## Practice problem 5-2-3-verify Zx for W18x50

### Practice Problem-5-2-3-verify Zx for W18x50.

Verify the value of Zx of the W section W18x50 that is tabulated in the dimensions and properties Tables in Part 1- of the manual. We will consider two ways to estimate the Zx of W18x50.

The first method is to consider the W section as composed of two Wt sections. each Wt section is WT 9×25.

The second method is to consider the W section as an assembly of three plates and find The Yct and the At/2 values.

We can represent the W18x50 as two Wt sections assembled. The dimension of each Wt is 9×25 as we can see in the sketch. From Table 1-8 of the manual, there are two parts of that table Part 1, which gives us the dimension of the Wt section. The breadth of the flange and its thickness and the overall height and thickness of the stem.

From part 1, I need to know the area for Wt 9×25, which is equal to 7.34 inch2, and the depth of the wt section which is 9 inches.

### The distance Y bar from the top of the WT9x25.

In the next slide, there is part 2 of Table 1-8 from which I need only the value of y bar which is the distance from the top of the flange to the Cg of the section the value is 2.12 inches.

In the third slide, I draw the W section, assembled from the Two WT sections, in which we can find the value of the YCt or the distance from the Compression force and the tension force each force acts on the CG.

The Yct value is equal to( d-2y bar), where d is the overall depth of the W18x50 section, the y bar, we have got from the previous slide. Then the distance YCT value is equal to 18-2*2.12=13.76 inches. the area of At/2 equals 7.34 inch2, which we obtained from Table 1-8. We apply the equation of Zx equal At/2*(yct)=7.34*13.76=101.0 inch3.

From the next slide, there are two parts for Table 1- 1, the first part gives the dimension of the W section. The breadth of the flange is 7.50″ and the overall depth is 18 inches. The area is 14.70 inch2.

### Find the Zx for W18x50 from Table 1-1.

In the next slide, we view the second part that gives the value of Zx which is 101.0 inch3. The same is the value estimated via Table 1-8. and matches with our previous calculations as a Two Wt section. The validation is ok.

### Verify Zx of W18x50 by considering areas of flange and web.

If we consider the W section as composed of areas, the first area is the flange which is 7.50″ by 0.57″.The second area is the web with a height of (18-2*0.57)= 16.86 inches. The last area is the lower flange area which is 7.50″x0.57″ inches. the total area can be found to be equal to 14.535 inch2. Consider the plastic section modulus as equal to Mp/Fy, which can be rewritten as C*yct/Fy=At/2*yct.

The area(At/2)=0.5*14.70=7.35 inch2. use the sum of areas*y distance and divide by At/2 to get the H-y bar distance.

The next slide shows that we get the (h-y )bar value as equal to 6.8622 inches, and the Zx value as 99.742 inches, which is less than 101.0 inch3.

The previous post is “6A-Practice problem 5-2-2 Find y bar, Zx, and Zy for the un-symmetric section.

For bending members, please refer to Chapter 8-**A Beginner’s Guide to the Steel Construction Manual, 15 ^{th} ed.**

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