Modulus of elasticity determines a materials stiffness.   It is really just a ratio of stress to strain within the elastic limit.   As the stiffness increases the slope of the line will become steeper.    A material that stretches easily will have a "flater" slope.   The modulus of elasticity is an important property in determining how much deformation will occur under load.   The diagram shown below illustrates the comparison of some selected metals.
 
EXAMPLE PROBLEM:
Modulus of elasticity can help determine the way a material behaves under load.  For example suppose we wish to find out how much a steel wire that has a diameter of .030 inches will stretch under a 50 lb. load.

 Modulus of elasticity for steel is 30 million pounds per square inch
                       Area = (.030 in)2 x .8754 = .00071 in.2
                       Stress = Load / Area
                                    = 50 lbs. / .00071 in.2
                                    = 70,423 psi  n = .00235 inches/ inch

                         Since Modulus = Stress / Strain  (E=S/n),  (n=S/E)
                                                   n = 70,423 psi / 30,000,000 psi
                                                   n = .00235 inches/ inch

A ten foot length of wire would stretch about .024 in
(.00235 in/in) X 10 in. = .0235 in.
 
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