Determine the required skirt thickness and the number of bolts needed in a vessel with an outside radius R = 7.0 ft. Let empty weight W1 = 160 kips, weight of contents W2 = 1440 kips, wind-bending moment M = 1500 ft-kips and temperature = 300°F. Assume A 307 bolts and use Figure 8.11 for the

Question

Determine the required skirt thickness and the number of bolts needed in a vessel with an outside radius R = 7.0 ft. Let empty weight [latex]W_1[/latex] = 160 kips, weight of contents [latex]W_2[/latex] = 1440 kips, wind-bending moment M = 1500 ft-kips and temperature = 300°F. Assume A 307 bolts and use Figure 8.11 for the external pressure chart.

Accepted Answer

Skirt design

Let t = 0.375 in. From Eq. 12.2

[latex]\sigma=\frac{-W}{2 \pi R t} \pm \frac{M}{\pi R^{2} t}[/latex] (12.2)

where σ = axial stress in skirt

W = weight of vessel

M = moment due to wind or earthquake forces

R = radius of skirt

t = thickness of skirt

[latex]\begin{aligned}\sigma &=-\frac{160+1440}{2 \pi(84-0.375 / 2)(0.375)}-\frac{1500 imes 12}{\pi(83.813)^{2}(0.375)} \&=-10.28 ksi\end{aligned}[/latex]

From Eq. 8.15,

[latex]\sigma_{l}=\frac{0.0625 E_{0}}{R_{o} / t}[/latex] (8.15)

[latex]\begin{aligned}A &=\frac{0.125}{R_{o} / t} \&=0.0011\end{aligned}[/latex]

Hence, from Fig. 8.11, B = 12,100 psi OK

Bolt design

Let N = 12 bolts. From Eq. 12.3,

[latex]P=\frac{-W}{N} \pm \frac{2 M}{N R}[/latex] (12.3)

where P = load / bolt

W = weight of vessel

N = number of bolts

R = radius of bolt circle

M = bending moment

[latex]\begin{aligned} ext { Load/bolt } &=-\frac{160}{12}+\frac{2(1500)(12)}{12(84)} \&=22.4 ext { kips }\end{aligned}[/latex]

From Table 12.1,

Table 12.1
Bolt Type	Allowable Tensile Stress (ksi)	Cross-Sectional Area (in.²)
A307	20	[latex]\frac{\pi}{4}\left(D-\frac{0.9743}{N^{\prime a}} ight)^{2}[/latex]
A325	40	Nominal
A449	40	Nominal
A490	54	Nominal
[latex]{ }^{a} N^{\prime} ext { is number of threads/in.}[/latex]

[latex]\begin{aligned} ext { area required } &=\frac{22.4}{20} \&=1.12 ext { in. }^{2}\end{aligned}[/latex]

From Table 12.2 try [latex]1 \frac{3}{8}[/latex]-in. diameter bolts [latex](N^{\prime}=8)[/latex]. Thus from Table 12.1,

