Stress-strain diagram using deformation ?

[the_rider]

Homework Statement

I have a lab report where I have to plot a stress-strain diagram for 2 beams. We apply an increasing load at midspan and record the deflection. I have to find the strain so I can plot the diagram. Also, the diagram willl be use to find the modulus of elasticity so I can use the stress = Ee

Homework Equations

I cannot use stress = Ee since the modulus need to be find. I know that strain = (l-lo)/lo but since it is not en elongation but a bending I don't know what's the relation between strain and deflection

The Attempt at a Solution

I was thinking about using trigonometry to find the change in length but I wouldn't be accurate and the error on the length will be to big to use. It's a lab report so usually it shouldn't be to complicated. I look on the internet, in all my books and didn't not find any relation between strain and deflection.

Thank you
Alex B.

 

[Mapes]

Hi Alex B., welcome to PF. I suggest you find any mechanics of materials book (Beer and Johnston is a classic) and look at the chapter on bending. You will find many useful relationships between stress and strain for a bending beam.

 

[the_rider]

Thanks Mapes.

I found the formula i need 1/p(rho) = M(x)/EI then I find my E, then use O=Ee to find my strain.