Question

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.

Answer 1

(a) maximum shear stress t=22.5mm

(b)maximum distortion energy t=19.48mm

Step-by-step 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