Pressure Vessel Design Manual - PVManagepvmanage.com/.../2019/...PRESSURE-VESSEL-DESIGN-MANUAL-full-v… · 564 Pressure Vessel Design Manual. Design of Kneebrace ... supports. Related

9Related Equipment

Procedure 9-1: Design of Davits . . . . . . . . . . . . . . . . . . . . . 558Procedure 9-2: Design of Circular Platforms .. . . . 563Procedure 9-3: Design of Square and RectangularPlatforms .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571Procedure 9-4: Design of Pipe Supports . . . . . . . . . . . 576Procedure 9-5: Shear Loads in BoltedConnections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

Procedure 9-6: Design of Bins and ElevatedTanks .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586Procedure 9-7: Field-Fabricated Spheres . . . . . . . . . . 594References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630

557

Procedure 9-1: Design of Davits [1,2]

Notation

Cv ¼ vertical impact factor, 1.5–1.8Ch ¼ horizontal impact factor, 0.2–0.5fa ¼ axial stress, psifb ¼ bending stress, psifh ¼ horizontal force, lbfv ¼ vertical force, lbFa ¼ allowable axial stress, psiFb ¼ allowable bending stress, psiFr ¼ radial load, lbFre ¼ equivalent radial load, lbFy ¼ minimum specified yield stress, psiM1 ¼ bending moment in mast at top guide or

support, in.-lbM2 ¼ maximum bending moment in curved davit,

in.-lbM3 ¼ bending moment in boom, in.-lbMx ¼ longitudinal moment, in.-lbMf ¼ circumferential moment, in.-lb

W1 ¼ weight of boom and brace, lbWD ¼ total weight of davit, lbWL ¼ maximum rated capacity, lb

a,b,K ¼ stress coefficientsP ¼ axial load, lbI ¼ moment of inertia, in.4

A ¼ cross-sectional area, in.2

Z ¼ section modulus, in.3

r ¼ least radius of gyration, in.tp ¼ wall thickness of pipe davit, in.a ¼ outside radius of pipe, in.

Moments and Forces in Davit and Vessel

• Loads on davit.

fv ¼ CVWL

fh ¼ ChWL

Figure 9-1. Types of rigging.

558 Pressure Vessel Design Manual

• Bending moment in davit mast, M1.

Type 1 : M1 ¼ 2fvL1 þ 0:5W1L1 þ fhL2

Type 2 : M1 ¼ fvL1 þ 0:5W1L1 þ fhL2

Type 3 : M1 ¼ fvð2L1 þ L5 � L2Þ þ 0:5W1L1 þ fhL2

• Radial force at guide and support, Fr.

Fr ¼ M1

L3

Fr is maximum when davit rotation f is at 0�, forother rotations:

Fr ¼ Fr cos f

• Circumferential moment at guide and support, Mf.

Mf ¼ FrL4

Mf is maximum when davit rotation f is at 90�, forother rotations:

Mf ¼ FrL4 sin f

• Axial load on davit mast, P.

Type 1 or 3 : P ¼ 2fv þWD

Type 2 : P ¼ fv þWD

• Longitudinal moment at support, Mx.

Mx ¼ PL4

Stresses in Davit

Mast PropertiesI ¼A ¼Z ¼r ¼tp ¼a ¼Slenderness ratio:

2:1L2

r¼

Fa ¼Fb ¼ 0:6Fy

Type A Davit

• Axial stressdmast.

fa ¼ PA

• Bending stressdmast.

fb ¼ M1

Z

Figure 9-2. Davit selection guide.

Related Equipment 559

• Combined stressdmast.

faFa

þ fbFb

� 1

• Bending stressdboom.

Type 1: fb ¼ 2fvL5

Z

Type 2 or 3: fb ¼ fvL5

Z

Type B Davit

• Axial stress.

fa ¼ PA

• Bending moment, M2.

M2 ¼ M1ðL2 � RÞL2

• Bending stress.

