Your task is to provide design specifications for spherical

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.

Solution

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 = S_Y/FS

FS=2

So _e = 36 ksi/2 = 18 ksi

This is the allowable stress in thin pressure vessel.

_{e =} [P*r] / [2*t]

P_max = [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 P_max = 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