Machine Design Databook Episode 1 part 7 doc

8-17 includesconsideration of nozzle area through shell forsna=sva< 1:0 A outside diameter of ﬂange or, where slotted holes extend to the outside of the ﬂange, the diameter to the bottom

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PROBLEM A closed end cylinder made of ductile material has inner diameter of 10 in (250 mm) and outsidediameter of cylinder is 25 in (625 mm) The pressure inside the cylinder is 5000 psi Use Clavarino’s equation fromTable 7-8

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 BookCompany, New York, 1994

R ¼do

di¼25

10¼ 2:5Mark on scale b at 2.5Draw a perpendicular from x and this perpendicularmeets scale d at y

Join y and 5 (5000 psi) on scale e Produce y–5 to meetscale f at z y–5–z meets scale f at 8.25

Stress¼ 8:25 ¼ 8250 psiStress in SI units¼ 8250 6:894 103¼ 56:88 MPaCheck by using Clavarino’s equation from Table 7-8

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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) (includesconsideration of nozzle area through shell forsna=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 ifsna=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 Am1and Am2, m2(in2)

Am1¼ Wm1=sb total cross-sectional area of bolts at root of thread or section of

least diameter under stress, required for the operatingcondition, m2(in2)

Am2¼ 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)

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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 tnor 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 excessthickness 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)

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 availablereinforcement)

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)

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

(When greater than one, this is the ratio of the stress in thesmall end of the hub to the stress in the large end For valuesbelow limit of ﬁgure, use f ¼ 1.)

fr strength reduction factor, not greater than 1.0

fr1 sna=sva

fr2 (lesser ofsnaorspaÞ=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 shellsand 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 gasketcontact 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 reinforcementcalculations the dimension shall not exceed the smaller of 2.5t

or 2.5tnwithout a reinforcing element and the smaller of 2.5t

or 2.5tnþ tewith a reinforcing element or integralcompensation.)

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

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

HG¼ W H gasket load (diﬀerence between ﬂange design bolt load and total

hydrostatic end force), kN (lbf )

HP¼

2b GmP

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

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HT ¼ H HD diﬀerence between total hydrostatic end force and the

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

Is required moment of inertia of the stiﬀening ring cross-section

around an axis extending through the center of gravity andparallel to the axis of the shell, m4or cm4(in4)

Is0 required moment of inertia of the combined ring-shell

cross-section about its neutral axis parallel to the axis of the shell,

m4(in4)

I available moment of inertia of the stiﬀening ring cross-section

about its neutral axis parallel to the axis of the shell, m4(in4)

I0 available moment of inertia of combined ring shell cross-section

about its neutral axis parallel to the axis of the shell, m4or

cm4(in4)

k1, k2, k3, k4, k5 coeﬃcients

k6 factor for noncircular heads depending on the ratio of short

span to long span b=a (Fig 8-10)

K ¼ A=B ratio of outside diameter of ﬂange to inside diameter of ﬂange

(Fig 8-20)

K ratio of the elastic modulus E of the material at the design

material temperature to the room temperature elasticmodulus, Eam, [Eqs (8-26) to (8-31), (8-55)]

K1 spherical radius factor (Table 8-18)

l length of ﬂange of ﬂanged head, m (in)

L eﬀective length, m (in)

distance from knuckle or junction within which meridional

stresses determine the required thickness, m (in)perimeter of noncircular bolted heads measured along the

centers of the bolt holes, m (in)distance between centers of any two adjacent openings, m (in)

length between the centers of two adjacent stiﬀening rings, m

(in) (Fig 8-1)

L ¼te þ 1

T þt3

d factor

m gasket factor, obtained from Table 8-20

m ¼ 1= reciprocal of Poisson’s ratio

Mb longitudinal bending moment, N m (lbf in)

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Mt torque about the vessel axis, N m (lbf in)

MD¼ HDhD component of moment due to HD, m N (in-lbf )

MG¼ HGhG component of moment due to HG, m N (in-lbf )

Mo total moment acting on the ﬂange, for the operating conditions

or gasket seating as may apply, m N (in-lbf )

MT ¼ HTh component of moment due to HT, m N (in-lbf )

N width, m (in), used to determine the basic gasket seating with bo,

based on the possible contact width of the gasket (seeTable 8-21)

pi internal design pressure, MPa (psi)

p maximum allowable working pressure or design pressure,

MPa (psi)

po load per unit area, MPa (psi)

external design pressure, MPa (psi)