At M1; fb ¼ M1

Z

At M2; fb ¼ M2aI

�2

3Kffiffiffiffiffiffi3b

p�

• Combined stress.

faFa

þ fbFb

� 1

Finding Equivalent Radial Load, Fre

Figure 9-3. Type A davit. Figure 9-4. Type B davit.

Figure 9-5. Forces in davit guide.

Figure 9-6. Graph of combined stress for various davitrotations.


• Equivalent unit load, w, lb/in.

w ¼ Frcos fB

þ 6Frsin f L4

B2

• Equivalent radial load, Fre, lb.

Fre ¼ wB2

• Calculate Fre for various angles of davit rotation.

Shell Stresses (See Note 1)

At Support: Utilizing the area of loading as illustrated inFigure 9-8, find shell stresses due to loads Mx, Mf, and Frby an appropriate local load procedure.

At Guide: Utilizing the area of loading as illustrated inFigure 9-9, find shell stresses due to loads Mf and Frby an appropriate local load procedure.

Note: Fre may be substituted for Mf and Fr as anequivalent radial load for any rotation of davit otherthan 0� or 90�.

f W Fre

Figure 9-8. Area of loading at davit support.

Figure 9-7. Dimensions of forces at davit support and guide.

Figure 9-9. Area of loading at davit guide.



Notes

1. Figure 9-6 illustrates the change in the totalcombined stress as the davit is rotated between0� and 90�. As can be seen from the graph the stressdue to Mx is constant for any degree of davit rota-tion. This stress occurs only at the support. Thestress due to Fr varies from a maximum at 0� to 0 at90�. The stress due to Mf is 0 at 0� and increases toa maximum at 90�. To find the worst combination ofstress, the equivalent radial load, Fre must be

calculated for various degrees of davit rotation, f.At the guide shell stresses should be checked by anappropriate local load procedure for the maximumequivalent radial load. At the support shell stressesshould be checked for both Fre and Mx. Stressesfrom applicable external loads shall be combined.Remember the force Fre is a combination of loadsFr and Mf at a given davit orientation. Fr and Mf aremaximum values that do not occur simultaneously.

2. Impact factors account for bouncing, jerking, andswinging of loads.

Procedure 9-2: Design of Circular Platforms

Notation

Area ¼�R2 � r2

�pf

360

Arc length; ‘ ¼ pRq180

Angle; q ¼ 180 ‘pR

X ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 � A2

p�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 � A2

p

Y ¼ L�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 � A2

p

f ¼ dead loadþ live load, psffb ¼ bending stress, beam, psifa ¼ axial stress, psi

fx,y,r ¼ bolt loads, lbF ¼ total load on bracket, lbA ¼ load area, ft2

A0 ¼ cross-sectional area of kneebrace, in.2

M1 ¼ moment at shell, ft-lbM2 ¼ moment at bolts, ft-lb or in.-lbC ¼ distance to C.G. of area, ftK ¼ end connection coefficient, use 1.0r0 ¼ radius of gyration, in.P ¼ axial load on kneebrace, lbZ ¼ section modulus of beam, in.3

Table 9-1Values of ladder spacing and for given

diameters

Diameter (ft) a

2 23�

4 17�

6 14�

8 11.5�

10 10�

12 9�

14 8�

16 7�

18 6�

20 5.5�

Note: Values in table are approximate only for

estimating use.

Figure 9-10. Dimensions of a typical circular platform.

AREA OF PLATFORMS

Platform f R r Area


Formulas for Chart

A ¼�R2 � r2

�pq

360F ¼ fA

C ¼ 38:197�R3 � r3

�sin q=2

ðR2 � r2Þq=2l1 ¼ C� rol2 ¼ l1 � d

M1 ¼ l1FM2 ¼ l2F

Figure 9-11. Dimensions, force, and local area for circular platforms.

COMPUTING MOMENTS IN SHELL AND BOLT LOADS

Moments in shell:Type

Clip

Bolt Loads

Platform q R r A F C I1 I2 M1 M2 fx fy fr

Table 9-2Allowable Shear loads in bolts (kips)

Material

Size (in.)

