How can I calculate the strain in a simply supported beam from having the maximum bending moment (25kNm) and the maximum bending stress (45MPa)?
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$\begingroup$ 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 '15 at 20:24
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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.
answered Oct 24 '15 at 20:00
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$\begingroup$ 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. $\endgroup$– DhatsahOct 24 '15 at 20:17
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1$\begingroup$ Strain is a material-dependent property. It is impossible to solve without the modulus of elasticity. $\endgroup$– Wasabi ♦Oct 24 '15 at 20:26
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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. $\endgroup$– AsymLabsOct 26 '15 at 11:48