When calculating the shear stress, what should the area be?

In summary, the conversation discusses the calculation of shear stress and the confusion over the use of pi/4 instead of pi*r^2 for the area of a circular rod. The correct formula for shear stress is V/A, with the cross section area of a circular rod being either (pi)(r^2) or (pi)(d^2)/4. The confusion is resolved when it is realized that the diameter (d) should be divided by 2 to get the correct area of pi*(d^2)/4.
  • #1
sunsee
4
0

Homework Statement



I'm looking at some problems and solutions to them, and when they calculate shear stress instead of having the area of the thing be pi*r^2, there is usually a (pi/4)*r^2.

Homework Equations



Shear Stress = V/A

The Attempt at a Solution



I don't understand where they get the 1/4 in the denominator.
 
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  • #2
You might want to review how shear stress is calculated. Your formula is not the usual one.
 
  • #3
SteamKing said:
You might want to review how shear stress is calculated. Your formula is not the usual one.
I'm using and reading the chapter of shear stress in the book. That is what it tells me that shear stress is... Unless, I'm missing something.
 
  • #4
The cross section area of a circular rod is (pi)(r^2) OR (pi)(d^2)/4
 
  • #5
PhanthomJay said:
The cross section area of a circular rod is (pi)(r^2) OR (pi)(d^2)/4

Yeah, I figured it out. They gave the diameter in the problem so it was pi (d/2)^2. which is pi*(d^2)/4. I was stumped, but luckily i understand.

THANKS!
 

1. What is shear stress?

Shear stress is a type of stress that occurs when two forces act on an object in opposite directions, causing the object to deform or break.

2. How is shear stress calculated?

To calculate shear stress, you need to know the force acting on the object and the area over which the force is applied. The formula for shear stress is shear stress = force/area.

3. What should the area be when calculating shear stress?

The area used in the shear stress calculation should be the cross-sectional area of the object that is experiencing the shear force. This is typically the area perpendicular to the direction of the force.

4. Why is the area important in calculating shear stress?

The area is important because it determines the amount of force that is distributed over the object. A larger area means that the force is distributed over a larger surface, resulting in a lower shear stress. A smaller area means that the force is concentrated, resulting in a higher shear stress.

5. Are there different units for shear stress?

Yes, there are different units for shear stress, depending on the unit system used. In the SI system, shear stress is measured in Pascal (Pa), while in the US customary system, it is measured in pounds per square inch (psi).

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