Last Updated on February 21, 2026 by Maged kamel
A solved problem 2-22 for structural steel -shear stress estimation-part 2
For item b, the I section with a thickened flange will experience the maximum shear stress at the neutral axis.
The first moment of the area at point 1 equals zero since no area is enclosed, while the first moment at 2 equals area*cg distance=7*3*4.50=94.50 inch2. The easiest way to calculate Ix is to consider the inertia of a bigger rectangle and deduct two inner rectangles. Please refer to the next slide image for more details. The Moment of inertia about the X-axis, Ix value= 900 inch4.
The first moment of the area at the N.A equals= 99.0 inch3. Moment of inertia about the x-axis is Ix=900 inch4,
The next slide image shows a detailed estimation of the shear stress at point 2 and at the Neutral axis N.A. At point 2, there are two values for shear stress because we have two widths; the first width is 7 inches, and the second is 1″. The first value equals 1.29 ksi while the second value equals 7.875 ksi. The maximum value is at N. A axis and equals 8.25 ksi.
Due to symmetry about the X axis we will have a cap shape as shown in the following slide image.
Immediately under the flange, the width decreases from 7″ to 1″, and the shear stress jumps to 7 times its original value; that is why the shear stress equals 7.825 ksi. The maximum shear stress is 8.25 ksi.
Shear stress diagram for part c of the solved problem 2-22.
For item C, in the solved problem 2-22. For the I section W12x87, the relevant data for the flange depth and web thicknesses were obtained from Table 1-1. the width of the flange=12.125″ and its width=0.81″.
While the web thickness = 0.515″, the overall height of the W section = 12.53″. Ix=740.0 inch4.
If we wish to draw the shear stress at points 1-2-2′ and 3, we will proceed as follows:
For point 1, the moment of area=0.
For point 2, the moment of area=Af*y CG to the N.A, the breadth=bf.
For point 2′, the moment of area=Af*y CG to the N.A, the breadth=bw.
For point 3′, the moment of area = Af*y CG +(A web)/2*ycg to the N.A, and the breadth = bw.
On the next slide, we can find the first moment of the area at point 2.
The V value at point 2′, for the solved problem 2-22, equals 57.55 inch3.
The first moment of the area at N.A. equals 65.212 inch3.
The max shear stress value at the N.A. is 12.83 ksi. If we assume the web will carry the shear, the average stress is 11.62 ksi.
AISC provision for shear.
The code specifies that h/tw should not be < 2.24*sqrt (E/Fy); the Vn equation is shown. Aw=d*tW.
These are the relevant h/tw values for different steel grades in zone 1. The list includes carbon steel: ASTM A36, min Fy=36 ksi, and tensile=58-80 ksi.
The PDF containing the data for this post can be viewed or downloaded from the following link.
In the next post, a solved problem 10-2 for beam adequacy for shear.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 14th ed. Section 8.3.1 Shear Behavior.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 15th ed. Section 8.3.1 Shear Behavior.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 16th ed. Section 8.3.1 Shear Behavior.