A vertical vessel with a cylindrical shell and hemispherical heads is installed inside a building in Boston. The shell is 5 ft inside diameter, 0.5 in. nominal thickness, and 30 ft from tangent to tangent. The vessel contains a fluid at 35 lb/ft³. The purchase order specifies that the UBC be

Question

A vertical vessel with a cylindrical shell and hemispherical heads is installed inside a building in Boston. The shell is 5 ft inside diameter, 0.5 in. nominal thickness, and 30 ft from tangent to tangent. The vessel contains a fluid at 35 lb/ft³. The purchase order specifies that the UBC be followed for earthquake design. What are the lateral earthquake forces used for the design?

Accepted Answer

The UBC specifies that the total lateral earthquake force is calculated from Eq. 16.1 by the following:

V = ZIKCSW (16.1)

Z = earthquake factor depending upon site location. Boston is located in earthquake zone 2

where Z = 3/8

I = 1.0

K = 2.0

W = total dead load of vessel and contents is

shell weight = π(30.5² - 30²)(360)(490 / 1728) = 9700 lb

weight of heads = (4 / 3) π(30.5³ - 30³)(490 / 1728) = 1630 lb

fluid in shell = π(30)² (360)(35 / 1728) = 20,620 lb

fluid in heads = (4 / 3) π(30)³ (35 / 1728) = 2290 lb

W = total weight = 34,240 lb

h = 360 in.

w = W/h = 34240/360 = 95.1 lb-in.

E = 30 × 10[latex]^{6}[/latex] psi

[latex]\frac{d+t}{t}=\frac{60+0.5}{0.5}=121[/latex]

[latex]I_{x}=0.049\left(61^{4}-60^{4} ight)=43,400 ext { in.}^{4}[/latex]

[latex]T=0.0908 \sqrt{\frac{(95.1)(360)^{4}}{\left(30 imes 10^{6} ight)(43,400)}}=0.1006[/latex]

[latex]C=\frac{1}{15 \sqrt{0.1006}}=0.2102 ; ext { maximum is } C=0.12[/latex]

KC = (2.0)(0.12) = 0.24 ; maximum is KC = 0.25

CS = (0.12)(1.5) = 0.18 ; maximum is CS=0.14

KCS = (2)(0.14) = 0.28 ; maximum KCS = 0.3

V is determined by using Eq. 16.1 and KCS = 0.28 as follows:

V = (3/8)(1)(0.28)(34,240) = 3600 lb

[latex]F_{t}[/latex] = 0 when T is less than 0.7(T = 0.1006). Therefore, V = 3600 lb and [latex]F_{t}[/latex] = 0.

Question 16.1: A vertical vessel with a cylindrical shell and hemispherical...

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