How do you find modulus of elasticity from load-displacement curve?

The modulus of elasticity is a property specific to a given material and in practice is derived through laboratory testing.

The modulus of elasticity is defined as stress/strain. One would have to apply a force uniformly over a known cross section of a material and monitor the strain utilising strain gauges. When the results are plotted you will notice that you get elastic behaviour up to a point of yield (this is known as the yield stress in normal carbon steels, however in stainless steel where the yield point is not as defined, we normally accept it to be the 0.2% strain) and the material should behave linearly in this area. If you take the gradient of the stress/strain, this will be your Elastic modulus.

Please note that the plotted curve will begin to flatten off roughly at the 0.2% strain line and this is due to the fact that the material has yielded. even after this point the material will not fail but will act 'plastically' up to a point where the material fractures which we call the ultimate stress.