Pressure Vessel Design Manual - pvmanage.compvmanage.com/wp...from-Pages-from-PRESSURE-VESSEL-DESIGN-M… · allow for the radial expansion of the vessel due to temperature and pressure

5Vessel Internals

Procedure 5-1: Design of Internal Support Beds. . 298Procedure 5-2: Design of Lattice Beams .. . . . . . . . . . . 310Procedure 5-3: Shell Stresses due to Loadings atSupport Beam Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316Procedure 5-4: Design of Support Blocks. . . . . . . . . . . 319Procedure 5-5: Hub Rings used for BedSupports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321Procedure 5-6: Design of Pipe Coils for HeatTransfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326Procedure 5-7: Agitators/Mixers for Vesselsand Tanks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

Procedure 5-8: Design of InternalPipe Distributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353Procedure 5-9: Design of Trays.. . . . . . . . . . . . . . . . . . . . . . 366Procedure 5-10: Flow Over Weirs. . . . . . . . . . . . . . . . . . . . 375Procedure 5-11: Design of Demisters . . . . . . . . . . . . . . . . 376Procedure 5-12: Design of Baffles . . . . . . . . . . . . . . . . . . . . 381Procedure 5-13: Design of Impingement Plates. . . . 391References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

297

Procedure 5-1: Design of Internal Support Beds

Process vessels frequently have internal beds thatmust be supported by the vessel shell. Sand filters,packed columns and reactors with catalyst beds are justa few examples of vessels that have internal beds. Thebeds are typically supported by a combination of beams,grids and a support ring welded to the vessel shell. Thesupport ring supports the periphery of the grating or trayplates. The support ring can be welded to the vessel wallby fillet welds or full penetration welds for larger loadedmembers. In some cases they are integrally forged intothe vessel wall.

This procedure can be used to design all the variouscomponents of a support structure consisting of thefollowing;

1. Beams2. Support ring3. Grating4. Beam seats5. Beam support clips and bolting6. Vessel wall

Beam Supports

The beams are typically supported by one of threemethods;

1. Beam seats2. Clips3. Support ring

Beams should never be welded directly to the vesselwall because of the restraint they would impose onvessel growth. All of the methods listed above willallow for the radial expansion of the vessel due totemperature and pressure. Slotted holes in the clip or forthe bolting attaching the beam to a beam seat, allow forexpansion.

Beam seats and clips allow the top flange, or top ofbeam, to be level with the top of the support ring. Thisis a very convenient feature for this type of support. Ineffect, it creates a level surface to support the gratingor tray plates. Conversely, if the beams are supportedby the support ring, then the bottom flange of the beamwill sit on top of the support ring. For most applica-tions this would be unacceptable. In order to make the

top of the bottom flange of the beam to be on the sameplane as the top of the support ring, support blocks areused. Support blocks can be used for solid beams,lattice beams or built up beams. For certain applica-tions, the web of the beam can be extended to createthe support surface in lieu of support blocks, orsupport blocks can be added to each side of the web toreinforce the web locally and provide a larger bearingarea.

Beams

There is really no limit to the number of cross beamsthat may be utilized, however this procedure onlyillustrates the use of up to eight beams. If accessthrough the center of the vessel is a concern, then onlyan even number of beams can be used. A center beamwould impede access. Beams can be solid members,welded I-Beam type, welded T-type, or open, latticetype structures.

One additional support method, not shown here, is the“Hub Ring” or “Ring Beam” approach. Hub rings areideal for many applications. They consist of two parallelrings attached to radial beams. The radial beams in turnare supported by the vessel shell or support rings.The upper ring is a compression ring. The lower ring isa tension member. The rings are naturally stiff membersthat are loaded in their strongest direction, perpendicularto the applied load. In theory they employ all the strengthaspects of the arch, and thus are sometimes referred to as“arcuate beams”. Design of hub rings with radial beamsare not detailed in this procedure. Only the design ofstraight beams are included.

Lattice beams are desirable, if possible, due to theirlight weight. Where internals are stainless steel toprevent or minimize corrosion, they will also reducecost. Unlike solid or built-up beams, the top and bottommembers of a lattice beam have distinct functions. Thebottom chord is the tension only member. The top chordis a compression only member. This is for beams abovethe line of support. For beams below the line of support,the reverse would be true.

In a lattice beam, the top chord is a compressionmember and must be capable of supporting a column axialload without buckling. A T-type compression member is

298 Pressure Vessel Design Manual

sometimes used to provide extra lateral stability in thecompression chord.

Solid and built–up beams must be checked for lateralstability against buckling. In the event this is exceeded, theneither the design must be changed or some anti-bucklingsupports installed. One style of anti-buckling devices is theanti-buckling comb.