⅝ ¾ ⅞ 1 1L1 =

8

A-307 3.68 5.30 7.21 9.42 11.9

A-325 7.36 10.6 14.4 18.8 23.8Figure 9-12. Bolt load formulas for various platformsupport clips. (See Figure 9-16 for additional data.)


Design of Kneebrace

• Reaction, R1.

XMR2 ¼ l1F� l3R1 ¼ 0 r R1 ¼ l1F

l3

• Shear load on bolts/radial load on shell.

R2 ¼ R3 ¼ R1 tan b

• Bending stress in beam.

fb ¼ jl1 � l3jFZ

• Axial load in kneebrace.

P ¼ R1

cos b

• Axial stress.

fa ¼ PA0

• Slenderness ratio/allowable stress.

Kl4r0

¼ Fa

Figure 9-13. Dimensions, forces, and reactions ofkneebrace support.

Figure 9-14. Typical bolted connections for kneebracesupports.


Figure 9-15. Nomograph to find moment at shell due to platform loads.

566

Pressure

VesselDesignManual

Table 9-3Grating: Allowable live load based on fiber stress of 18,000 psi

Main

Bar

Size

Sec. Mod./ft

width

Weight

lb/sq ft

Bearing Bars at 1 ⅜ Center to CenterdCross Bars at 4 in. Span (ft-in.)

Type* 1-0 1-6 2-0 2-6 3-0 3-6 4-0 4-6 5-0 5-6 6-0

1�¼ 0.380 9.0 U 4562 2029 1142 731 506 372 286 224

C 2283 1522 1142 912 762 653 571 506

1� 5=160.474 11.9 U 5687 2529 1423 910 633 465 355 282

C 2845 1898 1423 1139 947 812 712 633

1¼�¼ 0.594 10.9 U 7126 3169 1782 1141 793 583 446 353 286 236 196

C 3564 2376 1782 1426 1186 1019 892 792 713 648 595

1¼� 5=160.741 14.3 U 8888 3948 2221 1423 986 726 555 438 355 295 246

C 4445 2963 2221 1778 1482 1268 1112 986 889 808 742

1½�¼ 0.856 12.9 U 10265 4564 2567 1641 1142 836 641 506 412 339 286

C 5132 3423 2567 2052 1712 1468 1282 1140 1027 932 856

1½� 5=161.066 16.7 U 12796 5689 3198 2048 1423 1045 798 632 512 422 355

C 6396 4266 3198 2558 2133 1826 1599 1422 1279 1163 1066

1½� 3 =

8 1.276 19.6 U 15312 6806 3829 2451 1702 1251 958 758 613 506 425

C 7654 5105 3829 3063 2553 2188 1914 1702 1532 1393 1276

1¾�¼ 1.164 14.8 U 13963 6206 3492 2233 1553 1140 875 691 559 463 386

C 6981 4656 3492 2792 2326 1996 1745 1552 1396 1270 1165

1¾� 5=161.451 19.1 U 17411 7738 4352 2788 1936 1422 1087 861 696 576 484

C 8708 5805 4352 3483 2903 2488 2176 1935 1742 1583 1452

1¾� 3 =

8 1.737 22.5 U 20842 9262 5210 3336 2315 1702 1302 1029 834 688 579

C 10420 6949 5210 4169 3473 2978 2604 2315 2085 1895 1738

2�¼ 1.520 16.7 U 18242 8107 4562 2918 2026 1489 1141 902 730 604 507

C 9121 6082 4562 3648 3040 2608 2281 2027 1825 1858 1521

2� 5=161.895 21.5 U 22740 10102 5686 3637 2526 1858 1422 1123 910 753 633

C 11371 7581 5686 4547 3791 3248 2842 2529 2275 2067 1895

2� 3 =

8 2.269 25.4 U 27224 12098 6808 4356 3026 2223 1702 1344 1088 900 758

C 13613 9073 6808 5446 4536 3888 3401 3026 2723 2476 2269

* Cdconcentrated

Uduniform


Table 9-4Floor plate: Allowable live load based on fiber stress of 20,000 psi

Long Span

(ft-in.)

