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Lawrence on Design of Domed Roof

By: Lawrence 
Date: Tuesday, December 31, 2002
Time: 12:00:00 AM

What is the roof radius?

The minimum plate thickness must be 3/16-inch regardless.

Now, API-650 3.10.6 is very simplified meaning if it is followed you cannot go wrong.

Minimum radius means the roof radius and not the tank radius. The roof radius has to be some where between 33.6-feet and 50.4-feet.

. Roof Radius 33.6-ft and 50.4-ft
This is based on API-650 3.10.6.1 and the diameter of tank at 42-feet.


At 33.6-feet what is the minimum thickness of roof plates:
0.168-inches = 33.6-ft/200 or 33.6-ft/(16.667 x (1-ft/12-inches))

At 50.4-feet what is the minimum thickness of roof plates:
0.252-inches = 50.4-ft/200 or 50.6-ft/(16.667 x (1-ft/12-inches))



The maximum thickness for of any roof plate on this subject is 1/2-inch.
We have a non-dimensional number that will modify the thickness of the plates above the range of 0.168-inches to 0.252-inches. Lets assume you have a 85-pound live and dead load on the roof in worst case scenario because you live in snow country.

ratio = [ 85-pounds/45-pounds] ^0.5

ratio = 1.374



At 33.6-feet what is the minimum thickness of roof plates with 85-pound combination loading is::
0.231-inches = 0.168-inches x 1.374



At 50.4-feet what is the minimum thickness of roof plates with 85-pound combination loading is:
0.346-inches = 0.252-inches x 1.374

After this the roof load has to be distributed to the shell in a manner that will not split the shell open or buckle it. In 3.10.6.2 this issue is addressed. In your case you need

0.941 square inches of compensation for the 33.6 radius

1.411 square inches of compensation for the 50.4 radius

Go to Appendix F figure 2 to determine the window of compensation that is available [corrosion allowance cannot to be included.] Detail (a) has the outlines the basic window. A quick picture form in the mind that you can only include about 2-feet of the shell based on a 1/2 -inch shell [minus c.a.] at the top course and not less than 1-foot of the roof plate. Based on this you will not need stiffeners for the roof but remember you may need them for the wind loadings.

We have a non-dimensional number again to deal with for the 85-pound live and dead load on the roof in worst case scenario because you live in snow country [assuming].

ratio = 85-pounds / 45-pounds

ratio = 1.889

Therefore, the cross sectional area of compensation for the roof plate in the window of compensation is 1.889 x Area =

1.778 square inches of compensation for the 33.6 radius

2.665 square inches of compensation for the 50.4 radius

Finally, What you have available is 2.772 square inches on the top plate so no additional stiffening is needed but you may want to consider using 3/8 -inch roof plates.

If you do research on domed roofs and umbrella roofs look up Funicular Arches. A funicular arch has no bending moments or shear. Consider of this...a parabolic arch is a funicular arch under uniformly distributed loading. So when we look at a bridge or arched structure the parts we do not see are equally as important [the ends of the arch].

The API 650 code was written for engineering-technicians where units are not kept track off. As an engineer, I want to know if the units come out correctly too.

L.



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