Table 12.2 Bolt Dimensions and Clearances Bolting Data
Bolt Size	Threads		Nut Dimensions		Bolt Spacing B	Radial Distance R	Edge Distance E	Wrench Diameter a
Bolt Size	No. of Threads	Root Area (in.²)	Across Flats	Across Corners	Bolt Spacing B	Radial Distance R	Edge Distance E	Wrench Diameter a
[latex]\frac{1}{2}[/latex]	13	0.126	[latex]\frac{7}{8}[/latex]	0.969	[latex]1 \frac{1}{4}[/latex]	[latex]\frac{13}{16}[/latex]	[latex]\frac{5}{8}[/latex]	[latex]1 \frac{1}{2}[/latex]
[latex]\frac{5}{8}[/latex]	11	0.202	[latex]1 \frac{1}{16}[/latex]	1.175	[latex]1 \frac{1}{2}[/latex]	[latex]\frac{15}{16}[/latex]	[latex]\frac{3}{4}[/latex]	[latex]1 \frac{3}{4}[/latex]
[latex]\frac{3}{4}[/latex]	10	0.302	[latex]1 \frac{1}{4}[/latex]	1.383	[latex]1 \frac{3}{4}[/latex]	[latex]1 \frac{1}{8}[/latex]	[latex]\frac{13}{16}[/latex]	[latex]2 \frac{1}{16}[/latex]
[latex]\frac{7}{8}[/latex]	9	0.419	[latex]1 \frac{7}{16}[/latex]	1.589	[latex]2 \frac{1}{16}[/latex]	[latex]1 \frac{1}{4}[/latex]	[latex]\frac{15}{16}[/latex]	[latex]2 \frac{3}{8}[/latex]
1	8	0.551	[latex]1 \frac{5}{8}[/latex]	1.796	[latex]2 \frac{1}{4}[/latex]	[latex]1 \frac{3}{8}[/latex]	[latex]1 \frac{1}{16}[/latex]	[latex]2 \frac{5}{8}[/latex]
[latex]1 \frac{1}{8}[/latex]	8	0.728	[latex]1 \frac{13}{16}[/latex]	2.002	[latex]2 \frac{1}{2}[/latex]	[latex]1 \frac{1}{2}[/latex]	[latex]1 \frac{1}{8}[/latex]	[latex]2 \frac{7}{8}[/latex]
[latex]1 \frac{1}{4}[/latex]	8	0.929	2	2.209	[latex]2 \frac{13}{16}[/latex]	[latex]1 \frac{3}{4}[/latex]	[latex]1 \frac{1}{4}[/latex]	[latex]3 \frac{1}{4}[/latex]
[latex]1 \frac{3}{8}[/latex]	8	1.155	[latex]2 \frac{3}{16}[/latex]	2.416	[latex]3 \frac{1}{16}[/latex]	[latex]1 \frac{7}{8}[/latex]	[latex]1 \frac{3}{8}[/latex]	[latex]3 \frac{1}{2}[/latex]
[latex]1 \frac{1}{2}[/latex]	8	1.405	[latex]2 \frac{3}{8}[/latex]	2.622	[latex]3 \frac{1}{4}[/latex]	2	[latex]1 \frac{1}{2}[/latex]	[latex]3 \frac{3}{4}[/latex]
[latex]1 \frac{5}{8}[/latex]	8	1.608	[latex]2 \frac{9}{16}[/latex]	2.828	[latex]3 \frac{1}{2}[/latex]	[latex]2 \frac{1}{8}[/latex]	[latex]1 \frac{5}{8}[/latex]	4
[latex]1 \frac{3}{4}[/latex]	8	1.980	[latex]2 \frac{3}{4}[/latex]	3.035	[latex]3 \frac{3}{4}[/latex]	[latex]2 \frac{1}{4}[/latex]	[latex]1 \frac{3}{4}[/latex]	[latex]4 \frac{1}{4}[/latex]
[latex]1 \frac{7}{8}[/latex]	8	2.304	[latex]2 \frac{15}{16}[/latex]	3.242	4	[latex]2 \frac{3}{8}[/latex]	[latex]1 \frac{7}{8}[/latex]	[latex]4 \frac{1}{2}[/latex]
2	8	2.652	[latex]3 \frac{1}{8}[/latex]	3.449	[latex]4 \frac{1}{4}[/latex]	[latex]2 \frac{1}{2}[/latex]	2	[latex]4 \frac{3}{4}[/latex]
[latex]2 \frac{1}{4}[/latex]	8	3.423	[latex]3 \frac{1}{2}[/latex]	3.862	[latex]4 \frac{3}{4}[/latex]	[latex]2 \frac{3}{4}[/latex]	[latex]2 \frac{1}{4}[/latex]	[latex]5 \frac{1}{4}[/latex]
[latex]2 \frac{1}{2}[/latex]	8	4.292	[latex]3 \frac{7}{8}[/latex]	4.275	[latex]5 \frac{1}{4}[/latex]	[latex]3 \frac{1}{16}[/latex]	[latex]2 \frac{3}{8}[/latex]	[latex]5 \frac{7}{8}[/latex]
[latex]2 \frac{3}{4}[/latex]	8	5.259	[latex]4 \frac{1}{4}[/latex]	4.688	[latex]5 \frac{3}{4}[/latex]	[latex]3 \frac{3}{8}[/latex]	[latex]2 \frac{5}{8}[/latex]	[latex]6 \frac{1}{2}[/latex]
3	8	6.324	[latex]4 \frac{5}{8}[/latex]	5.102	[latex]6 \frac{1}{4}[/latex]	[latex]3 \frac{5}{8}[/latex]	[latex]2 \frac{7}{8}[/latex]	7
[latex]3 \frac{1}{4}[/latex]	8	7.487	5	5.515	[latex]6 \frac{3}{4}[/latex]	[latex]3 \frac{7}{8}[/latex]	3	[latex]7 \frac{1}{2}[/latex]
[latex]3 \frac{1}{2}[/latex]	8	8.749	[latex]5 \frac{3}{8}[/latex]	5.928	[latex]7 \frac{1}{8}[/latex]	[latex]4 \frac{1}{8}[/latex]	[latex]3 \frac{1}{4}[/latex]	8
[latex]3 \frac{3}{4}[/latex]	8	10.108	[latex]5 \frac{3}{4}[/latex]	6.341	[latex]7 \frac{5}{8}[/latex]	[latex]4 \frac{3}{8}[/latex]	[latex]3 \frac{1}{2}[/latex]	[latex]8 \frac{1}{2}[/latex]
4	8	11.566	[latex]6 \frac{1}{8}[/latex]	6.755	[latex]8 \frac{1}{8}[/latex]	[latex]4 \frac{5}{8}[/latex]	[latex]3 \frac{5}{8}[/latex]	9

[latex] ext { area }=\frac{\pi}{4}\left(1.375-\frac{0.9743}{8} ight)^{2}[/latex]

= 1.23 in² > 1.12 OK

[latex] ext { actual stress }=\frac{22.4}{1.23}=18.2 ksi[/latex]

total furnished area = 12 × 1.23 = 14.8 in.²

Use [latex]\frac{3}{8}[/latex]-in. skirt with [latex]12-1 \frac{3}{8}[/latex]-in. diameter bolts.

Question 12.1: Determine the required skirt thickness and the number of bol...

Related Answered Questions

The ring girder shown in Fig. 12.14 is supported at eight points. If W = 200 kips, find the forces in the ring at the supports and at the point of maximum torsional moment. ...

Verified Answer:

Determine the forces in columns A and B of the vessel shown in Fig. 12.9. ...

Verified Answer:

Design the base ring shown in Fig. 12.7a. Stress in the bolts is 17,500 psi; height of gussets 12 in. , and concrete-bearing stress is 100 psi. Allowable stress for base ring is 20,000 psi and yield stress is 36,000 psi. ...

Verified Answer:

In Example 12.1, it was found that 12-1 3/8 in. A 307 anchor bolts were needed for a vessel with an outside radius R = 7 ft , W1 = 160 kips, M = 1500 ft-kips, and a skirt thickness of 0.375 in. If fc¹ = 3000 psi, determine the actual stress in the concrete and bolts. ...

Verified Answer: