Last Updated on August 31, 2024 by Maged kamel

## 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 part 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 difference between W, M, and S shapes in the profile as 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.

#### Determine the values of compactness ratios for Fy=60 ksi.

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

for the web compactness ratio, the flange ฮปwp=3.76*sqrt(E/Fy), ฮปWp=3.76*sqrt(29000/60)=82.66. ฮปwr=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.

#### 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>ฮปFp but less than ฮปfr.

We will use an Excel sheet for Table 1-1 for W sections and sort W sections with bf/2tf bigger than 8.35, which is the value of ฮปFp, but smaller than 21.848, the value for ฮปFr. These are the non-compact sections for steel, with Fy=60 ksi.

The total number of W sections is 20, starting from W30x90 and ending with W6x0.50.

The next slide image shows the detailed dimension of these non-compact W shapes.

#### Find the non-compact web for W sections based on Fy=60ksi.

There is no non-compact web for W sections based on Fy=60 ksi; the maximum h/tw for W30x90 is 57.50, smaller than the value of ฮปwp, 82.66.

### 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 for M sections, we use Table 1-2. For S shapes, we use Table 1-3.

#### Sort M sections based on bf/2tf>ฮปFp but less than ฮปFr.

We will use an Excel sheet for Table 1-2 for M sections and sort M sections with bf/2tf bigger than 8.35, the value of ฮปFp, but smaller than 21.848, the value for ฮปFr. These are the non-compact sections for steel, with Fy=60 ksi. We have only five non-compact sections, starting from M12x10 and ending with M 3×2.9.

#### Find the non-compact web for M sections based on Fy=60ksi.

There is no non-compact web for M sections based on Fy=60 ksi; the maximum h/tw for M12.5×12.40 is 74.80, smaller than the value of ฮปwp, 82.66.

#### Sort S sections based on the flange and web compactness ratio.

e will use an Excel sheet for Table 1-3 for S sections and sort S sections with bf/2tf bigger than 8.35, which is the value of ฮปFp but smaller than 21.848, the value for ฮปFr. There are no non-compact S sections for steel, with Fy=60 ksi. As for the ratio h/tw, there are no non-compact S shapes for the web.

### Part b-Sort W, M, and S sections are based on slender sections.

Based on Fy=60 ksi, the W, M, and S sections do not have slender sections. We have reached the end of our post. Thanks a lot.

Here is the link for **Chapter 8 – Bending Members**.

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There is a newly added post, which is a p**ractice problem 5-5-6****-Compute Lp and Lr and ฯb*M**n.