Each beam supports the load consisting of one half thedistance between each adjacent beam or the support ring,though this would result in a non-uniform loading.However, one simplifying assumption, which is conser-vative, allows for a rectangular loading for each beambased on the overall length of the beams. This methodneglects the contribution of the support ring, and assumesthe beams support the entire load. While not completelyaccurate, it is much easier to apply.

It is most convenient from a design standpoint to havethe beams equally spaced. However, this is not alwayspossible because of the clearances, accessibility and otherinternals penetration. This procedure gives standard loadsfor uniformly spaced beams, but also describes theprocedure for the design of beams that are not uniformlyspaced.

Whether the beams extend above or below thesupport level is matter of application. Both methodshave their pros and cons. Basically, the method ofsupport is determined by the designer to accommodatethe space inside the vessel as well as the processfunction of the bed or tray that the beams are support-ing. lf the beam extends up into the bed, then a certainamount of media is displaced and removal of media ismore difficult. Conversely, in the case where the beamssupport a tray, then having the beams extend abovethe tray may impose restrictions on flow. Beams forcatalyst support grid (CSG) applications almost alwaysextend up into the bed to minimize the length ofthe vessel.

Loadings

The loading for a bed consists of dead load, liquid loadand live load. The dead load consists of the weight of thesupports and the media it supports, i.e. catalyst, packing,inert balls, sand, clay, etc. The live load consists of thedelta P, differential pressure, developed by the restrictionof the bed to downward flow. Typically there is someamount of fouling that occurs in beds that cause a buildup

of delta P across the bed during operation. The live loadcan easily become the major design load for the supports.

The last load is the weight of product. This could beeither liquid or solid. It could be the liquid on a tray or theliquid hold-up in the bed itself.

The grating is the support members that spanbetween the beams and support the media. The gratingmay be covered with screen to prevent egress of smallparticles. The screen may be installed in a single ormultiple layers of mesh. It can also be covered witha layer of wedge wire screen for the same purpose. Thegrating must be designed to support the total of allloads.

In reactors, the support bed configuration is frequentlyreferred to as a CSG. The CSG consists of beams, gratingand screen.

Procedure

The basic design procedure for the beams is as follows;

1. Estimate the dead loads to be supported to includethe media and weight of support members.

2. Calculate the live load based on the delta Pspecified.

3. Calculate the liquid (or solids) loading in the bed.4. Combine the three load cases to get a total load.5. The total load divided by the cross sectional area is

the uniform design load, p.6. Calculate the area supported by each beam and

multiply this area times the uniform load to get theload supported by each beam.

7. A standard AISC type beam type analysis is thenperformed to size the beam.

Notation

Ar ¼ Area of bolt required, in2

An ¼ Total area supported by beam, in2

Ac ¼ Cross sectional area of vessel, inB ¼ Ratio of actual force to allowable force per inch

on weldCn ¼ Compressive force in beam, LbsDL ¼ Dead load, LbsE ¼ Modulus of elasticity, PSI

Vessel Internals 299

fb ¼ Stress, bending, PSIfC ¼ Stress, compressive, PSIfT ¼ Stress, tension, PSIF ¼ Total load of bed, LbsFb ¼ Allowable bending stress, PSIFbr ¼ Allowable stress, bearing, PSIFC ¼ Allowable stress, compression, PSIFS ¼ Allowable stress, shear, PSIFy ¼ Minimum specified yield strength at design

temperature, PSII ¼ Moment of inertia, in4

K ¼ End connection coefficient per AISCK1 ¼ Vertical distance from bottom of beam flange to

top of fillet on web, inLL ¼ Live load, LbsM ¼ Moment, in-Lbsnb ¼ Number of bolts requiredng ¼ Number of bearing bars per footNb ¼ Minimum bearing length, inN ¼ Number of beamsP ¼ Concentrated load, Lbs

PL ¼ Product load, LbsPc ¼ Free area in packing/catalyst, %p ¼ Uniform load over entire bed, PSIr ¼ Radius of gyration, inR ¼ End reactions, LbsRa ¼ Root area of bolt, in2

S ¼ Allowable stress in shell, tension, PSISU ¼ Minimum specified tensile strength, PSIt ¼ Thickness, in

Tn ¼ Tension force in beam, Lbstw ¼ Thickness of web, in

WC ¼ Weight, contents, (catalyst, packing, etc) LbsWe ¼ Weight of entrained liquid, LbsWg ¼ Weight, grating, LbsWb ¼ Weight, beams, Lbswf ¼ Size of fillet weld, inwn ¼ Uniform load on beam, Lbs/inVc ¼ Volume, catalyst/packing, Ft3

Z ¼ Section modulus, PSId ¼ Deflection, in

DP ¼ Differential pressure loading

BeamRing

ClipBeam seat

r

D

Filter media,packing, catalyst,

etc.