Nominal

Thickness (in.)

Short Span (ft-in.)

2-6 3-0 3-6 4-0 4-6 5-0 5-6 6-0

Supports on Four Sides

2-6 ¼ 656

5=161026

3-0 ¼ 514 452

5=16806 708

3-6 ¼ 441 366 328

5=16691 573 515

4-0 ¼ 393 316 274 249

5=16617 496 431 391

4-6 ¼ 366 284 239 210 195

5=16575 446 376 331 307

5-0 ¼ 350 262 215 185 167 156

5=16550 411 338 291 264 246

5-6 ¼ 340 248 198 168 148 135 126

5=16532 391 312 265 234 214 201

6-0 ¼ 330 240 187 154 134 120 111 104

5=16517 377 293 244 213 191 173 166

6-6 ¼ 178 145 124 109 96 93

5=16281 230 197 174 158 140

7-0 ¼ 173 138 116 101 91 83

5=16273 218 184 162 145 135

7-6 ¼ 170 133 111 95 84 76

5=16268 210 175 152 135 122

8-0 ¼ 106 90 79 71

5=16168 143 127 114

8-6 ¼ 102 86 75 67

5=16163 137 120 106

9-0 ¼ 72 63

5=16114 101

Supports on Two Sides

N ¼ 255 174 125 93 71 55

N 5=16402 275 198 148 114 90 72 58



Notes

1. Dead loads: 30psf. Platform steel weight. Thisincludes grating or floor plate, structural framing,supports, toe angle or plate, and handrailing. Tofind weight of steel, multiply area of platforms by30 psf.

2. Live loads:• Operating: Approximately 25–30 psf. Live load issmall because it is assumed there are not a lot ofpeople or equipment on the platform while vesselis operating. Combine effects with shell stress dueto design pressure.

• Maintenance/construction: 50–75 psf. Live loadis large because there could be numerous persons,tools, and equipment on platforms; however, therewould be no internal pressure on vessel.

3. Assume each bracket shares one-half of the areabetween each of the adjoining brackets. Limitbracket spacing to 6 ft-0 in. arc distance and over-hangs to 2 ft-0 in. For stability, bracket spacingshould not exceed 60�.

4. Kneebraces should be 45� wherever possible.Always dimension to bolt holes, not to edge ofbrackets or top of clips.

5. Bracket spacing is governed by one of the followingconditions:• Shell stress: Based on dead-load and live-loadinduced stress from platform support brackets.Shell stresses may be reduced by using a longerclip or reducing the angle between brackets.

• Bolt shear stress: A-307 or A-325 in single ordouble shear. Bolt shear stresses may be reducedby increasing the size or number of bolts orincreasing the distance between bolts.

• Maximum arc distance: Measured at the outsideof the platform. Based on the ability of the toeangle to transmit loads to brackets. Affects“stability” of platform.

• Stress/deflection of floor plate or grating:Allowable live load affects “springiness of plat-forms.” Use Tables 9-3 and 9-4 and assume“allowable live load” of 150–200 psf.

6. Shell stresses should be checked by an appropriate“local load” procedure.


Procedure 9-3: Design of Square and Rectangular Platforms



Long Walkways or Continuous Platform on Horizontal Vessel

Horizontal Platform Splice (Not for Thermal Expansion)

Maximum Length of Unsupported Toe Angle (Based on105-psf Load and L63 3½3 5=16 )

Check of Toe Angle Frame

Check clip spacing:

P ¼ D:Lþ L:L: ¼ psf

w ¼ WP2

lbft

M ¼ wD2

8ft-lbs

s ¼ 12MZ

< 21:6 ksi

Z ¼ Section modulus of toe angle; in3


NotationA ¼ area, sq ftp ¼ unit load, psfP ¼ total load, lbw ¼ unit load on beam, lb/linear footR ¼ reaction, lbM ¼ moment, in.-lbd ¼ deflection, in.K ¼ end connection coefficient, use 1.0r ¼ radius of gyration of column, in.fa ¼ axial stress, psiFa ¼ allowable compressive stress, psi

Calculations

Main or Cross Beam

• Area, A.

