# How to calculate strain from maximum bending moment and stress?

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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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.