Question

A rectangular block of material with shear modulus G= 620 MPa is fixed to rigid plates at its top and bottom surfaces. Thelower plate remains fixed while the upper plate is subjected to a horizontal force, P. If the top plate displaces 2 mm horizontally, determine:

a. the average shear strain in the material
b. the force P exerted on the upper plate.

Answer 1

γ
`_(xy)` =0.01, P=248 kN

Step-by-step explanation:

Given Data:

displacement = 2mm ;

height = 200mm ;

l = 400mm ;

w = 100 ;

G = 620 MPa = 620 N//mm²; 1MPa = 1N//mm²

a. Average Shear Strain:

The average shear strain can be determined by dividing the total displacement of plate by height

γ
`_(xy)` = displacement / total height

= 2/200 = 0.01

b. Force P on upper plate:

Now, as we know that force per unit area equals to stress

τ = P/A

Also, τ = Gγ
`_(xy)`

By comapring both equations, we get

P/A = Gγ
`_(xy)` ------------ eq(1)

First we need to calculate total area,

A = l*w = 400 * 100= 4*10^4mm²

By putting the values in equation 1, we get

P/40000 = 620 * 0.01

P = 248000 N or 2.48 *10^5 N or 248 kN