Question

A strain gage is mounted at an angle of 30° with respect to the longitudinal axis of the cylindrical pressure. The pressure vessel is fabricated from aluminum [E = 10,000 ksi; ν = 0.33], and it has an inside diameter of 54 in. and a wall thickness of 1.00 in. If the internal pressure in the cylinder is 794 psi, determine the maximum shear strain on the outer surface of the cylinder. determine

a. internal pressure of the cylinder.
b. the absolute maximum shear stress on the outer surface of the cylinder
c. the absolute maximum shear stress on the inner surface of the cylinder

Answer 1

1790 μrad.

Step-by-step explanation:

Young's modulus, E is given as 10000 ksi,

μ is given as 0.33,

Inside diameter, d = 54 in,

Thickness, t = 1 in,

Pressure, p = 794 psi = 0.794 ksi

To determine shear strain, longitudinal strain and circumferential strain will be evaluated,

Longitudinal strain, eL = (pd/4tE)(1 - 2μ)

eL = (0.794 x 54)(1 - 0.66)/(4 x 1 x 10000)

eL = 3.64 x 10-⁴ radians

Circumferential strain , eH = (pd/4tE)(2-μ)

eH = (0.794 x 54)(2 - 0.33)/(4 x 1 x 10000)

eH = 1.79 x 10-³ radians

The maximum shear strain is 1790 μrad.