Machine Design Databook Episode 1 part 7 doc

PROBLEM A closed end cylinder made of ductile material has inner diameter of 10 in (250 mm) and outside

diameter of cylinder is 25 in (625 mm). The pressure inside the cylinder is 5000 psi. Use Clavarino’s equation from

Table 7-8

REFERENCES

1. ‘‘Rules for Construction of Power Boilers,’’ Section I, ASME Boiler and Pressure Vessel Code, American

Society of Mechanical Engineers, New York, 1983.

2. ‘‘Rules for Construction of Pressure Vessels,’’ Section VIII, Division 1, ASME Boiler and Pressure Vessel Code,

American Society of Mechanical Engineers, New York, July 1, 1986.

3. ‘‘Rules for Construction of Pressure Vessels,’’ Section VIII, Division 2—Alternative Rules, ASME Boiler and

Pressure Vessel Code, American Society of Mechanical Engineers, New York, July 1, 1986.

4. Nicholas, R. W., Pressure Vessel Codes and Standards, Elsevier Applied Science Publications, Crown House,

Linton Road, Barking, Essex, England.

5. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Engineering College Co-operative

Society, Bangalore, India, 1962.

6. Lingaiah, K., Machine Design Data Handbook, Vol. II (SI and Customary Metric Units), Suma Publishers,

Bangalore, India, 1986.

7. Courtesy: Durham, H. M., Stress Chart for Thick Cylinders.

8. Greenwood, D. C., Editor, Engineering Data for Product Design, McGraw-Hill Book Company, New York,

1961.

9. Lingaiah, K., Machine Design Data Handbook (SI and U.S. Customary Systems Units), McGraw-Hill Book

Company, New York, 1994.

R ¼ do

di

¼ 25

10 ¼ 2:5

Mark on scale b at 2.5

Draw a perpendicular from x and this perpendicular

meets scale d at y

Join y and 5 (5000 psi) on scale e. Produce y–5 to meet

scale f at z. y–5–z meets scale f at 8.25

Stress ¼ 8:25 ¼ 8250 psi

Stress in SI units ¼ 8250 6:894 103 ¼ 56:88 MPa

Check by using Clavarino’s equation from Table 7-8

¼ p1

0:4 þ 1:3R2

R2
1

¼ 5000

0:4 þ 1:3ð2:5Þ

2

ð2:5Þ

2
1

¼ 5000

0:4 þ 8:125

6:25
1

¼ 4:2625

5:25 104

¼ 8120 psi ð56MPaÞ

The stress obtained from nomogram 8250 psi

(56.88 MPa) is very close to stress value found from

Clavarino’s equation

Particular Formula

7.20 CHAPTER SEVEN

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PIPES, TUBES, AND CYLINDERS

CHAPTER

8

DESIGN OF PRESSURE VESSELS,

PLATES, AND SHELLS

SYMBOLS13;14;15

a length of the long side of a rectangular plate, m (in)

pitch or distance between stays, m (in)

major axis of elliptical plate, m (in)

long span of noncircular heads or covers measured at

perpendicular distance to short span, m (in) (see Fig. 8-10)

A factor determined from Fig. 8-3

A total cross-sectional area of reinforcement required in the plane

under consideration, m2 (in2

) (see Fig. 8-17) (includes

consideration of nozzle area through shell for
sna=
sva < 1:0)

A outside diameter of flange or, where slotted holes extend to the

outside of the flange, the diameter to the bottom of the slots,

m (in)

A1 area in excess thickness in the vessel wall available for

reinforcement, m2 (in2

) (see Fig. 8-17) (includes consideration

of nozzle area through shell if
sna=
sva < 1:0)

A2 area in excess thickness in the nozzle wall available for

reinforcement, m2 (in2

) (see Fig. 8-17)

A3 area available for reinforcement when the nozzle extends inside

the vessel wall, m2 (in2

) (see Fig. 8-17)

A41, A42, A43 cross-sectional area of various welds available for reinforcement

(see Fig. 8-17), m2 (in2

)

A5 cross-sectional area of material added as reinforcement (see Fig.

8-17), m2 (in2

)

Ab cross-sectional area of the bolts using the root diameter of

the thread or least diameter of unthreaded portion, if less, Eq.

(8-111), m (in)

Am total required cross-sectional area of bolts taken as the greater

of Am1 and Am2, m2 (in2

)

Am1 ¼ Wm1=
sb total cross-sectional area of bolts at root of thread or section of

least diameter under stress, required for the operating

condition, m2 (in2

)

Am2 ¼ Wm2=
sa total cross-sectional area of bolts at root of thread or section of

least diameter under stress, required for gasket seating, m2

(in2

)

8.1

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Source: MACHINE DESIGN DATABOOK

b length of short side or breadth of a rectangular plate, m (in)

short span of noncircular head, m (in) (see Fig. 8-10 and Eq. 8-86a)

b effective gasket or joint-contact-surface seating width, m (in)

bo basic gasket seating width, m (in) (see Table 8-21 and Fig. 8-13)

B factor determined from the application material–temperature

chart for maximum temperature, psi

B inside diameter of flange, m (in)

c corrosion allowance, m (in)

c basic dimension used for the minimum sizes of welds, mm (in),

equal to tn or tx, whichever is less

c1 empirical coefficient taking into account the stress in the

knuckle [Eq. (8-68)]

c2 empirical coefficient depending on the method of attachment to

shell [Eqs. (8-82) and (8-85)]

c4, c5 empirical coefficients depending on the mode of support [(Eqs.

