A circular bar of magnesium alloy is 32 in long. Answer the following questions using the strain graph below. (a) What is the proportional limit of the bar? (b) What is the modulus of Elasticity of

(a) The proportional limit of the bar is around 8 ksi (kips per square inch) as it is the point where the graph stops being linear and starts to curve. (b) The modulus of elasticity of the bar can be calculated using the formula: modulus of elasticity = stress/strain. From the graph, at around 16 ksi stress, the strain is \approx imately 0.0016 in/in. Thus, the modulus of elasticity is (16 ksi)/(0.0016 in/in) = 10,000 ksi. (c)(i) The strain at 0.225 in elongation is around 0.002 in/in. From the graph, we see that the strain corresponding to zero stress is around 0.001 in/in. Therefore, the permanent set of the bar is 0.002 in/in - 0.001 in/in = 0.001 in/in. (c)(ii) If the bar is reloaded, the new proportional limit would be slightly higher than the original limit, because the material has undergone some plastic deformation (as evidenced by the permanent set). From the graph, the new proportional limit appears to be around 8.5 ksi. (Graphical representation not possible as no graph/image provided)