A ¼ ð0:5w2 þ w1ÞL

• Load, P.

P ¼ Ap

• Unit load on beam, w.

w ¼ PL

R1 ¼whðaþ ‘Þ2�b2

i2l

M1 ¼ wa2

2

M2 ¼ wb2

2

M3 ¼ R1

�R1

2w� a

�

dend ¼ wa24EI

�‘3 � 6a2‘� 3a3

�

dcenter ¼ w‘2

384EI

�5‘2 � 24a2

�

Notes

1. Maximum distance between cross beams isgoverned by one of two conditions:a. Maximum span of grating or checkered plate.b. Deflection/stress of toe angle. Ability of toe

angle to carry the load.2. Each beam supports the load from one-half the area

between the adjacent beams.


BeamsdMultiple Loads

R2 ¼ l1P1 þ l2P2/þ/lnPnL

R1 ¼ PPn � R2

To find maximum moment:

1. Select maximum reaction.2. Total all downward loads, starting from the reac-

tion, until the value of the reaction is exceeded.This is the point where the maximum moment willoccur.

3. The moments are equal to the right or left of thatpoint. Sum the moments in either direction.

Design of Vessel Clips

• Slenderness ratio.

k‘r

Use k ¼ 1:0:

• F ¼ reaction from main beam columns.• Allowable compressive stress, Fa, based on slen-derness ratio.

• Axial stress, fa.

fa ¼ FA

• Check stress ratio.

faFa

< 0:15

• Radial load in shell, Pr.

Pr ¼ bFR


Procedure 9-4: Design of Pipe Supports

Unbraced Pipe Supports Types of Brackets

Table 9-5Pipe support dimensions

Dimension

Pipe Size

2 in. 3 in. 4 in. 6 in. 8 in. 10 in. 12 in. 14 in. 16 in. 18 in. 20 in. 24 in.

B 2.75 3.5 4.25 6 7.5 9 10.5 11.25 12.75 14 16 18

C 4 5 6.5 9 12 14 16 17 19 21 23 27

DdType 1 7.75 8.75 10.25 12.75 15.75 17.75 19.75 20.75

DdType 2 13.5 16.5 18.5 20.5 21.5 23.5

DdType 3 18 20 22 23 25 27 29 33


Table 9-6Weight of pipe supports, lb (without clips)

L

Dimension

Support

Type

Pipe Size

2 in. 3 in. 4 in. 6 in. 8 in. 10 in. 12 in. 14 in. 16 in. 18 in.

12 in. 1 12 13 15 18 22 25

2 22 27 31 35 37 41 45

3 44 51 57 61 67 72

14 in. 1 15 16 18 21 25 28

2 26 31 35 39 41 45 49

3 52 58 64 68 74 79

16 in. 1 18 19 20 24 28 31

2 30 35 39 43 45 49 51

3 59 65 71 74 81 86

18 in. 1 20 21 23 26 31 34

2 34 39 43 46 49 53 56

3 65 72 77 81 88 93

20 in. 1 23 24 26 29 33 36

2 38 42 46 50 53 57 60

3 72 79 84 88 95 100


Kneebraced Pipe Supports

Dimensions

a ¼ D2þ 3 in:

Y ¼ Cþ 2jþ 1 in:

x ¼ L� 5 in:

q ¼ arc sin

�Y2R

�

y ¼ R Cos q

h ¼ ðRþ 5 in:Þ � y

Q ¼ ðxþ hÞ þ ðq� zÞ

Table 9-7Usual gauges for angles, in.

