6c-Practice problem 6-17-5-find Sx and ZX for W18x35.

Last Updated on February 19, 2026 by Maged kamel

Practice problem 6-17-5-find Sx and ZX for W18x35.

Practice problem 6-17-5-find Sx and ZX for W18x35.

Determine the elastic and plastic section moduli for a W18×35 modelled as three rectangles, one for the flanges and one for the web. Compare the calculated values to those given in the Manual. This practice problem is taken from the Unified Design of Steel Structures book.

We will use Table 1-1 to obtain the information for W18x35, including the flange width and thickness, and the web’s overall height and width.

The sketch shows a flange width of 5 inches and a thickness of 0.425 inches. The web width is 0.30 inches, the total depth is 17.70 inches, and the area is 10.30 square inches.

Please refer to the next slide image for more details.

The value of elastic section modulus and plastic section modulus is shown in Table 1-1.

In the next slide, refer to part 2 of Table 1-1; the value of the elastic section modulus is 57.60 inch3, while the plastic section modulus zx is 66.50 inch3.

On the third slide, the W18x35 section is shown as an I shape, with the items for the flange and web explained. Next to the W section is an assembly of three rectangles representing the section.

The upper rectangle, measuring 6 inches wide by 0.425 inches high, represents the upper flange. The second rectangle, the web part, has a height of 16.85 inches and a width of 0.425 inches. The last rectangle, which represents the lower flange, has dimensions similar to those of the first rectangle. We need to find the moment of inertia for the Flanges and the web.

The value of the moment of inertia Ix of W18x35 by estimation.

The overall depth of the W section equals 17.70 inches, and due to symmetry, the elastic section modulus will pass by the middle portion of the W section.

The moment of inertia of the upper flange and the lower flange about the elastic section modulus is the same. It equals the Inertia about the cg of the flange plus the product of the flange area by the square of the distance from flange Cg to the elastic section modulus.

The moment of inertia of the upper flange to the neutral axis, Ix1, equals 190.284 inch^ 4. The moment of inertia of the web to the elastic neutral axis Ix2 equals the width by height^3/12, which is 119.60 inch4. The final moment of inertia of the three rectangles about the neutral axis equals 500.171 in 4.

The value of the elastic section modulus Sx for W18x50.

After we have estimated the moment of inertia, we need to find the value of Sx, the elastic section modulus, and the distance from the E.N axis to the top, which is 8.85 inches. Sx equals Ix/y, which is 500.171/8.85=56.52 inch3. The exact value of Sx from Table 1-1 is 57.60 in^3.

Verify Zx for W18x35 by considering the flange and web areas.

Again, we will use the three rectangles representing the W section to determine the plastic section modulus. The Plastic Neutral axis, or P.N. axis, cuts the section in half due to symmetry. The Plastic section modulus Zx is the sum of the product of area and distance to the P.N. axis.

We will consider the upper rectangle and half of the vertical rectangle. The upper rectangular area, A1, equals width × thickness, which is 6 × 0.425 = 2.5 inches. The perpendicular distance from Cg to the plastic axis is 8.85-0.5*0.425=8.6375 inches. The area of half of the web equals 0.5*16.85*0.30 = 2.528 in^2. The Cg distance to the P.N axis equals 19.85*0.25=4.1225 inch2.

Please refer to the next slide for more details.

The next slide shows the steps to get the Zx or the plastic section modulus for W18x35. By estimation, the Zx value is 65.35 in^3, while the exact value for the plastic section modulus from Table 1-1 is 66.50 in^3.

We could use a quicker way to estimate Zx by treating the section as a single rectangle with b1=6 and d1=17.70 inches, and an inner rectangle with width 5.70 and depth d2=16.85 inches. Zx can be estimated as (b1*d1^2/4-b2*d2^2/4), which equals 65.345 inch3. Thank You.

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The previous post is 6b-Practice problem 5-2-3-verify Zx for W18x50.

The following post is 6d-Practice problem 6-17-11-find Sx and ZX for WT5x22.50.

Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 14^th ed.

Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 15^th ed.

Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 16^th ed.

A newly added post, 6d-Practice problem 6-17-11-find Sx and ZX for WT5x22.50.