SPHERICAL VESSELS

Introduction:

A sphere is a very strong structure. The even distribution of stresses on the sphere's

surfaces, both internally and externally, generally means that there are no weak

points. That's why a drop of water forms a spherical shape when under free fall, in

short, it achieves a shape where all the resultant stresses neutralize when no

external force(gravity) is acting on it. Moreover, they have a smaller surface area

per unit volume than any other shape of vessel. This means, that the quantity of

heat transferred from warmer surroundings to the liquid in the sphere, will be less

than that for cylindrical or rectangular storage vessels. Thus less pressurization due

to external heat.

Pressure vessels are closed structures containing liquids or gases under pressure.

Examples include tanks, pipes, pressurized cabins, etc.

To determine the stresses in a spherical vessel let us cut through the sphere on a

vertical diameter plane and isolate half of the shell and its fluid contents as a single

free body. Acting on this free body is the tensile stress σ in the wall of the vessel

and the fluid pressure p. Shell structures: 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.

The pressure that acts horizontally against the plane circular area is uniform and

gives a resultant pressure force of :Where pis the gage or internal pressure (above

the pressure acting in the outside of the vessel).

The stress is uniform around the circumference and it is uniformly distributed

across the thickness t(because the wall is thin). The resultant horizontal force is :

Equilibrium of forces in the horizontal direction:

As is evident from the symmetry of a spherical shell that we will obtain the same

equation regardless of the direction of the cut through the center.

The wall of a pressurized spherical vessel is subjected to uniform tensile stresses σ

in all directions.

Stresses that act tangentially to the curved surface of a shell are known as

membrane stresses.

Limitations of the thin-shell theory:

1.The wall thickness must be small (r/t> 10)

2.The internal pressure must exceed the external pressure.

3.The analysis is based only on the effects of internal pressure.

4.The formulas derived are valid throughout the wall of the vessel except near

points of stress concentration.

Materials of construction

While steel and concrete remain one of the most popular choices for tanks, glass-

reinforced plastic, thermoplastic and polyethylene tanks are increasing in

popularity. They offer lower build costs and greater chemical resistance, especially

for storage of special chemicals. There are several relevant standards, such as

British Standard 4994 (1989), DVS (German Welding Institute) 2205, and ASME

(American Society of Mechanical Engineers) RTP-1 [4]

which give advice on wall

thickness, quality control procedures, testing procedures, accreditation, fabrication

and design criteria of final product.

In this project we will use the A-36 steel as material of the tank and the A-572 steel

for bolts.

Calculation:

The volume of sphere must be 250 m3

The tank is under a gauge pressure of 2 MPa

Dbolt=25mm

Allowable stress of tank=150 MPa(A-36 steel)

Allowable stress of bolts =250MPa(A-572 steel)

V=250 m3 =4πr

3/3

›r=4m ; Din(tank)=8m

σallow=pr/2t ; 150×106=(2×10

6×4)/2t

›t=0.02667m

Since r/t = 4/0.02667=150>10 then wall analysis is valid

F=p.A=2×106[π(8)

2/4]=32π×10

6 N

ΣFy=0

›32π×106 – nFb(allow)=0

›n=(32π×106)/Fb(allow)

Fb(allow) = σallow.Ab=250(106)[π(0.025)

2/4]=3.90625π×10

3 N

›nbolts=820 bolts

But the circumference of this sphere equal 2*pi*r = 2*(3.1416)*4 = 25.13m

And the distance occupied by the bolts equal 820*25mm =20.5m

Thus the distance between two bolts = (25.13-20.5)/820 =5.64 mm which is very

small. So we should minimize the number of bolts by increasing its diameter and

changing its material:

Fb(allow) = σallow.Ab and by tacking a 30 mm diameter bolts and a 390 MPa σallow

austenitic steel (SCS 16)

Fb(allow) = 390 MPa * [π(0.03)2/4]= 275.6747KN

nbolts = 365 bolts

distance occupied by the bolts equal 365*30mm =11 m

thus the distance between two bolts = (25.13-11)/365 =38.7 mm which is

acceptable.

