- Solved problem 3-8-1 for staggered Bolts.
- Introduction to solved problem 3-8-1 for staggered Bolts.
- The net area for the first route 1-3-1 with no staggered bolts.
- The net area for the second route is 1-2-3-2-1 with staggered bolts.
- The net area for the third route 1-2-2-1 with staggered bolts.
- The net area for the fourth route 4-5-6 with no staggered bolts.
- The net area for the fifth route 7-8 with no staggered bolts.
- The final net area for the section of plate A.

## Solved problem 3-8-1 for staggered Bolts.

In this post, we will start to discuss the concept of load transfer by fasteners to the estimation of the net area. We have solved problem 3-8-1 for the staggered Bolt that was introduced in the textbook of steel structures fifth edition by Salmon.

### 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 the 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.

The plate thickness id 5/8 inches and we add 1/8 inch to the diameter of each bolt to get the hole diameter, which will be equal to one inch.

In the next image, there is a detailed plan for the arrangements of fasteners for plate A which is under tension force p and its thickness is 5/8 inches. There is another plate B on the back side of plate A which is connected with plate A by using 10 bolts. Each bol carries one-tenth of the load P.

It is required to estimate the minimum net area for given plate A, by considering the different routes and finding out what is the modified net area values under the effect of load transfer as we will say in more detail.

### The net area for the first route 1-3-1 with no staggered bolts.

The first route 1-3-1 is a vertical line through three bolts taken at the right side of these bolts. if we have a look to the section, from the right side it is acted upon by force P and is balanced by the same value P.

If we have a look at the group of bolts for plate A in the same section, we will find that there are ten bolts each carrying P/10 so that the sum of these forces is equal to P and it is in compliance with the right section as shown for the solved problem 3-8-1 for staggered Bolts-fasteners lines.

We will deduct three holes of diameter one inch for each from the width of the plate then multiply by the plate thickness. the final value of the net area will not be modified due to load transfer since the section carries 100%p.

### The net area for the second route is 1-2-3-2-1 with staggered bolts.

The second route 1-2-3-2-1 is a staggered or zigzag line through five bolts taken at the right side of these bolts. If we have a look at the section, from the right side it is acted upon by force P and is balanced by the same value P.

If we have a look at the group of bolts for plate A in the same section, we will find that there are ten bolts each carrying P/10 so that the sum of these forces is equal to P and it is in compliance with the right section as shown for the solved problem 3-8-1 for staggered Bolts-fastners lines.

For the value of the net area, since we have staggered lines we start to estimate the deduction length we have five holts for which the diameter is 1 inch, and the sum of deductions is 5 inches. On the other hand, we have 4 staggered lines for which we need to add four values of (S^2/4g) where s is the spacing between bolts in the force direction. The g value is the value of spacing in the perpendicular direction to the force. the 4S^2/4g will give us a value of (+1.333) inches.

The net width will be (15+(-5+1.33)= 11.33 inches, when multiplied by the plate thickness, which is 5/8 inches will give a net area of 7.08 inches2.

The section carries 100% of force so no modification for the net area to be done.

This is a quote from The Author calculation and the detailed sections for solved problem solved problem 3-8-1 for staggered Bolts-fastners lines and matchs with our calculations.

### The net area for the third route 1-2-2-1 with staggered bolts.

The third route 1-2-2-1 is a staggered or zigzag line through four bolts taken at the right side of these bolts . If we have a look to the section ,from the right side it is acted upon by force P and one bolt carries (1/10)*P the acting force on the section is thus equals 9/10P.

For the left side of the section we have Nine bolts each carry P/10, the section carries 9/10P which is the same value for the right hand side section. the neta rea equals 7.29 inch2.A modification is made to the net area since the section carries (9P/10). The modified net area value will be equal to (10/9)*7.29 inch2.

### The net area for the fourth route 4-5-6 with no staggered bolts.

The fourth route 4-5-6 is a vertical line through three bolts taken at the left side of these bolts. If we have a look at the section, from the right side it is acted upon by force P and there are eight bolts carrying 8*P/10 force, at the section the balance of the force and bolt forces are equal to (2/10)P.

Again from the left side we have only two bolts having 2P/10 values.

The net area will be found to be equal to 7.50 inch2. The modified net area due to load transfer is 37.50 inch2.

### The net area for the fifth route 7-8 with no staggered bolts.

The fifth route7-8 is a vertical line through two bolts taken at the right side of these bolts. If we have a look at the section, from the right side it is acted upon by force P and there are eight bolts carrying 8P/10 force, at the section the balance of the force and bolt forces are equal to (2/10)P.

Again from the left side, we have only two bolts having 2P/10 values.

The net area will be found to be equal to 8.125 inch2. The modified net area due to load transfer is 40.625 inch2.

### The final net area for the section of plate A.

The table shows the different values of the net area for each route we are concerned with the minimum value of the net area and the modified area is used for the sake of comparison to finalize the net area. As we can see the lowest value of net area equals 7.08 inch2, this value is the minimum value for the modified net area due to load transfer. The section is route 1-2-3-2-1. the full details are shown fr each route ad its net area.

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

For a more detailed illustration of block shear, there is a very useful external link-**Block Shear Rupture**. **A Beginner’s Guide to the Steel Construction Manual, 14 ^{th} ed.**