pressure_vessel_support

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Design of Vessel Supports 167

= longitudinal bending at saddles (tension at top, compression at bottom)

S14= circumferential stress
in stiffener

L S , = longitudinal bending at LL s1=3circumferential compression
midspan in plane of saddle

/-1S5-, = tangential shear-results = circumferential bending at
in diagonal lines in shell horn of saddle

Se = tangential shear in head (A 5 R12)

S l l = additional tension in head (A 5 R12)
Figure 3-43. Stress diagram

1 L12 Id L12 I,
I I 4
a
/
I1 \

I I'

Mz is negative for M2 is positive for

0 Hemi-heads. 0 Flat heads where A/R < 0.707.
0 If any of the below conditions are exceeded. 0 100%-6% F&D heads where A/R < 0.44.
0 2:l S.E. heads where A/R < 0.363.

Figure 3-44. Moment diagram.

168 Pressure Vessel Design Manual

Longitudinal Forces, FL
Case 1: Pier Deflection

sa= s

Case 2: ExpansionIContraction
FLZ= PQO

sa=s

Case 3: Wind
F L=~F ~ L A=iCfGqz

sa= 1.33s

Case 4: Seismic
F L=~F, = ChW,

sa= 1.33s

Case 5: Shippingrrransportation
FL5(See Chapter 7 . )
Sa= 0.9Fy
Case 6: Bundle Pulling
F L=~Fp
Sa= 0.9F,

X = Fixed Saddle X
K = Fixed Saddle
Full load applies to fixed saddle only!

Note: For Cases 5 and 6, assume the vessel is cold and not pressurized.

Design of Vessel Supports 169

Transverse Load: Basis for Equations

Method I

w*= 62FB Therefore the total load, QF, due to force F is

E =E -3EF2B E 3FB
= -E
WU

QF = w ~

e Unit load at edge of base plate, w,,. Method 2

e Derivation of equation for W Z . k

c = -M M=FB Z = - E2 Q
Z 6

Therefore

M 6FB 1 E1

- - 11

-
Z E2

e Equiualent 3tal load Q Z . This method is based on the rationale that the load i
no longer spread over the entire saddle but is shifted o onc
side.

e Combined force, 9 2 .

This assumes that the maximum load at the edge of the Q2 = JFT@
baseplate is uniform across the entire baseplate. This is
very conservative, so the equation is modified as follows: e Angle, 8”.

e Using a triangular loading and 213 rule to dezjelop a 8~ = F
more realistic ‘‘unvormload”
(arctan)-Q
FB 3FB
e Modi$ed saddle angle, el.
FI=---
81 = 2[J - 0 H
(2/3)E - 2E

170 Pressure Vessel Design Manual

Types of Stresses and Allowables e Sg and Slo < 1.5 S and 0.9Fy: circumferential bending at
horn of saddle.
e S I to S:I longitudinal bending.
1. If a wear plate is used, t, may be taken as t,+t, pro-
Tension: S I , S7, or & + o x < SE viding the wear plate extends W10 above the horn of
the saddle. Stresses must also be checked at the top of
Compression: Se, S3, or 5 4 - oe< S, the wear plate.

where S, = factor "B" or S or t,E1/16r 2 . If stresses at the horn of the saddle are excessive:
a. Add a wear plate.
whichever is less. b. Increase contact angle 8.
c. Move saddles toward heads, A < R.
1. Compressive stress is not significant where R,/t < 200 d. Add stiffening rings.
and the vessel is designed for internal pressure only.
e S12 < 0.5Fyor 1.5S: circumferential compressioe stress.
2. When longitudinal bending at midspan is excessive,
move saddles away from heads; however, do not +1. If a wear plate is used, t, may be taken as t, t,, pro-
exceed A 2 0.2 L.
viding the width of the wear plate is at least
3. When longitudinal bending at saddles is excessive,
move saddles toward heads. +b 1 . 5 6 6 .

4. If longitudinal bending is excessive at both saddles and 2 . If the shell is unstiffened the maximum stress occurs at
midspan, add stiffening rings. If stresses are still exces- the horn of the saddle.
sive, increase shell thickness.
3. If the shell is stiffened the maximum hoop compression
e S.5 to S,v< 0.8s: tangential .shear. occurs at the bottom of the shell.

