Help me calculate a calculated bending stress (psi) in cantilever beam?

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Discussion Overview

The discussion revolves around calculating the bending stress in a cantilever beam using strain measurements. Participants explore the application of bending stress formulas and the relationship between strain and stress, particularly in the context of a specific experimental setup involving weights and a strain gauge.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • The original poster describes their setup, including the dimensions of the beam and the weights used, and seeks clarification on calculating the bending moment (M) for the bending stress formula.
  • One participant explains that the bending moment at the wall is calculated as W * 16, where W is the weight applied, resulting in a moment of 16W inch pounds.
  • Another participant mentions the conversion of strain to stress, indicating that stress equals strain multiplied by the modulus of elasticity.
  • The original poster expresses confusion regarding the modulus of elasticity value and its impact on the calculated stress compared to theoretical values.
  • A later reply questions whether strain gauges have a gauge factor that could affect the measurements.

Areas of Agreement / Disagreement

Participants generally agree on the method for calculating the bending moment and the relationship between strain and stress. However, there is uncertainty regarding the correct value of the modulus of elasticity and its implications for the calculations, as well as the role of the gauge factor in strain measurements.

Contextual Notes

There are unresolved aspects regarding the assumptions made in the calculations, particularly concerning the modulus of elasticity and its application in the context of the strain gauge readings.

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Homework Statement



I am using a Vishay strain indicator with it hooked up to a strain gage hooked up 1" away from the wall on the solid beam. The beam is .5" by .5", and it is solid. The beam is 16" long and I am putting weights at the end of the beam. The weights are 1, 2, 5, 10, 15, and 20 lbs. On each weight, I recorded a strain(uin/in). It states to use the modulus of elasticity E_aluminum 10x10^6 to convert to psi. My question is how do I calculate the M part for the bending stress?

Homework Equations



bending stress = MC/I

modulus of elasticity E_aluminum 10x10^6 to convert to psi.

The Attempt at a Solution



For C, .5/2= .25

For I, (1/12)*b*h^3 or (1/12)*.5*.5^3 = .0052083

How do I find my M?

For 1 lb, would it be M-1lb(16")=0 or M=16 lb.in but I don't get it why it says to use E_aluminum = 10x10^6 psi to convert.

Here is a picture of the cantilever beam setup I used.

http://tinypic.com/r/2q80eg1/5
 
Last edited:
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The moment is simply the distance the weight is from the point in question. So at the wall, the bending moment is W * 16 = 16W inch pounds.

The conversion they are talking about is how you convert strain to stress. Stress = strain times modulus
 
LawrenceC said:
The moment is simply the distance the weight is from the point in question. So at the wall, the bending moment is W * 16 = 16W inch pounds.

The conversion they are talking about is how you convert strain to stress. Stress = strain times modulus

Thank you! It makes sense now. The only weird thing is if I just 10^6 instead of 10*10^6, then it will be close to my theoretical value. But if I do 10*10^6, the calculated value is super off from the theoretical value.
 
I have never used strain gauges but does it have some sort of gauge factor associated with it?
 

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