Hold down orballs

Grating, support platevapor distributor,

etc.

Slot clip

Put slot inbeam seat forthermal expansion

Screen

Some applicationsrequire packingin this area

Figure 5-1. Typical support arrangements and details ofan internal bed.



ITEM SYMBOL VALUE ITEM VALUE

Dead load, DLMaterial, beams and grating

Material, vessel shell a. Weight of beams

b. Weight of gratingNQuantity of beams

c. Weight of trayDVessel ID

d. Weight of screenDTDesign temperature

Differential pressure ΔP e. Weight of packing/catalyst

Bed depth dC Product load, PL

Liquid/contents unit weight wc a. Weight of liquid on tray

Corrosion allowance Ca b. Weight of liquid in bed

Specific gravity Sg c. Weight of liquid above bed

d. Weight of solidsLiquid holdup (%)

Free area in bed (%) PC Live load, LL

Packing/catalyst unit weight wP

Volume of packing/catalyst VP Total load, F, Lbs

Packing/catalyst total wt WC F = DL + PL + LL

Weight of entrained liquid We

Weight of grating Wg Total cross sectional area, Ac

Weight of beams Wb Ac = π r2

Miscellaneous

Uniform load, p, PSI

Shell at design temperature p = F / Ac

E

Fy

Beams at design temperature

Fy

Bending = .66 Fy Fb

Compression, dependent on KL/r ratio

FC

Shear = .4 Fy FS

Bearing = .9 Fy Fbr

DATA

MATERIAL PROPERTIES & ALLOWABLE STRESS

DESIGN LOADS FOR BEAMS

LOADINGS

S

E


(6) Beams shown for example only!

L2

A2A1

A3

L1

L3

e3e1e2

a4a3 a2

a1

BEAM

1

BEAM

2

BEAM

3

b1

b2

b3

R



1.0. Design of Support Clip

• Moment in clip, M

M ¼ R e• Thickness required, tr

tr ¼ �6 M

��h2 Fb

�

• Area required per bolt, Ar

Ar ¼ R = Fs nbUse: n ¼ ____________Size: ________________Material: ____________

2.0. Design of Beam Seat

• Thickness required, gusset, tg

Tg ¼ �R�6 e� 2 a

��Fb a

2 Sin2 f�

Table 5-1Beam supports - Summary of forces and moments

Quantity of Beams Beam Ln An Fn Rn Mn wn

1 1 D .3927 D2 .3927 p D2 .1864 p D2 .0565 p D3 .393 p D

2 1 .943 D .2698 D2 .2698 p D2 .1349 p D2 .0343 p D3 .286 p D

3 1 D .2333 D2 .2333 p D2 .1167 p D2 .0311 p D3 .233 p D

2 .866 D .1850 D2 .1850 p D2 .0925 p D2 .0219 p D3 .214 p D

4 1 .98 D .1925 D2 .1925 p D2 .0963 p D2 .0240 p D3 .196 p D

2 .8 D .1405 D2 .1405 p D2 .0703 p D2 .0143 p D3 .176 p D

5 1 D .1655 D2 .1655 p D2 .0828 p D2 .0208 p D3 .166 p D

2 .943 D .1548 D2 .1548 p D2 .0774 p D2 .0185 p D3 .164 p D

3 .745 D .1092 D2 .1092 p D2 .0546 p D2 .0107 p D3 .147 p D

6 1 .99 D .142 D2 .142 p D2 .071 p D2 .0175 p D3 .143 p D

2 .904 D .129 D2 .129 p D2 .0645 p D2 .0146 p D3 .143 p D

3 .7 D .085 D2 .085 p D2 .0425 p D2 .0074 p D3 .121 p D

7 1 D .125 D2 .125 p D2 .0625 p D2 .0156 p D3 .125 p D

2 .968 D .121 D2 .121 p D2 .0605 p D2 .0146 p D3 .125 p D

3 .866 D .108 D2 .108 p D2 .0541 p D2 .0117 p D3 .125 p D

4 .66 D .0722 D2 .0722 p D2 .0360 p D2 .0059 p D3 .109 p D

8 1 .994 D .110 D2 .110 p D2 .055 p D2 .0137 p D3 .111 p D

2 .943 D .105 D2 .105 p D2 .052 p D2 .0123 p D3 .111 p D

3 .832 D .0924 D2 .0924 p D2 .046 p D2 .0096 p D3 .111 p D

4 .629 D .0611 D2 .0611 p D2 .0031 p D2 .00048 p D3 .097 p D

Notes:

1. Table is for uniformly spaced beams only

2. Equations are as follows;

An ¼ Ln en Fn ¼ An p Rn ¼ Fn=2 or wn Ln=2 Mn ¼ wn Ln2=8 wn ¼ Fn=Ln

Figure 5-4. Typical clip support.

