Question 16.11: A tall vessel is constructed with a cylindrical shell and tw...
A tall vessel is constructed with a cylindrical shell and two hemispherical heads. The vessel is designed for full vacuum (15 psi external pressure) at a design temperature of 550 °F. The material is SA-516 Grade 60. There is no corrosion allowance required. The vessel has 10 ft 0 in. inside diameter with 116 ft 8 in. from tangent to tangent. The vessel is to be installed in the vertical position and supported at the bottom tangent line. It contains a fluid weighing 50 lb/ft ^{3} . Three stiffening rings are evenly spaced at 30 ft 0 in. with 28 ft 4 in. from each tangent line. What are the longitudinal stresses above the support line?
Determine a preliminary thickness based on the external pressure alone, using the procedure of the ASME Code, VIII-1, UG-28(c)(1). Assume a thickness of t =0.75 in. Then D_{o} =120+2(0.75)=121.5 in. D_{o}/t =121.5/0.75=162, and L/D_{o} =360/121.5=2.9630.
From Figure G of II-D, A=0.00022
P_{ a }=\frac{2(0.00022)\left(26.38 \times 10^{6}\right)}{3(162)} =23.9 psi;
t=\frac{3}{4} in. (O.K.)
Determine the weight of the vessel and contents:
Shell: \pi\left(60.75^{2}-60^{2}\right)(1400)(490 / 1728)=112,950
Heads: \frac{4}{3} \pi\left(60.75^{3}-60^{3}\right)(490 / 1728)=9740
shell contents: \pi(60)^{2}(1400)(50 / 1728)=458,150
head contents: \frac{4}{3} \pi(60)^{3}(50 / 1728)=26,180
Determine the maximum compressive load (lb/in.) using Eq. (16.23) as follows:
P_{ v }=\frac{W}{\pi D_{ m }}=\frac{112,950+0.5(9740)}{\pi(120.75)} =310.6 lb / in.
P_{ o } = 15.0 psi
\alpha=\frac{P_{ v }}{P_{ o } D_{ o }}=\frac{310.6}{(15)(121.5)} =0.1704
m=\frac{1.23}{\left(L / D_{ o }\right)^{2}}=\frac{1.23}{(2.963)^{2}} =0.1401
𝜂 = 3.0 from Figure 16.11 for L∕D_{o}
= 2.963 and D_{o}∕t = 162
P_{ o }^{\prime}=\frac{9-1+0.14+0.14(0.1704)}{9-1+0.14}(15) =15.04 psi
As determined in step 1, the maximum allowable external pressure based on t =0.75 in. is P_{o} =23.9 psi at 550 °F. Because the required pressure of 15.04 psi is less than the permissible pressure of 23.9 psi, t =0.75 in. is satisfactory. Because 𝛼 is less than 1.0, no cantilever-beam check is needed.
