Question

1. A bar with an equilateral triangle cross section experienced a strain of 6.5983 x 10-4 due to an axial load of 2 kN. The dimensions of the cross section is 5 mm and the length is 300 mm. Assume that the poisson’s ratio is 0.28.

1. What is the value of the modulus of elasticity in GPa? Ans = 280 GPa
2. What is the value of the modulus of rigidity in GPa? Ans = 109.38 GPa
3. What is the bulk modulus in GPa? Ans = 212.12 GPa
4. What is the value of the constrained modulus in GPa? Ans = 357.95 GPa
5. What is the value of the dilatation in percent (%) if the change in pressure is 30 GPa? Ans = 14.14%

Answer 1

Solution:

The given data is:

Strain (s): 6.5983 x 10-4

Force (F): 2 kN =2000N

Length of the bar: 300mm = 300 x 10-3 m

Side of the triangular cross-section (a): 5mm = 5 x 10-3 m

Poisson’s ratio: 0.28

a) The modulus of elasticity (Y) can be calculated as:

Here, A is the area of the cross-section. The area of the cross-section is given as,

Substitute the relevant values.

  

b) The Modulus of rigidity can be calculated from the following relation between the modulus of rigidity and modulus of elasticity as,

Here, η, Y and σ represent the modulus of rigidity, modulus of elasticity, and the Poisons ratio, respectively.

Substitute the relevant values.

c) The relation between the bulk modulus and modulus of elasticity is given as:

Here, K represents the bulk modulus.

Substitute the relevant values.

d) The relation between the constraint modulus and modulus of elasticity is given as:

Here, M represents the constraint modulus.

Substitute the relevant values.