1. Tangential shear is not combined with other stresses. 4. If stresses are excessive add stiffening rings.
2. If a wear plate is used, t, may be taken as t,+t,, pro-
+ +e ( ) S I 3 o@< 1.5 S: circumferential tension stress-shell
viding the wear plate extends W10 above the horn of
the saddle. stiffened.
3. If the shell is unstiffened, the maximum tangential e ( - )S13 - oF< 0.5Fy:circumferential compression stress-
shear stress occurs at the horn of the saddle.
4. If the shell is stiffened, the maximum tangential shear shell stiffened.
occurs at the equator. e ( - )Sll - u, < 0.9FYc: ircumferential compression stres.9 in
5 . When tangential shear stress is excessive, move saddles
toward heads, A s 0 . 5 R, add rings, or increase shell stiffening ring.
thickness.
6. When stiffening rings are used, the shell-to-ring weld Procedure for Locating Saddles
must be designed to be adequate to resist the tangential
shear as follows: Trial 1: Set A=0.2 L and t3= 120" and check stress at the
horn of the saddle, S g or Slo. This stress will govern for
s t = -Q. . lb allowable shear most vessels except for those with large L/R ratios.
<
r r in. circumference in. of weld Trial 2: Increase saddle angle 8 to 150" and recheck stresses
at horn or saddle, S9 or Slo.
e S l 1 +a/,< 1.25 SE: additional .stress in head.
Trial 3: Move saddles near heads ( A = W2) and return 8 to
1. S is a shear stress that is additive to the hoop stress in 120". This will take advantage of stiffness provided by the
the head and occurs whenever the saddles are heads and will also induce additional stresses in the heads.
located close to the heads, A i 0 . 5 R. Due to their Compute stresses Sq, Sg, and S g or Slo. A wear plate may
close proximity the shear of the saddle extends into be used to reduce the stresses at the horn or saddle when
the head. the saddles are near the heads (A < W2) and the wear
plate extends W10 above the horn of the saddle.
2. If stress in the head is excessive, move saddles away
from heads, increase head thickness, or add stiffening Trial 4: Increase the saddle angle to 150" and recheck
rings. stresses Sd, Sg, and S g or Slo. Increase the saddle angle
progressively to a maximum of 168" to reduce stresses.

Trial 5: Move saddles to A =0.2L and t3 = 120" and design
ring stiffeners in the plane of the saddles using the equa-
tions for S13 and S14 (see Note 7).

Design of Vessel Supports 171

Figure 3-45. Chart for selection of saddles for horizontal vessels. Reprinted by permission of the American Welding Society.

~ ~~ ~ Table 3-21
Seismic Factors, C, (For I= 1.O)
Wind and Seismic Forces

Longitudinal forces, FL. Zone cs
Seismic: UBC (see Procedure 3-3)
FL= ChWo 0 0
Wind: A X E 7-95 (Exposure C, Type 111) 1 0.069
2A 0.138
2B 0.184
3 0.275
4 0.367

FL = Af Cf G,qz

where Af 7sD2 Table 3-22
=3
4 Effective Diameter, De

Cf = 0.8

G = 0.85 Diameter (in.) D.

q, = 0.00256KzV21 < 36 1.5D
36-54 1.37D
K, = from Table 3-23 54-78 1.28D
78-1 02 1.2D
I = 1.15 > 102 1.18D

V = basic wind speed, 70-100mph

(see Procedure 3-2)

172 Pressure Vessel Design Manual

Table 3-23 Kz S4 =longitudinal bending at midspan, tension at
Coefficient, K, bottom, compression at top
0.85
Height (ft) 0.9 S5 =tangential shear-shell stiffened in plane of
0.94 saddle
0-1 5 0.98
20 1.04 S6 =tangential shear-shell not stiffened, A > lU2
25 1.09 S7 =tangential shear-shell not stiffened except by
30 1.13
40 heads, A 5 W2
50 S8 =tangential shear in head-shell not stiffened,
60
A5W2
0 Transverseforces, Ft, per saddle. S9 =circumferential bending at horn of saddle-

Seismic: shell not stiffened, L ? 8R
SI0 =circumferential bending at horn of saddle-
Ft = (ChWo)0.5
shell not stiffened, L c 8 R
Wind: SI1=additional tension stress in head, shell not stif-

