Discussion in class Solution Chapter 5 Mechanical properties 1

Question 1(a) What is the final length of a 2m long bar of copper 10mm in diameter, stressed by a 5000 Newton force? (ans: 2.0011m)(4 marks)

(b) If a steel bar of the same diameter has the same force applied to it, how long must it be extend the same amount as the copper bar in part (a)? (ans: 3.577m)(4 marks)

Given: Youngs modulus of copper is 117 GPa; Youngs modulus for steel is 207 GPa

Solution Q1

Question 2(a) A circular steel rod 0.005 m in radius and 4.000 m long is subject to an axial force of 0.250 x 105 newtons. We observe that the rod elongates 0.616 x 10-2 m. Calculate the tensile stress and the axial strain in the rod.(ans: tensile stress= 3.183 x 108 N/m2; tensile strain= 0.154 x 10-2)(4 marks)

(b) Calculate the change in radius of the specimen while subject to stress. Assume that the deformation of this specimen is elastic and that Poissons ratio is equal to 0.29.(ans: 0.005m)(4 marks)

(c) Is there any significant difference between the true stress and the engineering stress for this specimen? (3 marks)

(d) Calculate the true strain for this application and compare it to the engineering strain for this specimen.(ans: 0.154 x 10-2)(4 marks)[total: 15 marks]

Solution Q2

Question 3A single crystal of BCC niobium is oriented in a tensile test so that the [001] crystal direction is parallel to the load axis. The critical resolved shear stress for niobium is 20 x 106 Pa for dislocation motion on the {011} type planes and in the type directions at 295 K.

What is the tensile proportional limit stress for this single crystal at 295 K?

Assume that the slip occurs on the {011} type planes and in the type directions.(ans : 49 x 106 Pa)(5 marks)