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

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SUMMARY

The calculation of shear stress involves the area of the cross-section of a circular rod, which can be expressed as either πr² or (π/4)d², where d is the diameter. The confusion arises when the diameter is provided instead of the radius, leading to the use of the formula (π/4)d² for shear stress calculations. The correct formula for shear stress is Shear Stress = V/A, where A is the appropriate area based on the given dimensions. Understanding the relationship between radius and diameter is crucial for accurate calculations.

PREREQUISITES
  • Understanding of shear stress and its formula: Shear Stress = V/A
  • Knowledge of circular cross-section area calculations: A = πr² or A = (π/4)d²
  • Familiarity with basic geometry concepts related to circles
  • Ability to interpret engineering problems involving shear stress
NEXT STEPS
  • Review the derivation of the area formulas for circular sections
  • Study examples of shear stress calculations in engineering contexts
  • Learn about the implications of shear stress in material science
  • Explore advanced topics in fluid mechanics related to shear stress
USEFUL FOR

Engineering students, mechanical engineers, and anyone involved in structural analysis or material science will benefit from this discussion on shear stress calculations.

sunsee
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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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You might want to review how shear stress is calculated. Your formula is not the usual one.
 
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.
 
The cross section area of a circular rod is (pi)(r^2) OR (pi)(d^2)/4
 
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!
 

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