P total pressure on an area bounded by the outside diameter of

gasket, kN (lbf )design pressure (or maximum allowable working pressure for

existing vessels), MPa (psi)

Pa calculated value of allowable external working pressure for

assumed value of t or h, MPa (psi)

r radius of circle over which the load is distributed, m (in)

ri inner radius of a circular plate, m (in)

inside radius of transition knuckle which shall be taken as

0:01dkin the case of conical sections without knuckletransition, m (in)

R inner radius of curvature of dished head, m (in)

Ri inner radius of shell or pipe, m (in)

ro, Ro outer radius of a circular plate, m (in)

outer radius of shell, m (in)

R ¼ ½ðC BÞ=2

g1

radial distance from bolt circle to point of intersection of hub

and back of ﬂange, m (in) (for integral and hub ﬂanges)

R inside radius of the shell course under consideration, before

corrosion allowance is added, m (in)

Rn inside radius of the nozzle under consideration, before

corrosion allowance is added, m (in)

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

pipe or tube, m (in)

t nominal thickness of the vessel wall, less corrosion allowance, m (in)

te thickness or height of reinforcing element, m (in)

tn nominal thickness of shell or nozzle wall to which ﬂange or lap is

attached, irrespective of product form less corrosionallowance, m (in)

tr required thickness of a seamless shell based on the

circumferential stress, or of a formed head, computed by therules of this chapter for the designated pressure, m (in)

trn required thickness of a seamless nozzle wall, m (in)

ts nominal thickness of cylindrical shell or tube exclusive of

corrosion allowance, m (in)

tx two times the thickness go, when the design is calculated as an

integral ﬂange, m (in), or two times the thickness, m (in), ofshell nozzle wall required for internal pressure, when thedesign is calculated as a loose ﬂange, but not less than 6.3 mm

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(1/4 in)

T factor involving K (from Fig 8-20)

U factor involving K (from Fig 8-20)

V factor for integral-type ﬂanges (from Fig 8-22)

VL factor for loose-type ﬂanges (from Fig 8-24)

w width, m (in), used to determine the basic gasket seating width

bo, based on the contact width between the ﬂange facing andthe gasket (see Table 8-21)

W total load to be carried by attachment welds, kN (lbf )

W ﬂange design bolt load, for operating conditions or gasket

seating, as may apply, kN (lbf )

Wm1 minimum required bolt load for the operating conditions, kN

(lbf ) (For flange pairs used to contain a tubesheet for afloating head for a U-tube type of heat exchanger, or for anyother similar design, Wm1shall be the larger of the values asindividually calculated for each flange, and that value shall beused for both flanges.)

Wm2 minimum required bolt load for gasket seating, kN (lbf )

y gasket or joint-contact-surface unit seating load, MPa (psi)

y deﬂection of the plate, m (in)

ymax maximum deﬂection of the plate, m (in)

Y factor involving K (from Fig 8-20)

Z factor involving K (from Fig 8-20)

a factor for non-circular heads [Eq (8-86b)]

, 1,2 angles of conical section to the vessel axis, deg (Fig 8-8(A)d)

diﬀerence between angle of slope of two adjoining conical

sections, deg (Fig 8-8(A)d)

normal or direct stress, MPa (psi)

sy 0.2 percent proof stress, MPa (psi)

sa maximum allowable stress value, MPa (psi)

e equivalent stress (based on shear strain energy), MPa (psi)

sam allowable stress at ambient temperature, MPa (psi)

sd design stress value, MPa (psi)

sa allowable stress value as given in Tables 8-9 to 8-12, MPa (psi)

sna allowable stress in nozzle, MPa (psi)

sva allowable stress in vessel, MPa (psi)

spa allowable stress in reinforcing element (plate), MPa (psi)

sbat allowable bolt stress at atmospheric temperature, MPa (psi)

sbd allowable bolt stress at design temperature, MPa (psi)

sfd allowable design stress for material of ﬂange at design

temperature (operating condition) or atmospherictemperature (gasket seating), as may apply, MPa (psi)

snd allowable design stress for material of nozzle neck, vessel or pipe

wall, at design temperature (operating condition) oratmospheric temperature (gasket seating), as may apply, MPa(psi)

H calculated longitudinal stress in hub, MPa (psi)

R calculated radial stress in ﬂange, MPa (psi)

calculated tangential stress in ﬂange, MPa (psi)