(8-92) to (8-94)]

C bolt-circle diameter, mm (in)

d finished diameter of circular opening or finished dimension

(chord length at midsurface of thickness excluding excess

thickness available for reinforcement) of nonradial opening

in the plane under consideration in its corroded condition, m

(in) (see Fig. 8-17)

d diameter or short span, m (in)

diameter of the largest circle which may be inscribed between

the supporting points of the plate (Fig. 8-11), m (in)

diameter as shown in Fig. 8-9, m (in)

d factor, m3 (in3

)

d ¼ U

V

hog2

o for integral-type flanges

d ¼ U

VL

hog2

o for loose-type flanges

d0 diameter through the center of gravity of the section of an

externally located stiffening ring, m (in);

inner diameter of the shell in the case of an internally located

stiffening ring, m (in) [Eq. (8-55)]

de outside diameter of conical section or end (Fig. 8-8(A)d),

m (in)

di, Di inside diameter of shell, m (in)

do, Do outside diameter of shell, m (in)

dk inside diameter of conical section or end at the position under

consideration (Fig. 8-8(A)d), m (in)

D inside shell diameter before corrosion allowance is added,

m (in)

Dp outside diameter of reinforcing element, m (in) (actual size of

reinforcing element may exceed the limits of available

reinforcement)

e factor, m
1 (in
1

)

e ¼ F

ho

for integral-type flanges

e ¼ FL

ho

for loose-type flanges

E modulus of elasticity at the operating temperature, GPa (Mpsi)

Eam modulus of elasticity at the ambient temperature, GPa (Mpsi)

8.2 CHAPTER EIGHT

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DESIGN OF PRESSURE VESSELS, PLATES, AND SHELLS

f hub stress correction factor for integral flanges from Fig. 8-25

(When greater than one, this is the ratio of the stress in the

small end of the hub to the stress in the large end. For values

below limit of figure, use f ¼ 1.)

fr strength reduction factor, not greater than 1.0

fr1
sna=
sva

fr2 (lesser of
sna or
spaÞ=
sva

fr3
spa=
sva

F total load supported, kN (lbf )

total bolt load, kN (lbf )

F correction factor which compensates for the variation in

pressure stresses on different planes with respect to the axis of

a vessel (a value of 1.00 shall be used for all configurations,

except for integrally reinforced openings in cylindrical shells

and cones)

F factor for integral-type flanges (from Fig. 8-21)

FL factor for loose-type flanges (from Fig. 8-23)

ga thickness of hub at small end, m (in)

g1 thickness of hub at back of flange, m (in)

G diameter, m (in), at location of gasket load reaction; except as

noted in Fig. 8-13, G is defined as follows (see Table 8-22):

When bo 6:3 mm (l/4 in), G ¼ mean diameter of gasket

contact face, m (in).

When bo > 6:3 mm (1/4 in), G ¼ outside diameter of gasket

contact face less 2b, m (in).

h distance nozzle projects beyond the inner or outer surface

of the vessel wall, before corrosion allowance is added,

m (in)

(Extension of the nozzle beyond the inside or outside surface of

the vessel wall is not limited; however, for reinforcement

calculations the dimension shall not exceed the smaller of 2.5t

or 2.5tn without a reinforcing element and the smaller of 2.5t

or 2.5tn þ te with a reinforcing element or integral

compensation.)

h hub length, m (in)

h, t minimum required thickness of cylindrical or spherical shell or

tube or pipe, m (in)

thickness of plate, m (in)

thickness of dished head or flat head, m (in)

ha actual thickness of shell at the time of test including corrosion

allowance, m (in)

hc thickness for corrosion allowance, m (in)

hD radial distance from the bolt circle, to the circle on which HD

acts, m (in)

hG ¼ ðC
GÞ=2 radial distance from gasket load reaction to the bolt circle, m

(in)

ho ¼ ffiffiffiffiffiffiffiffi

Bgo

p factor, m (in)

hT radial distance from the bolt circle to the circle on which HT acts

as prescribed, m (in)

H ¼ G2

P=4 total hydrostatic end force, kN (lbf )

HD ¼ B2

P=4 hydrostatic end force on area inside of flange, kN (lbf )

HG ¼ W
H gasket load (difference between flange design bolt load and total

hydrostatic end force), kN (lbf )

HP ¼

2b GmP

total joint-contact-surface compression load, kN (lbf )

DESIGN OF PRESSURE VESSELS, PLATES, AND SHELLS 8.3

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DESIGN OF PRESSURE VESSELS, PLATES, AND SHELLS