8495_Simple+Stresses_Thin+Walled---

8/10/2019 8495_Simple+Stresses_Thin+Walled---

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Stress

Thin-Walled Pressure Vessels


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A tank or pipe carrying a fluid or gas under a

pressure is subjected to tensile forces, which

resist bursting, developed across longitudinal

and transverse sections.


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TANGENTIAL STRESS(Circumferential Stress)

Consider the tank shown being subjected to

an internal pressure p. The length of the tank

is L and the wall thickness is t.

Isolating the right half of the tank:


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If there exist an external pressure poand an

internal pressure pi, the formula may be

expressed as:


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LONGITUDINAL STRESS, L

Consider the free body diagramin the transverse section of thetank:

The total force acting at the rearof the tank Fmust equal to thetotal longitudinal stress on the

wall PT. Since tis so smallcompared to D, the area of thewall is close to Dt


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If there exist an external pressure poand an

internal pressure pi, the formula may be

expressed as:

It can be observed that the tangential stress istwice that of the longitudinal stress.

t = 2 L


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SOLVED PROBLEMS IN THIN WALLED

PREASSURE VESSELS

1. A cylindrical steel pressure vessel 400 mm in

diameter with a wall thickness of 20 mm, is

subjected to an internal pressure of 4.5 MN/m2.

(a) Calculate the tangential and longitudinal

stresses in the steel. (b) To what value may the

internal pressure be increased if the stress in the

steel is limited to 120 MN/m2? (c) If the internalpressure were increased until the vessel burst,

sketch the type of fracture that would occur.


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2. The wall thickness of a 4-ft-diameter

spherical tank is 5/16 in. Calculate the allowable

internal pressure if the stress is limited to 8000psi.


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3. Calculate the minimum wall thickness for a

cylindrical vessel that is to carry a gas at a

pressure of 1400 psi. The diameter of thevessel is 2 ft, and the stress is limited to 12

ksi.


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4. A cylindrical pressurevessel is fabricatedfrom steel plating thathas a thickness of 20

mm. The diameter ofthe pressure vessel is450 mm and its lengthis 2.0 m. Determine themaximum internalpressure that can be

applied if thelongitudinal stress islimited to 140 MPa,and the circumferentialstress is limited to 60MPa.


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5. A water tank, 22ft in diameter, ismade from steel

plates that are in.thick. Find themaximum height towhich the tank may

be filled if thecircumferentialstress is limited to6000 psi. The

specific weight ofwater is 62.4 lb/ft3.


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6. The strength of longitudinal joint in Fig. 1-17

is 33 kips/ft, whereas for the girth is 16 kips/ft.

Calculate the maximum diameter of the cylindertank if the internal pressure is 150 psi.


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Problem Set:

1. The tank shown in Fig. P-141 is fabricated

from 1/8-in steel plate. Calculate the

maximum longitudinal and circumferential

stress caused by an internal pressure of 125psi.


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2. A 20m diameter spherical tank is to be used to storegas. The shell plating is 10 mm thick and the workingstress of the material, that is, the maximum stress towhich the material should be subjected, is 125 MPa.

What is the maximum permissible gas pressure?3. A steel pipe with inside diameter of 12 in. will be used

to transmit steam under a pressure of 1000 psi. If thehoop stress in the pipe must be limited to 10 ksi

because of a longitudinal weld in the pipe, determinethe maximum satisfactory thickness for the pipe.

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8495_Simple+Stresses_Thin+Walled---