0 hoop stress, MPa (psi)

r radial stress, MPa (psi)

s strength, MPa (psi)

su ultimate strength, MPa (psi)

zorl longitudinal stress, MPa (psi)

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tensile longitudinal stress, MPa (psi)

zc compressive longitudinal stress, MPa (psi)

shear stress (also with subscripts), MPa (psi)

joint factor (Table 8-3) or eﬃciency

¼ 1 (see deﬁnitions for trand trn)

1¼ 1 when an opening is in the solid plate or joint eﬃciency obtained

from Table 8-3 when any part of the opening passes throughany other welded joint

Note: and with initial subscript s designates strength properties of material

used in the design which will be used and observed throughout this Machine

Design Data Handbook

Other factors in performance or in special aspect are included from time to time

in this chapter and, being applicable only in their immediate context, are not

given at this stage

PLATES13;14;15

For maximum stresses and deﬂections in ﬂat plates

Plates loaded uniformly

The thickness of a plate with a diameter d supported

at the circumference and subjected to a pressure p

distributed uniformly over the total area

The maximum deﬂection

Plates loaded centrally

The thickness of a ﬂat cast-iron plate supported freely

at the circumference with diameter d and subjected to

a load F distributed uniformly over an area (d2

o=4)The deﬂection

Grashof’s formula for the thickness of a plate rigidly

ﬁxed around the circumference with the above given

type of loading

Refer to Table 8-1

h ¼ k1d

p

sd

1=2

ð8-1ÞRefer to Table 8-2 for values of k1

F

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The deﬂection

Rectangular plates

UNIFORM LOAD

The thickness of a rectangular plate according to

Grashof and Bach

CONCENTRATED LOAD

The thickness of a rectangular plate on which a

con-centrated load F acts at the intersection of diagonals

Elliptical plate

The thickness of uniformly loaded elliptical plate

SHELLS (UNFIRED PRESSURE VESSEL)

Shell under internal pressure—cylindrical

shell

CIRCUMFERENCE JOINT

The minimum thickness of shell exclusive of corrosion

allowance as per Bureau of Indian Standards11

h ¼ abk3

p

sdða2þ b2Þ

1=2

ð8-7Þwhere k3¼ coeﬃcient, taken from Table 8-2

h ¼ k4

abF

sdða2þ b2Þ

1=2

h ¼ abk5

p

sdða2þ b2Þ

1=2

Coeﬃcients in formulas for cover plates13;14;15

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Note: A minimum thickness of 1.5 mm is to be

pro-vided as corrosive allowance unless a protective

lining is employed

The design pressure or maximum allowable working

pressure

allowance as per ASME Boiler and Pressure Vessel

Code

The maximum allowable working pressure as per

ASME Boiler and Pressure Vessel Code [from Eq

Joint eﬃciency factor ()13;14;15

Maximum thickness 38 mm after adding corrosion allowance

Maximum thickness 16 mm before corrosion allowance is added

butt joints with full penetration excluding butt joints with metal backing strips which remain in place

Double-welded butt joints with full penetration excluding butt joints with metal backing strips which remain in place

Single-welded butt joints with backing strip not over

16 mm thickness or over 600 mm outside diameter

Single full ﬁllet lap joints for circumferential seams only

Single-welded butt joints with backing strip

Single-welded butt joints without backing strip

Source: K Lingaiah and B R Narayana Iyengar, Machine Design Data Handbook, Engineering College Cooperative Society, Bangalore, India, 1962; K Lingaiah and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1983; K Lingaiah, Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986; and IS: 2825-1969.

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LONGITUDINAL POINT

The minimum thickness of shell exclusive of corrosive

Code.[1-10]

The maximum allowable working pressure as

per ASME Boiler and Pressure Vessel Code [from

Eq 8-14)]

The design stress for the case of welded cylindrical

shell assuming a Poisson ratio of 0.3

The allowable stress for plastic material taking into

consideration the combined eﬀect of longitudinal

and tangential stress (Note: The design stress for

plas-tic material is 13.0 percent less compared with the

maximum value of the main stress.)

