Determining Shear Stress on Bolts

[stinlin]

So as you can see, the drawing I've attached shows two bolts through those 3 plates. There are the shown forces acting on the plates, and the maximum allowed shear stress is given to be 110 MPa. You're supposed to determine the minimum diameter required for the bolts. Also, the forces are assumed to be evenly distributed amongst the two bolts.

So I can ask my TA how to solve this problem, so I'm not entirely asking for a solution...What I want to know is really the theory of this. If I'm looking at the bolt alone, there are 3 forces acting on it, no? If that's the case, then how do I go about applying t = V/A?

Can I get an explanation of how to look at the bolt and determine the shear force? Thanks!

 

[Pyrrhus]

What do you know about planes of shears?

In your example each bolt will have 2 planes of shears, making the bolt in a double shear state. Which means each of the shear forces will be equal to the half of the total load transmitted per bolt.

With this in mind you know the total load is simply 80 Newtons, and for a bolt the average shear stress will be equal to the shear force divided by the cross section of the area where it acts. You have the total load, you have the allowed shear stress, and the only unknown is the diameter, so simply by using the equation you have stated, you can solve for the diameter of the bolts.

Remember: you have 2 cross section areas, because you have two bolts (which should be accounted in A).

 

[ravenprp]

Sure, I'd be happy to provide some clarification on how to determine shear stress on bolts in this scenario.

First, let's start with the basics. Shear stress is a type of stress that occurs when two forces act in opposite directions, parallel to each other, on an object. In this case, the two bolts are being subjected to shear stress due to the forces acting on the plates.

To determine the minimum diameter required for the bolts, we need to first calculate the shear force acting on each bolt. This can be done by summing up the forces acting on each bolt in the given scenario. Since the forces are assumed to be evenly distributed amongst the two bolts, we can divide the total force by 2 to get the shear force acting on each bolt.

Once we have the shear force, we can use the formula t = V/A to calculate the shear stress on the bolts. In this formula, t represents shear stress, V represents shear force, and A represents the cross-sectional area of the bolt. The maximum allowed shear stress given in this scenario is 110 MPa, so we can set t = 110 MPa and solve for A to determine the minimum required diameter for the bolts.

In terms of the theory behind this, it's important to understand that bolts are designed to resist shear forces. The diameter of the bolt is a key factor in determining its strength and ability to resist shear stress. A larger diameter bolt will have a larger cross-sectional area, allowing it to withstand higher shear forces without exceeding the maximum allowed shear stress.

Overall, the key steps in determining the minimum bolt diameter in this scenario are to calculate the shear force acting on each bolt, use the t = V/A formula to calculate the shear stress, and then solve for the minimum required diameter using the maximum allowed shear stress. I hope this explanation helps and good luck with your problem!