Figure 5-5. Typical beam seat support.


• Bearing length, Nb

Nb ¼ �R=

�:75 tW Fy

�� K1

• Ratio B;For E-60 Welds;

B ¼ R=�23040 Wf

�For E-70 Welds;

B ¼ R=�26880 Wf

�For other materials use B ¼ .384 SU

• Required height of gusset, hr

Hr ¼h:5B

�Bþ �

B2 þ 64 e2�1=2�i1=2

3.0. Design of Ring

• Find uniform load, w3, from table

• Find moment in ring, M3

M3 ¼ w3 L

• Thickness required, ring, tr

tr ¼ ð6 M3 =FbÞ1=2Select appropriate ring size.

4.0. Design of Grating

• Determine maximum span of grating, Lg

Lg ¼• Area of loading for a one foot wide panel, Ag

Ag ¼ 12 Lg

• Total load on panel, FgFg ¼ pAg

• Uniform loading on one bearing bar, wg

Wg ¼ Fg=Lg ng

• Bending moment in one bearing bar, M4

M4 ¼ wgLg=8

• Required section modulus of one bearing bar, Zr

Zr ¼ M4=Fb• Actual properties of grating;

Z ¼ �ng b d2

��6

I ¼ �ng b d3Þ=12

d ¼h5 p Lg

�12 Lg

�3i.384 E I

Notes

1. Recommended beam ratio, span over depth shouldbe between 15 and 18, 20 maximum.

2. For loading consider packing, catalyst, grating,weight of beams, liquid above packing or filtermedia, entrained liquid, and differential pressure.The weight of entrained liquid is equal to the volumeof bed � the open area � specific gravity � 62.4.

3. Minimum gusset thickness of beam seat should notbe less than the web thickness of the beam.

4. Main bearing bars of grating should run perpen-dicular to the direction of the support beams.

5. Make width of beam seat at least 40% of height.6. Make fillet weld size no greater than .75 tw.

Qty of Beams W3

1 P D / 4

2 P D / 6

3 P D / 8

4 P D /10

5 P D / 12

6 P D / 14

7 P D / 16

8 P D / 18

Figure 5-6. Loading diagram of a continuous ring.



SUPPORT BLOCK

BEAMS SUPPORTED ON VESSEL RING

SOLID BEAMS LATTICE BEAMS

BUILT UP BEAMSSOLID T-BEAMS

SUPPORT BLOCK

BEAM

BEAM FLANGE

SUPPORT BLOCK

WEB

SUPPORT BLOCKSUPPORT BLOCK


Table 5-2Properties of heavy T-Beams

y2 2"

2"5

x

y1

x

y2 3"

3"

6

y1

x

y24"

4"

7

y1


Procedure 5-2: Design of Lattice Beams



ITEM SYMBOL VALUE ITEM VALUE

Dead load, DLMaterial, beams and grating

Material, vessel shell a. Weight of beams

b. Weight of gratingNQuantity of beams

c. Weight of trayDVessel ID

d. Weight of screenDTDesign temperature

Differential pressure ΔP e. Weight of packing/catalyst

Bed depth dC Product load, PL

Liquid/contents unit weight wc a. Weight of liquid on tray

Corrosion allowance Ca b. Weight of liquid in bed

Specific gravity Sg c. Weight of liquid above bed

d. Weight of solidsLiquid holdup (%)

Free area in bed (%) PC Live load, LL

Packing/catalyst unit weight wP

Volume of packing/catalyst VP Total load, F, Lbs

Packing/catalyst total wt WC F = DL + PL + LL

Weight of entrained liquid We

Weight of grating Wg Total cross sectional area, Ac

Weight of beams Wb Ac = π r2

Miscellaneous

Uniform load, p, PSI

Shell at design temperature p = F / Ac

E

Fy

Beams at design temperature

Fy

Bending = .66 Fy Fb

Compression, dependent on KL/r ratio

FC

Shear = .4 Fy FS

Bearing = .9 Fy Fbr

DATA

MATERIAL PROPERTIES & ALLOWABLE STRESS

DESIGN LOADS FOR LATTICE BEAMS

LOADINGS

S

E


L3

A3

A1A2

L2

L1

e2 e1 e3

(6) Beams shown for example Only!

b3b2

b1

a1

BE

AM

3

BE

AM

2

BE

AM

1

a2a3

a4

R


6.0. Properties of Beam

• Properties of compression chord;