Ft = (AfCfGdqz)O.5 fened, A 5 lU2
S12 =circumferential compressive stress-stiffened
+A f = De(L 2H)
or not stiffened, saddles attached or not
0 Total saddle reaction forces, Q. S13 =circumferential stress in shell with stiffener in

Q=greater of Q1 or Qz plane of saddle
S14=circumferential stress in ring stiffener
Longitudinal, Q1
Longitudinal Bending

0 S I , longitudinal bending at saddles-without stiffeners,
tension.
Transverse, Qz
[ 1+ +Mi = 6 Q 8AH 6A2 - 3R2 3H2
W, 3FtB 3L+4H

Q2=3-+~ si =(+)-KMlr12t,

Shell Stresses 0 S2, longitudinal bending at saddles-without stiffeners,
compression.
There are 14 main stresses to be considered in the design
of a horizontal vessel on saddle supports: s2 = (-)- M1

S1 =longitudinal bending at saddles without stif- K7r2ts
feners, tension
0 S3, longitudinal bending at saddles-with stifenem.
S2 =longitudinal bending at saddles without stif-
feners, compression 0 S4, longitudinal bending at midspan.

S 3 =longitudinal bending at saddles with stiffeners I+ +M2 = 34 3L2
6R2 - 6H2 - 12AL - 16AH
3L 4H

a, Tangential Shear
Figure 3-46. Saddle reaction forces.
0 S5, tangential shear-shell stifened in the plane of the
saddle.

Design of Vessel Supports 173
Note: If shell is stiffened or A > 0.5R, SI1 =0.

Circumferential Tension/Compression

e S6, tangential shear-shell not stiffened, A > 0.SR. e S12, circumferential compression.

fi.=-[pK]zQ L-2A +s12 = (-1K5Q

rt, L + $ H t,(b 1.56fi)

e S7, tangential shear-shell not stiffened, A 5 0.SR. +Note: t, =t, t, only if wear plate is attached to shell and
+width of wear plate is a minimum of b 1.56fi.
s7 = -K3Q
dS e S13, circumferential stress in shell with stiffener (see
Note 8).
e Sg, tangential shear in head-shell not stiffened, A 5 0.5R.
Note: Add second expression if vessel has an internal
QS8 = -K3 stiffener, subtract if vessel has an external stiffener.

rth e S I 4 , circumferential compressive stress in stiffener (see
Note 8).
Note: If shell is stiffened or A > 0.5R, S8 =0.

Circumferential Bending

e Sg, circumferential bending at horn of saddle-shell not
stiffened ( L2 8R).

+ +Note: t, =t, t, and tf = tt only if A 5 0.5R and

wear plate extends W1O above horn of saddle. Pressure Stresses

Slo, circumferential bending at horn of saddle-shell not
stiffened ( L< 8R).

Q 12K6QR

1 . 5 6 6 )-
+ LtfSlO = (-1 4ts(b

Note: Requirements for t, are same as for Sg.

Additional Tension Stress in Head

e SI1, additional tension stress in head-shell not stifened,
A 5 0.5R.

a h = a+,maximum circumferential stress in head is equal to
hoop stress in shell

174 Pressure Vessel Design Manual

COMBINED STRESSES TENSION I COMPRESSION i
Stress
I Allowable Allowable
SE = S, =
Stress SE =
SE = s, =
s1 +ox - s2 - Ue
S, =
+s3 ox -S3-ue
- s4 - Ue
s4 +ox

