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Unformatted text preview: EGN3365-Structure and Properties of Materials TTR 8:30-9:45 Instructor: Dr. S. Seal TA: Mr. Himesh Bhatt Solutions: Home-Work 11 1. This problem asks that we derive an expression for the dependence of the modulus of elasticity, E , on the parameters A , B , and n in Equation (6.25). It is first necessary to take dE N / dr in order to obtain an expression for the force F ; this is accomplished as follows: F = = + = - The second step is to set this dE N / dr expression equal to zero and then solve for r (= r o ). The algebra for this procedure is carried out in Problem 2.13, with the result that r o = 1/(1 - n) Next it becomes necessary to take the derivative of the force ( dF / dr ), which is accomplished as follows: = + = - + Now, substitution for r o into this equation yields ro = - + which is the expression to which the modulus of elasticity is proportional. 2. (a) This part of the problem asks that we ascertain which of the metals in Table 6.1 experience an elongation of less than 0.072 mm when subjected to a stress of 50 MPa. The maximum strain which may be sustained is just = = = 4.8 x 10-4 Since the stress level is given, using Equation (6.5) it is possible to compute the minimum Since the stress level is given, using Equation (6....
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- Spring '10