Part A y A y A y2 I

1

2

S

y1 ¼ S A y=S A

y2 ¼ d� y1I ¼ S A y2 þ S I� y1 S Ay

Z ¼ I=y1 or Zr ¼ Mn=Fn

r ¼ ðI=S AÞ1=2

7.0. Diagonals

• All diagonals are in tension• Maximum load in diagonals, fd

Beam Fn fn dn

1

2

3

4

TENSIONCHORD

DIMENSIONS OF LATTICE BEAM

COMPRESSIONCHORDtc

Hn hn

tw

tb

y1

y2

d

• Axial load in diagonal, tension, fn

fn ¼ Fn=2 sin q

If q ¼ 45o, fn ¼ .707 Fn

• Diameter of diagonal, dmin

dmin ¼ ½ð4 fnÞ=ðp FTÞ�1=2

8.0. Beam End Diagonal

• Determine Loads;

Beam Rn Ra Rb

1

2

3

4

Rn ¼ Reaction; Lbs

Ra ¼ Rn sin q

Rb ¼ Rn cos q

• Determine minimum gusset thickness, tg

tg ¼ �6 Rb m

��Fb C

2

Use _______________

SUPPORTBLOCK

DIMENSIONS OF END CONNECTION

Rb

Ra

R

C

m

θ


• Determine properties;

Beam m Z M

1

2

3

4

• Section modulus, Z

Z ¼ �tg C2��6

• Moment, M

M ¼ Rb m

• Stress in end beam diagonal

Beam fa fb FC

1

2

3

4

fa ¼ Ra=tg C � FCfb ¼ M=Z � Fbfa=FC þ fb=Fb � 1

FC is based on L/r; L/r ¼ m/r

r ¼ C=121=2 ¼ :289C

9.0. Stability Check

• The allowable buckling stress for the compressionchord, FCB, is dependent on the K L /r ratio (fromAISC).

K LC / r Type FCB

<50 Short Fy

50 TO 200 Intermediate Interpolate

>200 Long Not Recommended

• For K LC/r ratios between 50 and 200, the followingapply;• If K LC/r < 4.71 (E/Fy)

1/2

Or Fe � .44 FyThen FCB ¼ (.658Fy/Fe) Fy

• If K LC / r > 4.71 (E/Fy)1/2

Or Fe < .44 FyThen FCB ¼ .877 Fe

• Where Fe ¼ (p2 E I) / (K Lc)2

10.0. Ring Analysis

• Uniform load in support ring, wS

wS ¼ R=b2

• Moment, MS

MS ¼ wS b1

• Bending stress, fb

fb ¼ �6 M

��tr2 � Fb

11.0. Notes

1. The allowable compressive stress in the compres-sion chord should be the lesser of FC or FCB.

2. See procedure “Design of Internal Support Beds”for terms and definitions not shown.

3. The compression chord can be made without a T-section, with a bolted on T-section or as a built-upT-beam. This is entirely dependent on rigidity of thevertical member. A bolted on T-section is utilizedwhere the assembly of tray plates or grating isdifficult with the T-section in place.

b1

b2

R

tr

SUPT RING BEAM

SHELL

DIMENSIONS AND LOADS - SUPPORT RING


Procedure 5-3: Shell Stresses due to Loadings at Support Beam Locations

Notation

A ¼ Bearing area, in2

D ¼ Flexural rigidity, Lbs-inE ¼ Modulus of elasticity, PSIFy ¼ Minimum specified yield strength at design

temperature, PSIfbr ¼ Bearing stress, PSIFb ¼ Allowable bending stress in shell, PSIJn ¼ Effective width of shell acting at support point, in

MLn ¼ Longitudinal moment at any point X or Ydistance from point of applied load, in-Lbs

Mrn ¼ Moment in ring due to uniform load, w, in-LbsMn ¼ Longitudinal moment in shell due to axial load,

P, in-Lbs/inNn ¼ Minimum bearing length, inPn ¼ Uniform compressive load, Lbs/inRn ¼ Reaction, Lbstr ¼ Thickness of support ring required, in

wn ¼ Uniform load in ring, Lbs/inX ¼ Distance from applied load in axial (longitu-

dinal) direction, inY ¼ Distance from applied load in circumferential

direction, iny ¼ Circumferential stress factor ratiol ¼ Damping factor

sXM ¼ Longitudinal membrane stress, PSIsfM ¼ Circumferential membrane stress, PSIsXB ¼ Longitudinal bending stress, PSIsfB ¼ Circumferential bending stress, PSI

n ¼ Poisson’s ratio, .3 for steel

Equations

• Angle fn;

sin fn ¼ mn=Ri therefore fn ¼• Angle an;

an ¼ 90� fn

• Minimum bearing length, Nn;

Nn ¼ �Rn sin an

��:75 Fy

�Kn

�< g

• Effective width of shell, Jn;

