9b-Practice problem 5-4-1-Check compactness for Fy=60 ksi.

Last Updated on September 13, 2026 by Maged kamel

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Practice problem 5-4-1: Check compactness for Fy = 60 ksi.

Practice problem 5-4-1: Check compactness for Fy = 60 ksi.

Practice problem 5-4-1:: For W-, M-, and S-shapes with Fy = 60 ksi,, the first parta)a):: List the noncompact shapes in Part 1 of the Manual (when used as flexural members). State whether they are noncompact because of the Flange, the web, or both.
b. List the shapes in Part 1 of the Manual that are slender. State whether they are slender because of the Flange, the web, or both. Practice problem 5-4-1 is from the Steel Design Handbook.

List the W, M, and S shapes based on compactness when Fy=60 ksi.

The three steel sections, W, M, and S shapes, follow item 10 in Table B4.1b for the lambda value for the unstiffened Flange. For the web compactness h/tw, these sections follow item 15 in the same table,

The following slide shows the main differences among the W, M, and S shapes in the profile as an I-section. W shape has a slope of 2:12 and a broader Flange width. The S shape has a slope of 6:1 and is available in a smaller range. The M stands for Miscellaneous beams.

Practice problem 5-4-1-The differences between W, M and S shapes.

Determine the compactness ratios for Fy = 60 ksi.

Based on item 10 in Table B4.1b, the flange λFp=0.38*sqrt(E/Fy), since we have E29000 ksi and the given Fy=60 ksi, then λFp=0.38*sqrt(29000/60)=8.35. λFr=1.0*sqrt(E/Fy)=1*sqrt(29000/60)=21.964.

for the web compactness ratio, the Flange λwp=3.76*sqrt(E/Fy), λWp=3.76*sqrt(29000/60)=82.66. λwr=5.70*sqrt(E/Fy)=5.70*sqrt(29000/60)=125.31. Please refer to the next slide image for the detailed estimate of compactness ratios.

The value of compactness ratios for fy=60 ksi.

Table B4.1b details stiffened and unstiffened elements.

The next two slides show the details of items 10 and 15 for compactness ratios for members subjected to flexure.

Sort W sections based on bf/2tf>λFp but less than λfr.

We will use an Excel sheet for Table 1-1 for W sections and sort them by bf/2tf, which equals λFp but is less than 21.848, the value of λFr. These are the noncompact steel sections with Fy = 660 ksi.

The total number of W sections is 20, ranging from W30x90 to W6x0.50.

The next slide image shows the detailed dimensions of these noncompact W shapes.

The details of the 20 non-compact W sections for Fy=60 ksi.

Find the noncompact web for W sections based on Fy = 60 ksi.

There is no noncompact W section based on Fy = 60 ksi; the maximum h/tw for W30x90 is 57.50, which is smaller than λwp = 82.66.

Non compact W section data for Fy=60 ksi.

What are the tables for properties of M and S sections?

The next slide shows the tables used to find the properties of W, M, and S shapes. We use Table 1-1 for W sections, and Table 1-2 for M sections. For S shapes, we use Table 1-3.

The Tables used for data for W,M and S shapes.

Sort M sections based on bf/2tf>λFp but less than λFr.

We will use an Excel sheet for Table 1-2 for M sections and sort M sections with bf/2tf greater than 8.35 (the value of λFp) and less than 21.848 (the value of λFr). These are the noncompact sections with Fy = 60si. We have only five noncompact sections, ranging from M12x10 to M3x2.9.

The list of Non compact M shapes for Fy=60 ksi.

Find the noncompact web for sections based on Fy = 60 ksi.

e nThe noncompact web for M sections based on Fy = 60 ksi; the maximum h/tw for M12.5×12.40 is 74.80, which is smaller than wp = 2.66.

Non compact web section data for M shape with Fy=60 ksi.

Sort S sections by flange-to-web compactness ratio.

We will use an Excel sheet for Tables 1- 3 for S sections and sort them by bf/2tf, which is greater than 8.35 (the value of λFp) and less than 21.848 (the value of λFr). No noncompact S sections exist for steel with Fy = 60 ksi. For the r/tw ratio, noncompact S shapes have a noncompact web.