Contact K1' K2 K3 K4 K5 K7 K8 Kg Contact K1* K2 K3 0.289 K5 K7 K8 Kg
Angle f3 Angle 0 0.283
~~ ~ ~~ 0.401 0.760 0.603 0.340 0.053 0.518 0.781 0.466 0.278 0.669 0.894 0.298 0.031
120 0.393 0.753 0.618 0.338 0.051 152 0.531 0.763 0.448 0.272 0.665 0.913 0.296 0.030
122 0.335 1.171 0.880 0.385 0.746 0.634 0.336 0.050 154 0.544 0.746 0.430 0.266 0.661 0.933 0.294 0.028
124 0.345 1.139 0.846 0.377 0.739 0.651 0.334 0.048 156 0.557 0.729 0.413 0.261 0.657 0.954 0.292 0.027
126 0.355 1.108 0.813 0.369 0.732 0.669 0.332 0.047 158 0.571 0.713 0.396 0.256 0.654 0.976 0.290 0.026
128 0.366 1.078 0.781 0.362 0.726 0.689 0.330 0.045 160 0.585 0.698 0.380 0.250 0.650 0.994 0.286 0.025
130 0.376 1.050 0.751 0.355 0.720 0.705 0.328 0.043 162 0.599 0.683 0.365 0.245 0.647 1.013 0.282 0.024
132 0.387 1.022 0.722 0.347 0.714 0.722 0.326 0.042 164 0.613 0.668 0.350 0.240 0.643 1.033 0.278 0.024
134 0.398 0.996 0.694 0.340 0.708 0.740 0.324 0.040 166 0.627 0.654 0.336 0.235 0.640 1.054 0.274 0.023
136 0.409 0.971 0.667 0.334 0.702 0.759 0.322 0.039 168 0.642 0.640 0.322 0.230 0.637 1.079 0.270 0.022
138 0.420 0.946 0.641 0.327 0.697 0.780 0.320 0.037 170 0.657 0.627 0.309 0.225 0.635 1.097 0.266 0.021
140 0.432 0.923 0.616 0.320 0.692 0.796 0.316 0.036 172 0.672 0.614 0.296 0.220 0.632 1.116 0.262 0.020
142 0.443 0.900 0.592 0.314 0.687 0.813 0.312 0.035 174 0.0687 0.601 0.283 0.216 0.629 1.137 0.258 0.019
144 0.455 0.879 0.569 0.308 0.682 0.831 0.308 0.034 176 0.702 0.589 0.271 0.627 1.158 0.254 0.018
146 0.467 0.858 0.547 0.301 0.678 0.853 0.304 0.033 178 0.718 0.577 0.260 0.624 1.183 0.250 0.017
148 0.480 0.837 0.526 0.295 0.673 0.876 0.300 0.032 180
150 0.492 0.818 0.505
0.505 0.799 0.485

'K, =3.14if the shell is stiffened by ring or head ( A < Ri2).

Figure 3-47. Coefficients.

Design of Vessel Supports 175

Table 3-24

Coefficients for Zick's Analysis (Angles 80' to 120")

I I I 1 I I I 1 I I 1-85 008851
0 1879 20648 18233 05877 09492 00221 00885 03513 03593

86 0.1914 2.0264 1.7831 0.5808 0.9417 0.0216 0.0873 0.3575 0.3592 0.0873

87 0.1949 1,9891 1.7441 0.5741 0.9344 0.0215 0.0861 0.3637 0.3591 0.0861

88 0.1985 1.9528 1.7061 0.5675 0.9273 0.0212 0.0849 0.3700 0.3590 0.0849

1. These coefficients are derived from Zick's equations.
2.The ASME Code does not recommend the use of saddles with an included angle, 8 , less than 120-. Therefore the values in this table should be used for very

small-diameter vessels or to evaluate existing vessels built prior to this ASME recommendation.

3. Values of & for NR ratios between 0.5 and 1 can be interpolated.

176 Pressure Vessel Design Manual Table 3-25
Slot Dimensions
A
Temperature Distance Between Saddles
G
"F loft 20 ft 30ft 40 ft 50 ft
GlLC_l_c,l
- 50 0 0 0.25 0.25 0.375
L 100 0 0 0.125 0.125 0.250
200 0 0.250 0.375 0.375 0.500
LO 300 0.250 0.375 0.625 0.750
400 0.375 0.625 0.875 1.125 1.oo
Figure 3-48. Saddle dimensions. 500 0.375 0.750 1.125 1.500
600 0.500 1.375 1375 1.375
700 0.625 1.oo 1.625 2.125 1.625
800 0.750 1.625 2.375 2.250
900 0.750 1.125 2.000 2.500 2.625
1.250 3.000
1.375 3.375

L 4Bol+t d1i1a8mine.ter
See
Table

Table 3-26
Typical Saddle Dimensions.