Jn ¼ ½ðKn=sin anÞ� þ 2 e

• Distance from centerline of shell to point of appliedload, a;

a ¼ :5 tþ e

• Uniform compressive load, Pn, Lbs/in:

Pn ¼ Rn=Jn

• Longitudinal moment in shell due to axial load, P,in-Lbs

Mn ¼ Pn a

• Flexural rigidity, D:

D ¼ �E t3

��12�1� n2

�� ¼ 0:0916 E t3

• Damping factor, l;

l ¼ �3�1� n2

��Rm

2 t2��1=4

l ¼ 1:285ðRm tÞ1=2• Longitudinal moment at any point X distance frompoint of applied load, MLn, in-Lbs/in

MLn ¼ Mn=2�e�lX coslX

�Note: At X ¼ 0 and Y ¼ 0, MLn ¼ Mn /2

• Longitudinal membrane stress, sXM PSI

sXM ¼ � Pn=t

• Circumferential membrane stress, sfM PSI

sfM ¼ �y E

��Rm

• Longitudinal bending stress, sXB, PSI

sXB ¼ � �6 Mn

��t2

• Circumferential bending stress, sfB, PSI

sfB ¼ � �6 n Mn

��t2

sfB ¼ � �1:8 Mn

��t2

sfB ¼ � :3sXB

• Uniform load in ring, wn, Lbs/in

wn ¼ Rn ðcos fn=KnÞ• Moment in ring due to uniform load, w, Mrn, in-Lbs/in

Mrn ¼ wn e

• Thickness of support ring required, tr, in

tr ¼ ½ð6 MrnÞ=Fb�1=2

Use largest value of Mrn

• Bearing area, Ab, in2;

Ab ¼ g Kn

• Bearing stress, fbr, PSI

fbr ¼ Rn=Ab


SUPPORT RING

VESSELSHELL

SUPPORTRING

t

f

e

R

a

Ri =

Rm =

Ro =

BEAM

Shell Stresses due to Loadings at Support Beam Location

Pn

Mn

XRm

BEAM ORSUPPORTBLOCKS

R

Nn

tr

SUPPORT RING

CROSS SECTION OF VESSEL SHELL

e

f

g

J n

w.p.

BEAM

POINT OF APPLICATIONOF LOAD

Kn

e

f gφn

=

=

VESSELSHELL

BEAM #2

BEAM #1

K2

K1

Ri VESSEL INSIDE RADIUS

Y

α2

m2

m1φ1

φ2α1

==

PLAN VIEW OF VESSEL QUADRANT



Procedure 5-4: Design of Support Blocks

Often times, when beams are supported on a supportring, the beam is supported by, or reinforced with a supportblock(s). This procedure shows how to design the supportblocks and attachment welds for the various load cases.There are two types of support blocks used.

Type 1: Support blocks are welded integral with theweb of the beam to expand the bearing area as well asreinforce the web in the area of local load. This type isused primarily with T-Type beams but could also be usedwith a built-up I beam.

Type 2: This type is used with solid beams where the topof the beam is located level with the top of the support ringto create a uniform support plane. The support block, alsocalled a support plate, is welded to the top of the beam andcantilevers beyond the end of the beam to support the load.

Type 1: Support Blocks Welded Integral with Beam

t2

SUPPORT BLOCK

RING

Plan View Beam with Support Blocks

= =

h2

SUPPORTBLOCK

BEAM

b1R

SHEL

L

b2

MT

ω

Type 1-Loads and Dimensions of Support Block

• Moment, MT

MT ¼ :5 R b1

• Section modulus required, Zr

Zr ¼ MT=Fb

• Actual section modulus, Z

Z ¼ �t2 h2

2��6• Height of block required, hr

hr ¼ ½ð6 ZrÞ=t2�1=2

• Maximum force on weld (treated as a line):

• Polar moment of inertia of weld group, Jw

Jw ¼ ðb2 þ h2Þ3=6

• Shear on weld due to twisting moment in horizontaldirection, fth, and vertical direction, ftv

fth ¼ MT C=Jw ¼ ðMT ð0:5 b2ÞÞ=Jwftv ¼ MT C=Jw ¼ MT ð0:5 h2Þ=Jw

• Area of weld group, Aw

Aw ¼ 2b2 þ 2h2

• Vertical shear on weld

fsv ¼ 0:5R=Aw

R2⁄

b2

h2b1

ω

Loads on Welds of Support Blocks


• Resultant shear force on weld, sr

fr ¼�f2th þ ðftv þ fsvÞ2

�1 =

2

• Size of fillet weld required, w

w ¼ fr=ð0:707FsÞ

Type 2: Support Block Welded to Top of Beam

• Moment in support block, M1

M1 ¼ R b1

• Required section modulus, Zr

Zr ¼ M1=Fb

• Actual section modulus, Z

Z ¼ �t2 h2

2��6• Section modulus of weld group, Zw

Zw ¼ b23=3

• Maximum force on weld group, f

f ¼ �R b1

��b23=3

�

• Size of fillet weld required, w

w ¼ f=ð0:707 FsÞNotes

1. An end plate can be welded to the end of the supportblock to stiffen the end of the plate and distribute theload on the ring.

