Learn How 6 is Derived in Strain Gage Bending Formula

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SUMMARY

The discussion focuses on the derivation of the constant 6 in the bending strain formula S_b = (F * L * 6) / (E * b * h). The formula is used to measure bending strain in a project involving strain gages for weights between 0 and 10 lbs with an accuracy of 0.1 lbs. The constant 6 is derived from the relationship between bending stress and strain, specifically from the moment of inertia formula I = (b * h^3) / 12 and the application of Hooke's law. The correct formulation of strain includes the squared height dimension, leading to the equation ε = (6 * F * L) / (E * b * h^2).

PREREQUISITES
  • Understanding of bending strain and its measurement using strain gages
  • Familiarity with Young's Modulus (E) and its role in material science
  • Knowledge of moment of inertia calculations, specifically I = (b * h^3) / 12
  • Basic principles of Hooke's law and its application in stress-strain relationships
NEXT STEPS
  • Research the derivation of bending stress and strain equations in material mechanics
  • Explore the application of strain gages in experimental mechanics
  • Study the implications of Young's Modulus in different materials
  • Investigate the effects of varying dimensions (b and h) on bending strain measurements
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Mechanical engineers, materials scientists, and students involved in experimental mechanics or structural analysis will benefit from this discussion.

sean882
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In strength of materials, we have to do a project using strain gages to measure a weight between 0 and 10 lbs with an accuracy of .1lbs. My group is using bending strain. We have a formula, S_{}b=\frac{F*L*6}{E*b*h}, where F is the weight applied, L is the length, E is the Young's Modulus, b and h are base and height dimensions, respectively. We need S_{}b to equal between 500 and 1,000. Where does the 6 come from in the formula? We have a feeling it comes from moment of inertia formulas somehow, but could you explain how it is derived? Thanks,

-Sean
 
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My LaTeX equations aren't working right in PF. I think you can decipher the LaTeX code :-)

The stress due to bending is \sigma = \frac{Mc}{I}. The strain is given by Hooke's law: \epsilon = \frac{\sigma}[E] = \frac{Mc}{EI}. I = \frac{bh^3}{12} and c = \frac{h}{2} and M = F*L. This yields \epsilon = \frac{6FL}{Ebh^2}.

I'm pretty sure in your equation the h needs to be squared.
 
Thanks a bunch!
 

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