The gas tank is made from A-36 steel and has an inner diameter of 1.50 m. If the tank is designed to withstand a pressure of 5 MPa, determine the required minimum wall thickness to the nearest millimeter using (a) the maximum shear stress theory, and (b) maximum distortion energy theory. Apply a factor of safety of 1.5 against yielding.

(a) maximum shear stress t=22.5mm

(b) maximum distortion energy t=19.48mm

Explanation:

Ф₁ (sigma) = pd/2t

Ф₁ = (5*10⁶*1.5) / 2t

Ф₁=3.75*10⁶/t

Ф₂=pd/4t

Ф₂=1.875*10⁶/t

(a) According to maximum shear stress theory

|Ф₁|=ФY/1.5

3.75*10⁶/t=250*10⁶/1.5

t=22.5 mm

(b) According to distortion energy theory

Ф₁²+Ф₂² - (Ф₁Ф₂) = (ФY/1.5) ²

(3.75*10⁶/t) ² + (1.875*10⁶/t) - { (3.75*10⁶/t) (1.875*10⁶/t) } = (250*10⁶/1.5) ²

t=19.48mm