2. See Procedure “Design of Internal Support Beds”for terms and definitions not shown.

b2

b3

h2

h1

t3

t2

t1

b1

R

SUPPORT BLOCK

BEAM

Type 2 - Loads and Dimensions

b3

b3

b1

b1

R

R

ƒ

ƒ

WELD

Loads on Welds


Procedure 5-5: Hub Rings used for Bed Supports

The traditional way of supporting beds inside vesselshas been to use straight beams. An alternative approach tothe conventional straight beam design is to utilizea circular beam, commonly referred to as a “hub ring”,supported by equally spaced radial beams. The radialbeams are like the spokes of a wheel.

While this application may be new, the technology ormethod has been in use for many years. This type ofsupport structure has long been recognized as a veryefficient support structure. Efficiency in this case is theweight of the structure versus the weight supported. Hubrings can support up to 150 times their weight, whilestraight beams are in the range of 100.

The loadings demanded by industry have gone updramatically over the years. As these loadings have goneup, the size of straight support beams has also increaseddramatically. The design of the conventional straightbeams is in some cases approaching physical limitationsdue to manway sizes required to insert or remove thebeams.

As design loadings have increased, the spacing ofbeams has decreased. The height, width and thus weightof beams has increased, as well as the cost. This in turn hasled to increasing the manway size to accommodate deeperbeams while the access between the beams has becomesmaller and smaller. The hub ring can provide an inno-vative solution to this problem.

This type of support structure is ideal for pressurevessels because of the convenience of putting a roundstructure in a round vessel. The hub ring is comprised oftwo circular rings separated by the radial beams. Thenatural couple created by the loadings puts the top ringinto compression and the lower ring in tension. Thesteel works great in tension and the circular beam isequally efficient at resisting the compressive loads. Theadvantage is achieved by utilizing the best properties ofthe material as well as the shape of the section. It ismerely an application of the old adage, “form followsfunction”.

In the hub ring design the radial beams are typicallyone quarter of the vessel diameter in length. Since themoment formula for a simply supported, uniformlyloaded beam is wl2/8, the beams are proportional, not to

the length but to the square of the length. By comparison,straight beams have to span practically the whole diam-eter of the vessel, while radial beams only span ¼ of thediameter.

Another advantage, besides efficiency, weight, andcost, is safety. Not safety in design, but safety duringmaintenance periods. The design of straight beams drivesthe designer to increase the quantity of beams witha corresponding decrease in beam spacing. This reducesthe loads on any individual beam, but in some casesnarrows the passageway between the flanges of thebeams to minimal levels. During plant shutdowns andmaintenance periods, this reduction in access space cancost valuable time and create a hazard for maintenancepersonnel. When you consider the array of workers,ladders, lights, power cords, vacuum lines and loadingsocks that have to pass between these supports, thisrestriction is more than a major inconvenience. Since thehub ring is open in the center it can easily provide largeaccess space.

For vessels larger than about 10 feet in diameter,a cross beam, or multiple cross beams, may be requiredinside the hub ring to support tray decks or gratingpanels. Once again, these cross beams can be spaced suchthat more than adequate space is allowed for personnelaccess.

The ideal proportion for the centerline diameter of thehub rings is Dm ¼ 0.5 D.

The design is based on “N” number of equally spaced,radial loads. The upper ring is in compression. The lowerring is in tension.

The entire assembly can be welded up and inserted inthe vessel prior to installation of the top head or closureseam. Or, the entire thing can be made in pieces to passthrough a manway. When made in pieces, the typicalsplice point is at the radial beams. Thus the quantity ofspokes selected is typically a function of what will fitthrough a given manway size, rather than what loadingsthe components can handle.

Hub rings really have no limitations. They have beendesigned to support loads in excess of 1,000,000 poundsand diameters up to 60 feet, but not simultaneously, ofcourse.