The thickness of shell from Eq (8-17) without taking

into account the joint eﬃciency and corrosion

allowance

The design thickness of shell taking into consideration

the joint eﬃciency and allowance for corrosion,

negative tolerance, and erosion of the shell (hc)

The design formula for the thickness of shell

accord-ing to Azbel and Cheremisineﬀ10

The factor of safety as per pressure vessel code, which

is based on yield stress of material used for shell

Shell under internal pressure—spherical shell

allowance as per Bureau of Indian Standards

The design pressure as per Bureau of Indian

The factor of safety n should not be less than 4, which

is based on yield strengthsyof material

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Code

The design pressure (or maximum allowable working

pressure) as per ASME Boiler and Pressure Vessel

Code

Shells under external pressure—cylindrical

shell (Fig 8-1)

(a) The minimum thickness of cylindrical shell

exclu-sive of corrosion allowance as per Bureau of

do

2=3

SI ð8-26aÞwhere h, do, and L in m; and p in MPa and

do

2=3

USCS ð8-26bÞwhere h, do, and L in in; and p in psi

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(b) The minimum thickness of cylindrical shell

exclu-sive of corrosion allowance according to Bureau

of Indian Standards11

Standards from Eq (8-28)

(c) In other cases, the minimum thickness of the shell

exclusive of corrosion allowance as per Bureau of

Indian Standards

h ¼ 2:234 104doð pKÞ1=3but not less than

where doand h in m and p in MPa

h ¼ 4:25 103doð pKÞ1=3 but not less than

do

3but not greater than 2h

3:5do

SI ð8-29aÞwhere p in MPa and h and doin m

p ¼ 13 106K

h

do

3but not greater than 2

3:5

h

doUSCS ð8-29bÞwhere p in psi and h and doin in

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Standards

Reference Chart for ASME Boiler and Pressure

Vessel Code,Section VIII, Division 112

(d) Maximum allowable stress values

(1) The maximum allowable stress values in

ten-sion for ferrous and nonferrous materialssa

The maximum allowable stress values (sa)

for bolt, tube, and pipe materials

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(2) The maximum allowable longitudinal

com-pressive stress (ac) to be used in the design

of cylindrical shells or tubes, either seamless

or butt-welded subjected to loadings that

produce longitudinal compression in shell

or tube shall be as given in either Eq (a)

or (b)

(3) The procedure for determining the value of

the factor B

The value of factor A

The expression for value of factor B

ac< sa from Tables 7-1, 8-9 to 8-13 (a)

where B ¼ a factor determined from the applicablematerial/temperature chart for maximumdesign temperature, psi, Figs 8-4, 8-5.[Note: US Customary units (i.e., fps system of units)were used in drawing Figs 8-3 to 8-5 of ASME Pres-sure Vessel and Boiler Code, which is now used to findthe thickness of walls of cylindrical and sphericalshells and tubes, unless it is otherwise mentioned touse both SI and US Customary units Figures 8-3 to8-5 are in US Customary units The values fromthese figures and others can be used in the appropriateequation to find the values or results in SI units, ifthese values and equations are converted into SIunits beforehand.]

Select the thickness t (¼ h) and outside diameter Dooroutside radius Roof a cylindrical shell or tube in thecorroded condition Then calculate the value of Afrom Eq (8-32)

A ¼0:125

Using this value of A enter the applicable material/temperature chart for the material (Figs 8-4 and 8-5)under consideration to ﬁnd B In case the value of Afalls to the right of the end of the material/tempera-ture line (Figs 8-4 and 8-5), assume an intersectionwith the horizontal projection of the upper end ofthe material/temperature line From the intersectionmove horizontally to the right and ﬁnd the value of

B This is the maximum allowable compressivestress for the value of t and Roassumed

If the value of A falls to the left of the applicablematerial/temperature line, the value of B, psi, shall

be calculated from Eq (8-33)

B ¼AE

where E ¼ modulus of elasticity of material atdesign temperature, psi

Compare the value of B determined from Eq (8-33)

or from the procedure outlined above with thecomputed longitudinal compressive stress in thecylindrical shell or tube using the selected values of tand Ro If the value of B is smaller than the computed,compressive stress, a greater value of t must be

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FIGURE 8-3 Geometric chart for cylindrical vessels under external or compressive loadings (for all materials) (Source:

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FIGURE 8-4 Chart for determining shell thickness of cylindrical and spherical vessels under external pressure when constructed of carbon or low-alloy steels (speciﬁed minimum yield strength 24,000 psi to, but not including, 30,000 psi);

of carbon or low-alloy steels (speciﬁed minimum yield strength 30,000 psi and over except for materials within this range where

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