Maximum

Vessel Operating Bolt Approximate

O.D. Weight ABC D EF G H Diameter e WeighVSet

30 16,700 27 24 94 16.5 120" 100

36 15,700 33 27 12 6 18.8 125" 170

42 15,100 38 30 ;: 20.0 123" 200
22.3 127" 230
48 25,330 44 33 ~

54 26,730 48 36 20 22.7 121" 270

60 38,000 54 39 23 25.0 124" 310

66 38,950 60 42 26 27.2 127" 35D
172 27.6 122" 420
ii ; 19050,700 64 45 10 28 0.i75 29.8 124" 710
30.2 121" 810
78 56,500 70 48 11 0.75 31 32.5 123" 880

84 57,525 74 51 12

64,200 80 54 13

96 65,400 86 57 14 39 34.7 125" 940
126" 1,350
102 94,500 92 60 15 Ib42 0.500 37.0 1%

108 85,000 96 63 16 I44 37.3 123" 1,430
125" 1,760
114 164,000 102 66 17 47 0.625 39.6

120 150,000 106 69 18 49 40.0 122" 1,800

132 127,500 118 75 20 55 125" 2,180

144 280,000 128 81 22 60 124" 2,500

156 266,000 140 87 24 66 51.6 126" 2,730

Design of Vessel Supports 177

Notes and the wear plate extends W10 (5.73 deg.) above the
horn of the saddle.
1. Horizontal vessels act as beams with the following 7 . If it is determined that stiffening rings will be required
exceptions : to reduce shell stresses, move saddles away from the
a. Loading conditions vary for full or partially full ves- heads (preferable to A = 0 . 2 L). This will prevent
sels. designing a vessel with a flexible center and rigid
b. Stresses vary according to angle Q and distance "A."
c. Load due to weight is combined with other loads. ends. Stiffening ring sizes may be reduced by using a

2 . Large-diameter, thin-walled vessels are best supported saddle angle of 150".
near the heads, provided the shell can take the load 8. An internal stiffening ring is the most desirable from a
between the saddles. The resulting stresses in the
heads must be checked to ensure the heads are stiff strength standpoint because the maximum stress in the
enough to transfer the load back to the saddles. shell is compressive, which is reduced by internal pres-
sure. An internal ring may not be practical from a pro-
3. Thick-walled vessels are best supported where the cess or corrosion standpoint, however.
longitudinal bending stresses at the saddles are about 9. Friction factors:
equal to the longitudinal bending at midspan.
However, "A" should not exceed 0.2 L. S ufaces Friction
Lubricated steel-to-concrete Factor,
4. Minimum saddle angle Q =EO", except for small ves- Steel-to-steel
sels. For vessels designed for external pressure only 0 Lubrite-to-steel 0.45
should always = 120". The maximum angle is 168" if a 0 Temperature over 500°F 0.4
wear plate is used. 0 Temperature 500°F or less
0 Bearing pressure less than 500psi 0.15
5. Except for large L/R ratios or A > lU2, the governing Teflon-to-Teflon 0.10
stress is circumferential bending at the horn of the 0 Bearing 800psi or more 0.15
saddle. Weld seams should be avoided at the horn of 0 Bearing 300psi or less
the saddle. 0.06
0.1
6. A wear plate may be used to reduce stresses at the horn
of the saddle only if saddles are near heads ( A 5 W2),

PROCEDURE 3-11

DESIGN OF SADDLE SUPPORTS FOR LARGE VESSELS [4, 15-17, 211

Notation Fa = allowable axial stress, psi (see App. L)
N = number of anchor bolts in the futed saddle
A, = cross-sectional area of saddle, in.'
a, =cross-sectional area of bolts in tension, i n 2
Ab =area of base plate, in.2 Y =effective bearing length, in.
A,-= projected area for wind, ft2
A, =pressure area on ribs, in.2 T =tension load in outer bolt, lb
A, =cross-sectional area, rib, in.2 nl = modular ratio, steel to concrete, use 10
Q =maximum load per saddle, lb
F1, =allowable bending stress, psi
+Q i = Q o + Q K , 1b F, =yield stress, psi

4 2 = Qo QL, 1b f,, = saddle splitting force, lb
E, = axial stress, psi
QI,=load per saddle, operating, lb
fb =bending stress, psi
QT=load per saddle, test, lb
f,, = unit force, Ib/in.
QL=vertical load per saddle due to longitudinal loads, lb B, =bearing pressure, psi

