15A-Solved problem 3-8-1 for staggered Bolts.

Last Updated on February 14, 2026 by Maged kamel

Solved problem 3-8-1 for staggered Bolts.

In this post, we’ll discuss fastener load transfer and its relationship to net area estimation. The approach used in the solved problem can be considered a refinement for determining the final net area.

We have solved problem 3-8-1 for the staggered Bolt, introduced in Salmon’s textbook, Steel Structures, Fifth Edition.

Introduction to solved problem 3-8-1 for staggered Bolts.

Calculate the governing net area for plate A of the single lap joint in Fig. 3.8.1 and show free body diagrams of portions of plate A with sections through each line of holes. Assume that plate B has an adequate net area and does not control the strength T.

In the next image, a detailed plan shows how to arrange fasteners on plate A, which is under the tension force P and has a thickness of 5/8 inch. Another plate, B, is on the back of plate A and is connected to it using 10 bolts. Each bolt carries one-tenth of the load P.

It is necessary to estimate the minimum net area for plate A by considering different routes and determining the modified net area values resulting from load transfer.

We add 1/8 inch to the bolt diameter to get the hole diameter, which will equal 1 inch.

The net area for the first vertical route E-1-2-3-E2.

The first route, E1-2-3-E, is a vertical line through three bolts, taken on the right side of these bolts. If we look at the section, there is a force P on the right side that is balanced by the same value P. No bolts are located at the rightside of the section.

The gross area of Plate A is equal to (159*5/8) = 9.7375 in^2; the area of the holes is 1.875 in^2. The net area of the route is 7.50 inch2, the section can carry 100% of the load.

The net area for the second route is E1-4-2-5-3-E2 with staggered bolts.

The second route, E1-4-2-5-3-E2, has three staggered lines: 1-4, 4-2, 2-5, and 5-3. There are no bolts on the rightside of the route.

The gross area of Plate A is 9.7375 inch2, The route passes through five holes and the area of these holes to be deducted from the gross area to get the net area. The area of the holes is 3.125 inch2. We use the sum of S^2/4g*tp to get the added areas for the route, where S is the distance between bolts and g is the vertical distance between bolts. The s value is 2 inches, and the g value is 3 inches.

The area added equals 0.833 inch2. The final net area equals (9.375-3.125+0.833 )=7.083 inch2.
No net area modification is to be made, since the section carries 100% P.

The net area for the third route E1-4-5-E2.

The third route, E1-4-5-E2, is a vertical section that passes by three bolts. We notice that on the rightside of the section, there are three bolts, each carrying P/10 P of the load P.

On the left side of the section, we have 7 bolts; each carries P/10. The net area equals 8.125 inch2. A modification is made to the net area since the section carries (7P/10). The modified net area value equals (10/7)*8.125 = 11.607 in^2.

The net area for the fourth route E1-4-5-3-E2 with staggered bolts.

The fourth route E1-4-5-3-E2 is it has three staggered lines 1-4 and 5-3 . There is only one bolt at the rightside of the route.

At the left side of these bolts, there are 9 bolts. The net area will be found to be equal to 7.925 inch2. The modified net area due to load transfer is 8.12 inch2.

The net area for the fifth vertical route E1-6-7-8-E2 with no staggered bolts.

The fifth route, E1-6-7-8-E2, is a vertical line through five bolts. There are five bolts on the right side. Again from the left side, we have also five bolts.

The net area will be 7.50 in^2. The modified net area due to load transfer is (7.50*10/2) = 15.0 in^2.

What is the final net area for the section of plate A?

The table shows the net area values for each route. We are concerned with the minimum value of the net areafor 100% P. As we can see, the lowest net area is 7.083 in^2 for the section carrying 100% P. The section is route E1-1-4-2-5-2-E2. The full details are shown for each route and its net area.

The PDF file for this post can be viewed or downloaded from the following link.

The next post is Problem 3-4-3 for staggered bolt-tension members-1/2.-staggered bolts-1/2.

There is a very useful external link, Block Shear Rupture–A Beginner’s Guide to the Steel Construction Manual, 14^th ed.

There is a very useful external link, Block Shear Rupture–A Beginner’s Guide to the Steel Construction Manual, 15^th ed.

There is a very useful external link, Block Shear Rupture–A Beginner’s Guide to the Steel Construction Manual, 16^th ed.