homework

EGR236 Mechanics of Materials HW Set 04 Spring 2014Problem 3:4A tension test was performed on a steel specimen having an original diameter of 12.5 mm and a gauge length of 50 mm. The data is listed in table 3.4. Plot the stress-strain diagram and determine approximately the modulus of elasticity, the ultimate stress, and the rupture stress. Use a scale of 20 mm = 50 MPa and the same 20 mm = 0.05 mm/mm. Redraw the linear elastic region using the same stress scale, but a strain scale of 20 mm = 0.001 mm/mm. Use either Excel, Mathematica, Matlab, or other computational software for making your graphs.___________________________________________________________________________Table 3.4Load: (kN)

Elongation (mm)

011.131.937.840.943.653.462.364.562.358.8

00.01750.06000.10200.16500.24901.01603.04806.35008.8900

11.9380

EGR236 Mechanics of Materials HW Set 04 Spring 2014

Problem 3:9

The stress strain diagram for a steel alloy having an original diameter of 0.5 in and gauge length of 2 in is given in the figure below. Determine approximately the modulus of resilience and the modulus of toughness for the material.___________________________________________________________________________Solution:

EGR236 Mechanics of Materials HW Set 04 Spring 2014

0.0005 0 .001 0 .0015 0 .002 0 .0025 0 .003 0 .0035

Problem 3:19.The two bars are made of polystyrene, which has the stress-strain diagram shown. If the cross sectional area of bar AB is 1.5 sq. in and BC is 4 sq. in, determine the largest force P that can be supported before any member ruptures. Assume that buckling does not occur. ----------------------------------------------------------------------------------------------------------------Solution:

EGR236 Mechanics of Materials HW Set 04 Spring 2014

Problem 3:25The steel wire AB and AC support the 200 kg mass. If the allowable axial stress for the wires is σallow = 130 MPa, determine the required diameter of each wire. Also, what is the new length of wire AB after the load is applied? Take the unstretched length of AB to be 750mm. Est = 200 GPa.

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