Question

On all the six surfaces of a unit cube, equal tensile force of f is applied. The increase in length of each side will be (y = young's modulus, = poission's ratio)

Answer 1

The increase in length of each side will be F/Y (1 - 2σ)

Given-

• Tensile force applied on all six surfaces of a unit cube = F
• Young's modulus = Y
• Poission's ratio = σ

Unit cube means all the sides is equals to 1

From the attached figure

Δx = Δy = Δz

Due to force F strain in the x direction is

exf = Lf-Li/Li = 1+Δx-1/1 = Δx            (ex is the strain in x direction)

σ = Ee = F/A = Y. Δx

From above equation we get

Δx = F/AY

Net strain in x direction = Δx - σey - σez

(σey and σez are the lateral strains from x direction)

We know that poission's ratio (σ) is the ratio of negative lateral strain upon longitudinal strain.

So,

ex net = Δx - σΔy - σΔz = Δx (1 - 2σ)

By substituting the value of Δx we get

ex net = F/AY (1 - 2σ)

A is 1. So

ex net = F/Y (1 - 2σ)