How to get an Effective area for a staggered bolted angle?
In this post, I will introduce a solved problem for the effective area for a staggered bolted angle. This is a problem 3-21, determine the effective area of L7x4x1/2 shown in figure P3-21. Assume the holes are for 1-inch-diameter bolts.
The angle is termed LLV which stands for Long leg vertical. We have two lines of bolts in the long leg. the first line of bolts is a distance of 2 1/2 inches from the edge and the distance between the two lines of bolts is 3 inches.
There is a concept of the length of connection, how to measure it?
The first solved problem- how to get an Effective area for a staggered bolted angle?
In this problem we have an equal amount of bolts distributed in two rows, these bolts are staggered, and the length of connection is to be from the first bolt which is located in the first row to the last bolt which is located in the second row.
The diameter of each bolt is one inch, we need to add 1/8 inch to get the diameter of the hole of the bolt. The hole diameter will be 1 1/8 inches.
We can get the area for L7x4x1/2 from the table, it will be equal to 5.26 inch2. the length of the connection will be (7*2=14 inches).
We have case 2 for the shear lag factor value, where U=1- x̅/ L, where x̅ is the distance perpendicular to the load, from the Cg to the edge. We notice that the distance is parallel to the unconnected leg.
The value of x̅ for the angle in question is 0.91 inches.
Estimation of the net area.
We will check the minimum value for the net area of the given angle by inspecting the first route line EAE’ which is a vertical line passing by one hole, for which the net area is the gross area minus the area of holes, the net area for this case is equal to 4.697 inch2.
Since we have staggered bolts, we will check another route E ABE’, that route passes by two staggered bolts, and the distance g is 3 inches, which is the vertical distance between the lines of bolts, while the spacing s is the distance between bolts in the direction of the load, S equals 2 inches.
For the second route, we will add the area of the staggered path and will deduct the area of holes, or the area of the two holes from the gross area of the angle.
The final value of the net area for the second route is found to be equal to 4.302 inch2, which is less that the net area estimated from the first route.
The final value of the net area is equal to the minimum value of the two estimated values which equals 4.302 inch2.
Estimation of the effective area.
We have two cases, case 2, where the shear lag factor U=1- x̅/ L, we will estimate the value of U as equals (1-(0.91/14)=0.935.
The second case is case 8b when we have the number of bolts in one line as four or more, the U value is given as equal to 0.80. We will select the bigger U value which is 0.935.
Multiply U by the net area, the final effective area will be equal to 4.02 inch2.
The second solved problem-Determine the service load capacity for a staggered bolted angle.
In this problem we have an equal amount of bolts distributed in two rows, these bolts are staggered, and the length of connection is to be from the first bolt which is located in the first row to the last bolt which is located in the second row.
We can get the area for L6x4x1/2 from the table, it will be equal to 4.75 inch2. The length of the connection will be (7*2=14 inches).
Estimation of the net area.
We will check the route E ABE’, that route passes by two staggered bolts, and the distance g is 2 1/2 inches, which is the vertical distance between the lines of bolts, while the spacing s is the distance between bolts in the direction of the load, S equals 2 inches.
The first route area will pass by one bolt for which the net area equals (4.75-1*1/2*1)=4.25 inch2.
The final value of the net area for the route is found to be equal to 3.95 inch2, which is less that the net area estimated from the first route.
The final value of the net area is equal to the minimum value of the two estimated values which equals 3.95 inch2.
Estimation of the effective area.
We have two cases, case 2, where the shear lag factor U=1- x̅/ L, we will estimate the value of U as equals (1-(0.981/14)=0.930.
The second case is case 8b when we have the number of bolts in one line as four or more, the U value is given as equal to 0.80. We will select the bigger U value which is 0.93. Multiply U by the net area, the final effective area will be equal to 3.677 inch2.
Estimation of the Service load capacity and the value of Dead and live loads.
We will find the nominal load due to yielding which equals the product of gross area by the yield stress, We have ASTM-A 592, grade 50 for which the yield stress is 50ksi, while the ultimate stress is 65ksi.
The nominal load for yielding will be equal to (4.75*50)=237.50 kips, the LRfd value is equal to (0.9*237.50)=213.75 kips.
We will find the nominal load due to rupture which equals the product of effective area by the ultimate stress, the nominal load for rupture will be equal to (3.673*65)=238.76 kips, the LRfd value is equal to (0.75*238.76)=179 kips.
The minimum LRFD value is equal to 179 kips, which is the service load capacity.
We will equate to the ultimate load, since the Live load equals 3 times the dead load, we can find that the Dead load equals 29.80 kips and the live load equals 89.40 kips.
The next post is post #10, about the Introduction to block shear.
There is a very useful source- introduction to tension members
