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

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Discussion Overview

The discussion revolves around the calculation of shear stress, specifically the area used in the formula for shear stress in relation to circular rods. Participants explore the differences between using the area as πr² versus (π/4)r² and clarify the implications of using diameter in calculations.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant questions the use of (π/4)r² in the calculation of shear stress, noting confusion about the origin of the 1/4 factor.
  • Another participant suggests reviewing the calculation of shear stress, implying that the initial formula provided may not be standard.
  • A participant asserts that the cross-sectional area of a circular rod can be expressed as both πr² and (π/4)d², indicating a relationship between radius and diameter.
  • A later reply clarifies that the diameter was given in the problem, leading to the realization that the area can be expressed as (π/4)d², which resolves the initial confusion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial formula for shear stress, but there is agreement on the correct expression for the area when diameter is used. The discussion reflects a mix of confusion and clarification regarding the formulas.

Contextual Notes

The discussion highlights the dependence on whether radius or diameter is used in the calculations, which may lead to different expressions for the area. There are unresolved aspects regarding the standardization of the shear stress formula among participants.

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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