QK=vertical load per saddle due to transverse loads, lb M =bending moment, or overturning moment, in.-lb
I =moment of inertia, in.4
FL=maximum longitudinal force due to wind, seismic,
z =section modulus, in.3
pier deflection, etc. (see procedure 3-10 for
r = radius of gyration, in.
detailed description) K I = saddle splitting coefficient

178 Pressure Vessel Design Manual

32

30

28

26

24

22

20

18

16 n-. . . . . . . . - . - .- J
I.
YI VII I I i I I I I I i I 1I 1.75
0.875 1.0 1.125 1.25 1.375 1.5
0 . 6 r 0.75 1.625
Web and Rib Thickness, t, and J, in.

Figure 3-49. Graph for determining web and rib thicknesses.

I

D

I

4A Optional 168‘ saddle-optimum size for large vessels

Figure 3-50. Dimensions ot horizontal vessels and saddles.

Design of Vessel Supports 179

n =number of ribs, including outer ribs, in one saddle Maximum Loads
P =equivalent column load, lb
Vertical.
+d = distance from base to centroid of saddle arc, in. greater of Q1, Qz, or QT

W, =operating weight of vessel contents, lb Q~=Q~+QR
W, =vessel weight full of water, Ib
+QZ =Qo QL
UT =tension stress, psi
w =uniform load, lb 0 Longitudinal.
F L =greater of FL1through FL(,
Forces and Loads (see procedure 3-10 for definitions)

Vertical Load per Saddle Saddle Properties

?rF 0 Preliminary web and rib thicknw.r.es, ttc atid J . Froin
Figure 3-45:
Longitudinal
J = t,
0.5
0 Number of ribs required, II
n = - A+ l
24
Round up to the nearest even number.

0 Minimum width of .snddle at top, GT,in

Transverse where FL and F1, are in kips and ksi or 11) and psi, and J , 11.
A are in in.
Figure 3-51. Saddle loadings. Minimum wear plate diuiensiori,y,
Width:
For loads due to the following causes, use the given
formulas. +H = GT 1 . 5 6 f i
0 Operating weight.
Thickness:
Q = -wo
O2 (H - GT)'
t, =
0 Test weight.
2.43R
0 Longitudinal wind or seismic. 0 Moinent of inertici of saddle, I

0 Transverse wind or seismic.

0 Cross-sectional area of saddle (escliiding ,shell).
A, = A-A1

180 Pressure Vessel Design Manual

to center

in.'

A Y AY A V 1. Note: Circumferential bending at

0 horn is neglected for
Q this calculation.
Figure 3-54. Bending in saddle due to splitting forces.
bh3NO^: iofor mangles I
12 e Saddle splitting force.
Figure 3-52. Cross-sectional properties of saddles.
fi,=K,(Q or QT)
e Tension stress.

~~ ~~

Design of Saddle Parts

Web Note: For tension assume saddle depth "h as W3
maxim u m .
Web is in tension and bending as a result of saddle split-
ting forces. The saddle splitting forces, fl,, are the sum of all e Bending moment.
the horizontal reactions on the saddle.
d=B-- R sine
e Saddle coefficient.
e

+1 cos j3 - 0.5 sin2B 6' is in radians.

+Ki = M = fhd
j7 - j3
sin j3 cos j3

A'ote: j? is in radians. See Table 3-18. e Bending stress.

Ifl, = MC1 < 0.66FY

-E-fh Table 3-27

Varying unit radial Values of kl
pressure
ki 20
Figure 3-53. Saddle splitting forces.
0.204 120"
0.214 126'
0.226 132'
0.237 138"
0.248 144"
0.260 150"
0.271 156
0.278 162'
0.294 168"

Design of Vessel Supports 181

1 fb 1

b --d2

Figure 3-55. Loading diagram of base plate. t /

Base plate with center web Figure3-56. Load diagram and dimensions for base plate with an offset
e Area. web.

Ai, =A F e Unit linear load, j i i .
e Bearing pre,ssure.
fu = -Q lb/linear in.
B - -Q
CL
- AI,
e Ba.se plate thickness. e Distance.7 e l and &.

