To understand the relationship between E and G, take square block ABCD

Shear strain = ϕ

Strain of AC = AC_{1} – AC / AC = C_{1} C_{2} / AC

= CC_{1} cos 45° / √2 = CC_{1} / 2 AB

1 /2 (CC1 / AB) = 1/2 (CC1 / BC) = 1/2 ϕ

= 1/2 x t / G

Again, AC has the tensile strain and it takes place due to the stress

σ = σ / E

= t / E

On the diagonal AC the tensile stress takes place because of the compressive stress on BD

= µ . t /E

Combined effect of the two different stresses on the given

Diagonal AC = t / E + µ t /E = t /E (1+µ)

By equating both the equation, we have

t = 2G = t / E (1+µ)

G = E / 2 (1 +µ)

where ,

µ = Poisson’s ratio

G = modulus of rigidity

E = modulus of elasticity.

**Links of Previous Main Topic:-**

- Linear momentum
- Force mass acceleration
- Simple stress introduction
- Normal strain
- Statically indeterminate system
- Thermal stresses

**Links of Next Mechanical Engineering Topics:-**