what is the strain in a flat plate of 1m x 3m if its subject

Solution

The question does not specify the material. We take it as steel.

We note the following properties for the steel :

= Coefficient of thermal expansion for steel 12 x 10^-6 m/m/^ok

E = Young’s modulus for steel = 200 GPa

= poison’s ratio = 0.3

Temperature raise : 200 ^oC

e = Strain in the material is defined as elongation/contraction per unit length = expansion due to temperature raise = 12 x 10^-6 m/m/^ok x 200 = 2.40 x10^-3 m/m

This thermal expansion is same in both x and y directions.

When this thermal expansion is constrained, it will result in compressive stress corresponding to e.

Let _x and _y be the stresses in x and y directions. Then e_x= (_x- _y)/E and e_y= (_y- _x)/E

As we know the expansion is same in all directions we get same stresses induced in x and y directions.

Then we have _x= _y = eE/(1-) substituting the values we get _x= _y= 720 MPa