# Shear Stress, Area of Projection

• dlacombe13
In summary: The shear area is the area between the plate and the shaft. It is the area of a cylinder with height t and diameter d.
dlacombe13
I am learning about shearing stress, and I am a little confused about the area of projection mentioned in my book. When it introduces it, it shows a plate with a rivet through it. The plate is of thickness t, and the diameter of the rivet, d. It shows the plate and the rivet cut in half by a plane, and reveals the rectangular area exposed as the rivet is cut, and claims that A = dt.

I am trying a practice problem where the same type of thing is going on, and asks me to find the shearing stress between the plate and the shaft. However, the solution states that A = pi*d*t. In this case, is it cutting straight through the shaft, or is it the area of half of the hole the shaft creates? Basically, why is pi included here?

It's the area between the plate and the shaft: the area of a cylinder with height t and diameter d

It is the area on the plate in the shape of a through hole. You will have to imagine it without rivet in it.

If possible, post the figure and complete text for the practice problem.

For some reason I was thinking of bearing stress, when it was actually asking for shearing stress. It just so happens that the area must include d and t. Either way, I am starting to understand this a little more. It is asking for the stress between the plate and the shaft, which is the area of the hole that touches the collar. My confusion now is about how to picture where this will shear. Is the shaft physically connected to the collar, or does it rotate within it? In either case, how exactly would this piece break under this shear stress? I have included a rough sketch of what my book has:

Given the limited information apparently limited provided to you for the practice problem the simplest assumption is to treat it as a one piece shaft with a collar section; in which case the shear area for the longitudinal joint between the shaft and it collar is, as described A = pi d t. (Given the longitudinal direction of the force, no rotation will occur).

The actual failure mode for this type of piece is a bit complex because it depends upon the thickness of the collar and at what diameter the collar is restrained and whether the shaft loading pushing force applied to the top end of the shaft or as a pulling force on the the bottom of the shaft.
As an example, if the shaft load is applied from the top and the support for the collar is directly at the diameter of the shaft , as though the shaft is passing through a hole, then the failure would be a direct shearing though the joint at the diameter of the shaft, which is the case with a bolt and nut connection. Alternatively, if the collar is thin and/or the collar support is at its outer diameter, then the collar is likely to deform downward in a conical manner, which will result in a combined radial tensile stress at the bottom face joint of the collar and shaft and direct shearing stress thru the collar at the diameter of the shaft.

Is direction of force F correct? I don't see any shear for the rivet in that case. The only shear is the so called punching shear to the plate due the pressure of the rivet head but i don't think that's the case here. Is it a single plate or there are two of them connected with the rivet?

## 1. What is shear stress?

Shear stress is a type of stress that occurs when forces are applied parallel to each other in opposite directions, causing the material to deform or undergo shear strain.

## 2. How is shear stress calculated?

Shear stress is calculated by dividing the force applied parallel to the area of the material over which the force is applied. This is represented by the formula: τ = F/A, where τ is shear stress, F is the applied force, and A is the area over which the force is applied.

## 3. What is the area of projection in shear stress?

The area of projection in shear stress refers to the cross-sectional area of the material that is perpendicular to the direction of the applied force. This area is used in the calculation of shear stress because it represents the amount of material that is being affected by the force.

## 4. How does the area of projection affect shear stress?

The area of projection directly affects shear stress, as the larger the area over which the force is applied, the lower the shear stress will be. This is because the force is distributed over a larger area, resulting in less deformation and therefore less shear stress.

## 5. What factors can influence shear stress?

Some of the factors that can influence shear stress include the type of material, the magnitude of the applied force, the area of projection, and the direction of the force. Additionally, the temperature and state of the material (e.g. solid, liquid, or gas) can also affect shear stress.

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