12x50 is not a slender column because the C letter is not included in W12x50.
What are the data for W12x50 from Table 1-1? The Area is 14.60 in2; rx is 5.18 in, and ry is 1.96 in.
What is the requirement of Table 4-1?
Table 4-1 requires that the tabulated effective length concerning ry is the maximum Value of ly required from the X, or the ly modified, which is Lex*(ry/rx), direction, and the ly Value from the y-direction, the lc y, equals 6.81 feet; please refer to the following slide image.
The Ly Value equals 18 feet; the selected effective length is the maximum of 8.61 and 18 feet; we will proceed to Table 4-1 to obtain the available strength (LRFD) Value.
What is the available strength from Table 4-1?
We use Ly = 18 feet, move horizontally, and drop a line from the top W12x50 section; the intersection gives an available strength of 270 kips, which matches option B.
Solved problem 13-28-Use Provision E-1 from AISC-360-16.
We could achieve the same result by using the E-1 provision of AISC-360-16, determining whether the given column is short or long, and then selecting the appropriate Fcr equation.
The curve we discussed, at KL/r = 4.71*sqrt(E/Fy), distinguishes between short and long columns.
If Le/r = KL/r > 4.71*sqrt (E/Fy), then the column is considered a Long column, and hence the Euler Elastic stress. The division of pi^2 EI/ (kl)^2 over the Area; then the stress will be (pi^2 E/ (le/r)^2).
The limiting Value for Fy = 50 ksi and E = 29000 ksi is 113.43.
We will estimate the lengths of column lcx, Lcy, and KL/r = 4.71* sqrt (E/Fy), which distinguishes between short and long columns.
If KL/r > 4.71* sqrt (E/Fy), the column is considered a Long column and therefore uses Euler Elastic stress. The division of pi^2 EI/ (kl)^2 over the Area; then the stress will be (pi^2 E/ (kl/r)^2). The Value of Lcx = 41.70; the Value of lcy equals 110.240. Select the larger Value: 110.204.
In the next slide, there is a hint: what is Lcy from the column in the x direction compared to Lcy in the y direction?
We will apply the Fcr equation for the short column; the critical stress equals 0.658^lambda-2* Fy, where lambda^2 = Fy/Fe. The Euler stress equals 23.567 ks; the Fcr=20.574 ksi, multiplied by phi and the Area to get the LRFD Value of the available strength, which equals 270.34, very close to option B.
Please refer to the following slide image for more details.
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