Question

How do you solve this?

A thin-wall pressure vessel is shown below. Internal diameter=d, wall thickness=t.

In addition to the internal pressure p (p=100 psi), a torque T is applied. Assume d=20 inch (r=10 in), t=0.1 inch, T=502,640 in-lb. Determine the wall stress components. Assume that the longitudinal direction is labeled as x and the circumferential (hoop) direction is label as y.

Use Mohr's circle to determine the principle strains and maximum shear strain. Assume that E=10,000 ksi and Poisson's ratio v=0.3 and plane stress case.

Find epsilon x, y, and z. Find gamma xy

Answer 1

Solution:-

P=100 psi, d=20inch, r = 10inch, t= 0.1 inch, T =502,640 lb-in

E = 10,000 ksi =10,000 x 10³Psi, v =0.3

shear stress = Tr/I_p

I_p = r⁴/2 = x 10⁴/2 = 15707.96 inch⁴

= 502,640 x 10/15707.96 =319 psi

hoop stress = p. r/t

= 100 x10/0.1

= 10000 Psi

so that linear strain will

_l = /E = 10000/(10000 x 10³)

Now for _l = 0.001

so that lateral strain lt = v x longitudenal strain

= 0.3 x 0.001 =0.0003

By principal strain

_1,2 =( _l + _lt)/2 +_- ((_l - _lt/2) - _s²)^1/2

shear strain _s = /G

G = E/2(1+v)

G = 3846153. 84 psi

so that shear strain _s = 319/3846153.84 =0.0000829

Now putting all the values in principal strain is

_{1,2 =} 0.00065 +_- ((0.00035)- (6.8 x10^-9)) ^1/2

_1,2 = 0.019, - 0.018

_{x = 0.001}

_{y =0.0003}

_z = 0.003