21- Case 2 for block Shear-Coped Beam Problem.

Last Updated on September 14, 2026 by Maged kamel

Case 2 for block Shear-Coped Beam Problem.

In this post, I will include a solved problem for Case 2 for block Shear-Coped Beam problem where the UBS=1/2—the solved problem number #10.8 from the Unified Design of Steel Handbook.

Determine the resistance to block Shear of the coped Beam W16x40, grade A992, which is the same coped Beam from the first solved problem in the previous post but with a different steel grade, ASTM A992.

The horizontal distance between the Beam edge and the centerline of the first line of bolts is 1.25 inches, and the vertical distance between the edge of the Beam and the first line of bolts is 2 inches. The vertical spacing between bolts is 3 inches.

There are two vertical lines of bolts; the horizontal edge distance to the first line of bolts is 1 1/4″. The horizontal spacing between Bolt lines is 3 inches. Please refer to the next slide image for more details. The Bolt diameter is 5/8 inches. Because we have more than one line of bolts, this is case 2, where the UBS value is 1/2.

What are the gross sections for the given Beam?

For W16x40, the web width is 0.305 in.he Flange breadth is 7 in.in.The Flange width is 0.505 in. The yield stress for A992 is 50 ksi, while the ultimate stress is 65 ksi.

For the Hole diameter, we add 1/8 inch to the Bolt diameter, so the Hole diameter is 6/8 inches.

2-There is one section that is subjected to Shear, and that is the vertical section through the bolts. There is also one section under tension: the lower section.

The value of Shear Yielding.

3-We estimate the gross Area for the vertical section subjected to Shear, which equals (11 x 0.305) = 3.355 in2. We can estimate the Shear Yielding value, which is the Product of the gross Area and (0.6*Fy), where Fy=50 ksi. The shear-yielding value is equal to 100.65 kips.

Gross and net Area for tension-UBs=1/2 and tension rupture.

4-We estimate the gross Area for the horizontal section subjected to tension, which can be found to be equal to (4.25×0.305) = 1.296 in^2.

To get the net Area for tension, or Ant, we deduct the Area of one and a half Bolt holes; the net Area Ant equals 0.9531 inch2. This is case 2 for the block Shear-Coped Beam Problem. For the tension rupture force, multiply (ubs*Ant*Fu), which is (1/2*0.9351*65)=30.976 kips.

Estimate the Shear rupture and tension rupture.

We can get the values of Shear Yielding and tension rupture. To estimate the Shear rupture, we need to find the net Area for sShear which is the gross Area for Shear minus (3.5 hole Area). The Bolt Hole diameter is 6/8 inches, the web thickness is 0.305 inches, and the height is 11 inches. The net Area for Shear is 2.554 in². Multiply by (0.6*Fy) to get the Shear rupture force value, which is 99.60 kips. For tension rupture, we estimated it earlier as 30.976 kips.

Estimate the LRFD value of the block Shear force, Case 2, for the block Shear-Coped Beam Problem.

We list all the data that we have obtained and group it into two groups. The first group is Shear Yielding and tension rupture. The second group will be Shear rupture and tension rupture. We can find that the failure is controlled by Shear rupture and tension rupture since their sum is less than the Shear Yielding and tension rupture.

We select the minimum, 130.576 kips; we multiply by phi = 0.75 to get the LRFD value of 98 kips. Please refer to the next slide image for more details.

Estimate the ASD value of the block Shear force, Case 2, for the block Shear-Coped Beam Problem.

We list all the data we have obtained and group them into two groups. The first group is Shear Yielding and tension rupture. The second group will be Shear rupture and tension rupture. We can find that the failure is controlled by Shear rupture and tension rupture since their sum is less than the Shear Yielding and tension rupture.

We select the minimum, 130.576 kips; we divide by omega, which is 2, to get the ASD value of 65.30 kips. Please refer to the next slide image for more details.

I have reached the end of Case 2 for the block Shear-Coped Beam Problem. Thanks a lot.

You can view or download the PDF for this post from the following Document.

For more details on block Shear, please refer to the post “Quickstart to the introduction to block Shear resistance.”

For an introduction to coped beams, please refer to the previous posts, post 13-The relation between Block Shear and coped beams.

Post-19-Solutions for Block Shear-Coped Beam Problem.

Post-20-Aisc Tables 9-3a,b, and C for Block Shear-Coped Beam.

For a more detailed illustration of block Shear, see the very useful external Link: Bolted connection—a Beginner’s Guide to the Steel Construction Manual, 15^th ed.

For a more detailed illustration of block Shear see this useful external Link: Tensile Yielding and tensile rupture—a Beginner’s Guide to the Steel Construction Manual, 16^th ed.

For a more detailed illustration of block Shear, see this useful external Link: Bolted connection—a Beginner’s Guide to the Steel Construction Manual, 16^th ed.