Last Updated on September 13, 2026 by Maged kamel
Nominal Shear strength for S41x121- use CM#14.
Compute the Nominal Shear strength for S41x121.
We have an S41x121 steel section of A572 Grade 65; we want to compute the nominal Shear strength. We will apply CM#14 and the related specification 2010 in this example.
First, we will use Table 2-4 to find the yield stress Fy value for A572 steel grade 65. This type of steel has a yield stress Fy = 65 ksi and an ultimate stress Fu = 80 ksi.
The next question concerns the table to get the full data for S41x121; in Part 1, we will find that Table 1-3 is used to get the information for sections.
You can obtain the data for S21x121from Table 1-3 in Part 1. The following slide image shows the different S-shaped dimensions. The flFlangeidth bf is 8.05 inches, and the Flange thickness is 1.09 inches.
The depth of S21x121 is d = 24.50 inches, and the web thickness is 0.80 inches. The most critical parameter is h/tw, which is in part 2 of the same table.
Find h/tw from Table 1-3, part 2.
The h/tw ratio is 25.90. h is the distance between the web’s two filleted portions. The following slide image shows part 2 of Table 1-3. The ratio of the height of the web to the thickness of the web equals 25.90.
Find the limiting h/w based on Fy.
The limiting h/tw and h/w values based on Fy are related, as shown in the next slide. Based on the Fy of the given S41x121 for grade 65, the limiting h/w equals 47.30.
The following slide image shows the relation between h/tw and the nominal Shear value. There are four zones; the first Zone is from zero to 47.30, marked as point 1 on the x-axis, which is obtained from the relation 2.24*sqrt(E/Fy); in this Zone, Cv equals 1, and φv equals 1.
The equation gives the nominal Shear value for nominal shear Vn = CvShearFy*d*tw and can be written as 1*0.60Fy*Aw.
The second Zone is from h/tw equal to 47.30 to 52, marked as point 2 on the x-axis, and is obtained from the relation 1.1*sqrt(kv *E/Fy); in this Zone, Cv equals 1, and φv equals 0.90. The Kv factor equals 5.00 in the 2010 specification. The nominal Shear value is given by Vn = Cv*0.60*Fy*d*tw and can be written as 1*0.60*Fy*Aw.
The third Zone is from h/tw = 52 to 64.70; Cv1 is less than 1, and φv equals 0.90. The nominal Shear value is given by the equation Vn=Cv*0.60*Fy*d*tw; Cv equals 1.1*sqrt(kv *E/Fy)/(h/tw) or 53.69/(h/tw).
For section S24x121, h/tw is 64.71; in Zone 3, Cv equals 0.80292.
The last Zone extends from Cv=0.80292 at h/tw=64.71 till h/tw=260, and the Cv value is given by 1.51*kv*E//(h/tw)^2*Fy. Please refer to the next slide image.
The nominal Shear strength for S41x121.
The Area of the web equals the Product of the depth by the web thickness, or d*tw, which equals 24.50*0.80=19.60 inch2; The h/h/tw=25.90 from Table 3.1. Check against H/tw=2.24*sqrt(E/Fy=47.31.Since the section h/tw is less than 47.31, the cv value equals 1.0, and the nominal Shear equals 1.0*(0.60*Fy)*(Aw)=1.02*0.6*65*19.60=764 Kips. The detailed calculations are shown on the next slide.
Excel plot for h/tw versus Vn for S41x121.
An Excel plot for the relation between h/tw and the nominal Shear Vn shows the four zones for Shear. Zone 3 ranges from Vn = 764 kips to Vn = 613.75 for h/tw = 46.71; our section is shown on the graph with h/tw = 25.90 and a nominal Shear value of Vn = 764 kips. I have used an Excel formula (IF, THEN, and) to incorporate the equations for the nominal Shear value. Thanks a lot.
You can view or download the PDF containing the data for this post from the following Link.
As an external resource for the Shear stress limit state: A Beginner’s Guide to the Steel Construction Manual, 15th ed.
The previously solved problem was checked based on CM#14-post 22S.
The following post is a solved problem: Nominal Shear strength for M10x7.50 based on AISC-360-16.
Here is the Link to Chapter 8 – Bending Members, Section A, Beginner’s Guide to the Steel Construction Manual, 14th ed.
Here is the Link to Chapter 8 – Bending Members, Section A, Beginner’s Guide to the Steel Construction Manual, 15th ed.
Here is the Link to Chapter 8 – Bending Members, Section A, Beginner’s Guide to the Steel Construction Manual, 16th ed.