F

LOS

INSIDE RADIUS- VESSEL

UPPER HUB RING(COMPRESSION)

LOWER HUB RING (TENSION)

SUPPORTRING

SPLICEJOINTS

RADIALBEAM

rGENERAL LOADS AND DIMENSIONS

DETAILS OF BOLTED SPLICE CONNECTION

Dm

Rm

d1

Rm

d1

R R

f

f

ff

h

THE SPACING OF BOLTS SHOULD FOLLOW STDBOLTING CONVENTIONS

h

RADIAL BEAM

WASHERSHOULDER BOLTS MAY BE USED TOPROVIDE GREATER SHEAR AREAWHILE REQUIRING LESS ROOMFOR THE NUT


RADIAL BEAM

SUPPORTRING

HUB RING MADE IN (8)SEGMENTS

TYPICAL PLAN VIEW

(8) RADIAL BEAMS SHOWN ARE EXAMPLE ONLY

HUB RING SUPPORT FOR LARGE DIAMETER COLUMN

RADIAL BEAMS ARE LATTICE TYPE

VESSELSHELL

LOS

DM


TOP FLANGE OPTIONAL

WINDOWS FORLIQUID OR VAPORIF REQUIRED

GUSSET OPTIONAL

ENDPLATE

LOS

LOS

LOS

TRAY PLATE

BEAM SUPPORT ON TRAY RING

BEAM ABOVE LOS

BEAM SEAT TYPE

SUPPORTS FOR RADIAL BEAMS

CLIP TYPE - BEAM BELOW LOS CLIP TYPE - BEAM ABOVE LOS

LOS

TRAY PLATE OR GRATING (TYP)


Procedure 5-6: Design of Pipe Coils for Heat Transfer [1-9]

This procedure is specifically for helical pipe coils invessels and tanks. Other designs are shown for illustrativepurposes only. Helical coils are generally used wherelarge areas for rapid heating or cooling are required.Heating coils are generally placed low in the tank; coolingcoils are placed high or uniformly distributed through thevertical height. Here are some advantages of helical pipecoils.

1. Lower cost than a separate outside heat exchanger.2. Higher pressures in coils.3. Fluids circulate at higher velocities.4. Higher heat transfer coefficients.5. Conservation of plot space in contrast with a sepa-

rate heat exchanger.

Manufacture

Helical pipe coils can be manufactured by variousmeans:

1. Rolled as a single coil on pyramid (three-roll) rollingmachine. This method is limited in the pitch that canbe produced. Sizes to 8 inches NPS have beenaccommodated, but 3 inches and less is typical. Thecoil is welded into a single length prior to rolling.

2. Rolled as pieces on a three-roll, pyramid rollingmachine and then assembled with in-place buttwelds. The welds are more difficult, and a trimmingallowance must be left on each end to remove thestraight section.

3. Coils can also be rolled on a steel cylinder that isused as a mandrel. The rolling is done with sometype of turning device or lathe. The coil is weldedinto a single length prior to coiling. The pitch ismarked on the cylinder to act as a guide for thosedoing the forming.

4. The most expensive method is to roll the pipe/tubingon a grooved mandrel. This is utilized for very smallDc-to-d ratios, usually followed by some form ofheat treatment while still on the mandrel. Groovedmandrels create a very high-tolerance product andhelp to prevent flattening to some extent.

Coils are often rolled under hydro pressures as high as85% of yield to prevent excessive ovalling of the pipe ortube. To accomplish this, the hydrotest pump is put on

wheels and pulled along during the rolling process. Endcaps are welded on the pipe to maintain the pressureduring rolling.

Stainless steel coils may require solution annealingafter forming to prevent “springback” and alleviate highresidual stresses. Solution heat treatment can be per-formed in a fixture or with the grooved mandrel to ensuredimensional stability.

Springback is an issue with all coils and is dependenton the type of material and geometry. This springbackallowance is the responsibility of the shop doing the work.Some coils may need to be adjusted to the right diameterby subsequent rolling after the initial forming.

The straight length of pipe is “dogged” to the mandrelprior to the start of the rolling to hold the coil down to themandrel. Occasionally it may be welded rather thandogged.

Applications for grooved mandrel are very expensivedue to the cost of the machining of the mandrel. Mandrelsthat are solution heat treated with the coil are typicallygood for only one or two heat treatments due to the severequench. Thus the cost of the mandrel must be included inthe cost of the coil.

Design

There are two distinct aspects of the design of pipecoils for heat transfer. There is the thermal design andthe physical design. The thermal design falls into threeparts:

1. Determine the proper design basis.2. Calculating the required heat load.3. Computing the required coil area.

Physical design includes the following:

1. Selecting a pipe diameter.2. Computing the length.3. Determine the type of coil.4. Location in the tank or vessel.5. Detailed layout.

To determine the design basis, the following data mustbe determined:

1. Vessel/tank diameter.2. Vessel/tank height.


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Pressure Vessel Design Manual - pvmanage.compvmanage.com/wp...from-Pages-from-PRESSURE-VESSEL-DESIGN-M… · allow for the radial expansion of the vessel due to temperature and pressure