Your task is to provide design specifications for spherical thin-walled pressure

Question

Your task is to provide design specifications for spherical thin-walled pressure vessels. Prompt the user for the maximum pressure required (psi). The other preset inputs should be the yield strength of the material (A-36 steel) and the factor of safety (2). Make a table that includes standard wall thicknesses from 1/16" to 1/2" in 1/16" increments. For each thickness, calculate the maximum allowable size of the tank; display this result as both the outer diameter (ft) and the internal volume (ft3). Display of intermediate results is acceptable. Apply the maximum distortion energy theory as the failure criterion.

Explanation / Answer

For A-36 Steel

Yield Strength = 36 ksi

t1 = 1/16 in = 0.0625 in

t2 = t1+0.0625 = 0.125

t3 = t2+0.0625 = 0.1876

t4 = t3+0.0625 = 0.25

t8 = t7+0.0625 = 0.5

As per distortion energy theory

This states that failure occurs when the von Mises stress e in the component being designed equals the von Mises stress e in a uniaxial tensile test at the yield stress:

e = SY/FS

FS=2

So e = 36 ksi/2 = 18 ksi

This is the allowable stress in thin pressure vessel.

e = [P*r] / [2*t]

Pmax = [e *2*t] / r = 18*2*0.0625/r = 2.25 /r ksi = [2250 /r] psi

When pressure vessels have walls that are thin in comparison to their radii and length. In the case of thin walled pressure vessels of spherical shape the ratio of radius r to wall thickness t is greater than 10. A sphere is the theoretical ideal shape for a vessel that resists internal pressure.

r > 10*t

Let assume that r = 0.8 in [r = inner diameter ]

So Pmax = 2812.5 psi

This is a approximate value and user can replace this with actual no.

Volume of sphere = 4/3 [pi* r^3]

Sr No Thickness
inch Pressure
psi Allowable Stress
psi Inner Radius
[r] inch Dia in
ft Outer Dia
D [ft] Volume in
ft^3 1 0.0625 2812.5 18000 0.8 0.07 0.14 0.0012 2 0.125 2812.5 18000 1.6 0.13 0.28 0.0099 3 0.1875 2812.5 18000 2.4 0.20 0.42 0.0335 4 0.25 2812.5 18000 3.2 0.27 0.55 0.0794 5 0.3125 2812.5 18000 4 0.33 0.69 0.1551 6 0.375 2812.5 18000 4.8 0.40 0.83 0.2679 7 0.4375 2812.5 18000 5.6 0.47 0.97 0.4255 8 0.5 2812.5 18000 6.4 0.53 1.11 0.6351

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