NOW M =-QF
8

Therefore

Assumes uniform load fixed in center. e Load.9 moment

Base plate analysis for offset web (see Figure 3-56) we;
M=-
e Overall length, L.
6
Web = A - 2dl - 2J
e Bending .stres.y,f;,.
ribs L, = n(G - t,)
6M
E L= L,+ L, fh =

182 Pressure Vessel Design Manual

Anchor Bolts

Anchor bolts are governed by one of the three following
load cases:

1. Longitudinal loud: If Qo> Q L , then no uplift occurs,
and the minimum number and size of anchor bolts
should be used.

If Qo< Q L , then uplift does occur:

QL - Qo = load per bolt ,, x , Pivot Pt. fc
N
I Y ,,
2. Shear: Assume the fixed saddle takes the entire shear
load. 11

-FNL= shear per bolt Figure 3-57. Dimensions and loading for base plate and anchor bolt
analysis.
3. Trunszjerse load: This method of determining uplift
and overturning is determined from Ref. 21 (see +Y3+ K1Y2+ K2Y K3 = O
Figure 3-57).
If not equal to 0, then proceed with Step 3.
M = (0.5F, or F*T)B Step 3: Assume a new value of Y and recalculate the equa-
e=-M
tion in Step 2 until the equation balances out to approxi-
Q" mately 0. Once Y is determined, proceed to Step 4.
Step 4:Calculate the tension force, T, in the outermost bolt
If e < %, then there is no uplift. or bolts.
If e 2 %, then proceed with the following steps. This is an
AY
iterative procedure for finding the tension force, T, in the
outermost bolt.

Step 1: Find the effective bearing length, Y. Start by calcu-
lating factors K1-3

K1 = 3(e - 0.5A) Step 5: From Table 3-28, select an appropriate bolt material
and size corresponding to tension force, T.
+K2 = -6(fn 1at e)
F Step 6: Analyze the bending in the base plate.

Step 2: Substitute values of K1-3 into the following equation +Distance, x = 0.5A f - Y
and assume a value of Y = % A as a first trial.
Moment, M = Tx
6M

Bending stress, fb = -
ti

Table 3-28
Allowable Tension Load on Bolts, Kips, per AlSC

Nom. Bolt 1 1% 1% 1% 1%
Dia., in. 0.7854 0.994 1.227 1.485 1.767

Cross-sectional Area, ab, 0.3068 0.4418 0.6013 24.5 29.7 35.3
in.' 54.0 65.3 77.7
6.1
A-307 Ft=20 ksi 13.5 8.8 12.0 15.7 19.9
19.4 26.5 34.6 43.7
A-325 Ft=44ksi

Ribs Design of Vessel Supports 183
e Bending stress, fh =0.66 Fy.
Outside Ribs
f b = -MIC1
rJ I e Combined stress.

& ,I0.5e or 1h -fa+ - <fh 1

rib spacing Fa Fh

eaA = area of rib and web, in.? Inside Ribs

4 = pressure area, = 0.5Fe t Inside rib

Figure 3-58. Dimensions of outside saddle ribs and webs. 1 eo1 1 L

Outside Ribs 'I rib spacing 1

e Axial load, P. aA, = area of rib and web, in.2

P = B,A, A+ = pressure area, F x e

e Compressiue stress,J,. l2= moment of inertia, 1JG3 C2 = 0.5Gb

f a = AP, 12

e Radius of gyration, r Figure 3-59. Dimensions of inside saddle ribs and webs.

r=g e A d load, P.
P = B,A,
e Slenderness ratio, f21lr.
ll/r = e Compressiue stre.as,fn.
F, = (See App. L.)
f a = AP,
e Unit force, f;,
e Radius of gyration, r.
FI,
f,, = e Slenderness ratio, &/r.
e Bending moment, M .
M = 0.5f,,ell Czlr =

Fa =

e Unit force,f;,.