Construction of the sphere :

Surface of the sphere equal 4*Pi*r^2 = 201 m

Thus by using a plate ( 3m,1m 3m^2) we should use 67 plate with a thickness

of 0.02667 m

But I will use plates with t = 0.013335 m joined by rivets thus the total nbre of

plates = 134 plates (3m,1m,0.013335m)

Construction of the basement :

Density of steel varies between 7750 and 8050 kg/m3;

Let Ro = 8050 kg/m3 mass 0f the vessel M=3/2[PV*Ro/sigma] =40250 kg

Mass gaz = 250 m3 * Ro(gaz)

Total mass = mass gaz+mass vessel;

The bending moment exerted on the basement M = (Mass total*r) = 4*Mass total

N.m

And by using the formula of pure bending σ=MY/I

So σ is determined by the material chosen,Y (maximum distance from the neutral

axis )and I(second moment of inertia) is determined according to the gas putted on

the vessel;

Design Features

Safety Valves

As the pressure vessel is designed to a pressure, there is typically a safety valve or relief valve to

ensure that this pressure is not exceeded in operation.

Pressure vessel closures

Pressure vessel closures are pressure retaining structures designed to provide quick access to

pipelines, pressure vessels, pig traps, filters and filtration systems. Typically pressure vessel

closures allow maintenance personnel to load a sphere or pig into a pig trap for pipeline cleaning

purposes

Other types of tank:

TYPES OF WATER STORAGE TANKS There are three basic types of potable water-storage tanks: ground storage tanks, elevated storage

tanks, and hydropneumatic tanks.

Ground storage tanks can be installed either below or above ground. They are fabricated of concrete

or steel. They generally have the function of providing large volumes of storage for peak-day

demand when the capacity of the source of supply is less than the maximum daily volume the

specific system may need. An example of a situation in which the peak-day demand is larger than

what the system can deliver daily is a system served by a well that can deliver only enough water to

satisfy the distribution system for a short time of high-volume need. Having a large ground storage

tank allows the operator to set the pumps to operate mainly during off-peak hours, usually overnight

when power rates are lower, to fill the tank for the daytime peak period demand.

Hydropneumatic tanks are used to provide pressure to very small public water systems such as

resorts, mobile home parks and very small communities. They are not a good storage vessel for fire

protection purposes due to the small volume of water within the vessel. Hydropneumatic tanks must

be housed in a heated building to prevent freezing of the tank and associated piping, air

compressor, and controls.

Elevated storage tanks are usually constructed of welded, bolted, or riveted steel, although a few

wooden tanks still exist. Configurations for elevated steel tanks include standpipes, leg or supported

tanks, and single pedestal tanks.

Stand pipes are essentially ground storage tanks constructed to a height that will provide adequate

system pressure in the operating range. Their diameter is constant from the ground to the top, and

they are completely filled with water. While a standpipe contains a large volume of water, only the

upper volumes would be available for use if pressure demands throughout the system are to be

maintained. There is a tendency for lower-level standpipes to freeze unless they are operated very

carefully or equipped with circulation or air bubblers to prevent or reduce ice build-up in the winter.

Stand pipes are generally constructed of welded or bolted steel. Access to the top of the tank is

usually by an exterior ladder. The inlet pipe generally only extends one to two feet above the floor at

the base.

Leg supported tanks are the most common type of elevated tank seen in our area. A large volume

tank is supported by a structural system of legs and cross or wind bracing. Water enters and leaves

the tank through an insulated riser pipe usually located in the center of the support structure for the

tank. This type of elevated tank is less prone to freezing than a standpipe because the water tends to

circulate better throughout the stored volume. Leg supported tanks still require careful operation to

minimize ice sheet build up during the winter months.

Single pedestal tanks have a single support structure in the center of the tank with a large volume

tank at the top. A pedestal tank is easier and less expensive to maintain, but more costly to construct.

The riser pipe and access ladder are contained within the pedestal tube and, since the pedestal and

base are not normally heated, the riser pipe is insulated to reduce the potential for freezing.

References:

materialsAndStructures/Hibbeler8thEditionBook

*http://www.mrwa.com/OP-Storage.pdf

*http://www.tyconalloy.com/TYC/images/en_US/media/products/pdf/Comm_Steel_Standards.pdf

*http://academic.uprm.edu/pcaceres/Courses/MMII/IMoM-6A.pdf

TEAM ; Adam Dahaby 201203071

Toufik el etri 201203323