Learn How 6 is Derived in Strain Gage Bending Formula

[sean882]

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[tex]_{}b[/tex]=[tex]\frac{F*L*6}{E*b*h}[/tex], 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[tex]_{}b[/tex] 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

 

[timthereaper]

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.

 

[sean882]

Thanks a bunch!