Strength of Materials Questions and Answers

Answer: B

The elastic constants are connected by \(E = 2G(1 + \nu)\), where E is Young's modulus, G the modulus of rigidity and \(\nu\) Poisson's ratio. So

The value 0.2 is just Poisson's ratio. The values 2.8 and 3.2 would come from using a Poisson's ratio of 0.4 or 0.6 and are not consistent with the data. The ratio of E to G for any real material lies between 2 and 3.

Answer: B

The elongation of an axially loaded bar is \(\delta = PL/(AE)\). The area is \(20 \times 20 = 400\) mm\(^2\), the load is 40,000 N, the length is 1000 mm and \(E = 200{,}000\) N/mm\(^2\):

The options 0.25, 0.75 and 0.95 mm correspond to a wrong load, area or modulus (for example 0.25 mm would be found with an area of 800 mm\(^2\)).

Answer: D

Hooke's law says that strain is proportional to the applied stress up to the proportional limit. The constant of proportionality is the modulus of elasticity. The law does not link strain to temperature, pressure or the volume of the solid in this way, so the options A, B and C are wrong.

Answer: A

The correct match is a-ii, b-iii, c-i. Young's modulus is the ratio of linear stress to linear strain (ii). The bulk or volume modulus is the ratio of bulk stress to bulk strain (iii). The shearing or rigidity modulus is the ratio of the shearing stress applied to the body to the shearing strain produced (i). \[ Y = \frac{\text{linear stress}}{\text{linear strain}} \] Each of the other options gives at least one modulus the definition of a different one.