The stress-strain behavior of a steel alloy was determine using a cylindrical test specimen having a diameter of 15.000 mm. The stress-strain plot for this steel alloy is shown in the figure below. Using this figure, answer the following questions: (a) Determine the yield stress at a strain offset of 0.002 Oy = 350 MPa] (b) What was the fracture stress? Ox=400MPa (c) When a load of 86,000 N was applied to the test specimen did it experience elastic or plastic deformation? Explain your answer. (d) If the original gauge length of the test specimen was 250.00 mm, what was the increase in length when the load of 86,000 N was applied. Note: For part (e) below, do not used the strain value from the plot. (e) Given that for the steel, E = 210 GPa and y = 0.3) calculate: (i) The increase in length on a gauge length of 250.00 mm when a load of 35,000 N is applied. (ii) The longitudinal strain when the 35,000 N load was applied. (iii) The new diameter of the specimen with the 35,000 N load applied Stress (MPa) 600 500 400 -500- ✗ 300 400 200 Stress (MPa) 300 200 100 100 0.000 0.002 0.004 0.006 Strain 0.00 0.04 0.08 0.12 0.16 0.20 Strain

Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300

On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.

The figure below shows the tensile engineering stress-strain behavior for a steel alloy. (a) What is the modulus of elasticity? (b) What is the yield strength at a strain offset of 0.002? (c) What is the tensile strength? Stress (MPa) 600 500 400 300 200 100 T I 0.00 Stress (MPa) 0.04 500 400 300 200 100 0.000 0.08 0.002 Strain 0.004 Strain 0.12 I 0.006 0.16 0.20 In the previous problem, A load of 85,000 N (19,100 lbf) is applied to a cylindrical specimen of the steel alloy that has a cross-sectional diameter of 15 mm (0.59 in.). (a) Will the specimen experience elastic and/or plastic deformation? Why? (b) If the original specimen length is 250 mm (10 in.), how much will it increase in length when this load is applied?