Table 9-8Kneebraced pipe support dimensions

Allowable

Load (kips)

Bracket

Type “L” Max Angle Size

Bolt Qty &

Size b e d j

12.5 1 36 2 ½� 2�⅜ (2) ¾ 2.5 1.25 2.5 1.92

17.5 1 36 3� 2�⅜ (2) ⅞ 2.75 1.5 3 1.92

24 1 36 3� 2�⅜ (3) ⅞ 2.75 1.5 3 1.92

21.5 1 54 3½� 3�⅜ (2) 1 3 1.75 3.25 1.92

24 2 54 3½� 3�⅜ (2) 1⅛ 3.25 2 4 2.26

26.5 2 54 4� 3�⅜ (2) 1¼ 3.5 2.25 4.5 2.26

30 2 54 4� 3�⅜ (3) 1 3 1.75 3.25 2.26

33.5 2 54 5� 3�⅜ (3) 1⅛ 3.25 2 4 2.26

37.5 2 54 5� 3�⅜ (3) 1¼ 3.5 2.25 4.5 2.26

26.5 3 66 6� 3½�⅜ (2) 1¼ 3.5 2.25 5.25 2.942

37.5 3 66 6� 3½�⅜ (3) 1¼ 3.5 2.25 5.25 2.942

26.5 3 75 6� 4�⅜ (2) 1¼ 3.5 2.25 5.25 2.942

37.5 3 75 6� 4�⅜ (3) 1¼ 3.5 2.25 5.25 2.942

50 3 75 6� 4�⅜ (4)1¼ 3.5 2.25 5.25 2.942


High-Temperature Brackets


Design of Supports

NotationA ¼ cross-sectional area of kneebrace, in.2

F ¼ ½ of the total load on the support, lbRn ¼ reaction, lbP ¼ compression load in kneebrace, lbPr ¼ radial load in shell, lbM1 ¼ moment at shell, in.-lbM2 ¼ moment at line of bolts, in.-lbr ¼ radius of gyration, in.N ¼ number of bolts in clips ¼ shear load, lbsE ¼ modulus of elasticity, psiI ¼ moment of inertia, in.4

Z ¼ section modulus, in.3

K ¼ end connection coefficientd ¼ deflection, in.fa ¼ axial stress, psifb ¼ bending stress, psiFa ¼ allowable axial stress, psiFb ¼ allowable bending stress, psi

Cantilever-Type Brackets

• Dimensions.

sin q ¼ C2R

r q ¼

y ¼ R cos q

L1 ¼ ðR� yÞ þ Lþ 12

pipe dia

E ¼ L1 � ½ðR� yÞ þ e�

• Loads.

M1 ¼ FL1

M2 ¼ FE

• Bracket check.

fb ¼ M1

Z< Fb

d ¼ FL31

3EI

• Bolting check.

fy ¼ FN

fr ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffif2x þ f2y

q

Compare with allowable shear.

• Check shell for longitudinal moment, M2.

Type fx

1 0.167 M2

2 0.1 M2

3 0.067 M2


Design of Kneebraced Supports

Case 1

R1 ¼ R2 ¼ F tan a

P ¼ Fcosa

L2 ¼ L1

cosa

fa ¼ PA< Fa

KL2

rFa

Pr ¼ R1 cos q

s ¼ PN

orR1

N

Case 2

R3 ¼ L3FL4

R1 ¼ R2 ¼ R3 tana

P ¼ R3

cosa

fa ¼ PA< Fa fb ¼ L4 � L3

Z

KL2

rFa

s ¼ PN

orR1

N

Case 3

R3 ¼ L3FL4

R1 ¼ R2 ¼ R3 tana

P ¼ R3

cosa

fa ¼ PA< Fa fb ¼ L3 � L4

Z

KL2

rFa

s ¼ PN

orR1

N


Documents

Pressure Vessel Design Manual - PVManagepvmanage.com/.../2019/...PRESSURE-VESSEL-DESIGN-MANUAL-full-v… · 564 Pressure Vessel Design Manual. Design of Kneebrace ... supports. Related