2
$\begingroup$

How can I calculate the strain in a simply supported beam from having the maximum bending moment (25kNm) and the maximum bending stress (45MPa)?

$\endgroup$
1
  • $\begingroup$ This looks like a homework question. In order for such questions to be within the scope of this site, we ask that you show some of your own work and describe where exactly you're having trouble. $\endgroup$
    – Wasabi
    Oct 24, 2015 at 20:24

1 Answer 1

3
$\begingroup$

From Wikipedia's page on Euler-Bernoulli Beam Theory: $$ \sigma_x = -zE\cfrac{\mathrm{d}^2w}{\mathrm{d}x^2}\,,~~ M = -EI\cfrac{\mathrm{d}^2w}{\mathrm{d}x^2} \,,~~ \varepsilon_{x} = -z\cfrac{\mathrm{d}^2w}{\mathrm{d}x^2} \,. $$ Therefore, $$ \sigma_x = E\,\varepsilon_x ~,~~ M = \frac{EI}{z}\,\varepsilon_x \,. $$ You can eliminate the ratio $$ \frac{I}{z} = \frac{M}{\sigma_x} \,. $$ But you will still need to know $E$ to find the strain.

$\endgroup$
3
  • $\begingroup$ Thats the problem. I have to calculate the Modulus Elasticity and I am only given the Maximum Bending Moment and Maximum Bending Stress. It seems like the question is impossible to solve. $\endgroup$
    – Dhatsah
    Oct 24, 2015 at 20:17
  • 1
    $\begingroup$ Strain is a material-dependent property. It is impossible to solve without the modulus of elasticity. $\endgroup$
    – Wasabi
    Oct 24, 2015 at 20:26
  • 1
    $\begingroup$ The equation above assumes that the response to load remains within the elastic zone. The problem, as described, does not even permit this assumption to be validated. $\endgroup$
    – AsymLabs
    Oct 26, 2015 at 11:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.