f - -2FAL
-

184 Pressure Vessel Design Manual

e Bending moment, M . minimum depth from the bottom of the wear plate
to the top of the base plate.
M = f,&e 2 . The full length of the web may be assumed effective
in carrying compressive stresses along with ribs. Ribs
e Bending stress, fb. are not effective at carrying compressive load if they
are spaced greater than 25 times the web thickness
f b = -MC2 apart.
3. Concrete compressive stresses are usually considered
I to be uniform. This assumes the saddle is rigid enough
to distribute the load uniformly.
e Combined stress. 4. Large-diameter horizontal vessels are best supported
with 168" saddles. Larger saddle angles do not effec-
-f +a - < If h tively contribute to lower shell stresses and are more
Fa Fb difficult to fabricate. The wear plate need not extend
beyond center lines of vessel in any case or 6" beyond
Notes saddles.
5. Assume fixed saddle takes all of the longitudinal
1. The depth of web is important in developing stiffness loading.
to prevent bending about the cross-sectional axis of
the saddle. For larger vessels, assume 6 in. as the

PROCEDURE 3-12

DESIGN OF BASE PLATES FOR LEGS [ZO, 211

Notation A, =total cross-sectional area of bolts in tension, in.2
(Y =coefficient
Y =effective bearing length, in. T, =shear stress
M =overturning moment, in.-lb
Calculations
M h =bending moment, in.-lb
e Axiul loading only, no moment.
€'=axial load, lb Angle legs:

ft =tension stress in anchor bolt, psi f P

A =actual area of base plate, --
A, =area required, base plate, in.2 - BD
f; =ultimate 28-day strength, psi
f, =bearing pressure, psi L = greater of m, n, or n'
fl =equivalent bearing pressure, psi
Fb=allowable bending stress, psi -
Ft =allowable tension stress, psi
F, =allowable compression stress, psi Beam legs:
E, = modulus of elasticity, steel, psi P
E, = modulus of elasticity, concrete, psi
n = modular ratio, steel-concrete A -A -0.7fL
n' =equivalent cantilever dimension of base plate, in.
B, = allowable bearing pressure, psi - 0.95d
K1,2,3=factor m=

T=tension force in outermost bolt, lb 2
C =compressive load in concrete, lb

V =base shear, Ib
N =total number of anchor bolts
N t =number of anchor bolts in tension
Ab =cross-sectional area of one bolt, in.2

Design of Vessel Supports 185

n = B - 0.8d
2

b - t,

CY=

2(d - 2tf)

Assumed
load area

BEAM or from Table 3-29
Pipe legs:

B - 0.707W
m=

2

ANGLE 0 Axid loud plus bending, load condition #I, full compres-

For pipe legs; sion, up/$, e 5 D/6.
Eccentricity:
m = D - 0.707 W e = -M < -D

2 P-6
assume B = D Loadings:

PIPE 16e(D - 2a)

Figure 3-60. Dimensions and loadings of base plates. fl = PA [ l + D2
Moment:

Thickness:

0 Axial load plus bending, loud condition #2, partial corn-
pre,rsion, up&, e > D/6.
Eccentricity:
e = -M- > -D

P6

186 Pressure Vessel Design Manual Load Condition #2

Load Condition #1

I- =I- X

Full compression, no uplift, e 2 D/6 Partial compression, uplift, e > D/6

Figure 3-61. Load conditions on base plates.

Table 3-29 Table 3-30
Values of n’ for Beams Average Properties of Concrete

Column Section n’ Column Section n’ Ult f; Allowable
-
W14~73O-Wl4~145 5.77 W10 x 45 -W10 x 33 Water 28-Day Compression, Allowable Coefficient,
W14 x 132 -W14 x 90 5.64 3.42
w 1 4 x 8 2 - w 1 4 61 4.43 wax 6 7 - w a X 31 3.14 ContenUBag Str (psi) F, (psi) B, (Psi) n
W 1 4 ~ 5 3 -W 1 4 ~ 4 3 3.68 wa X 2a -wa X 24 2.77
W12~336-Wl2~65 4.77 2.38 7.5 2000 aoo 500 15
~ 1 2 x 5 8 -~ 1 2 x 5 3 4.27 W6 x 25 - W6 x 15 1.77
W12 x 5 0 - W12 x 40 3.61 W6 x 16 -W6 x 9 1.91 6.75 2500 1000 625 12
W10 x 112 - W10 x 49 3.92 W5 x 19 - W5 x 16 1.53
W4 x 13 6 3000 1200 750 10

5 3750 1400 938 a

Reprintedby permissionof John Wiley & Sons, Inc.

Coefficient: By successive approximations, determine distance Y.
E Substitute K1-3 into the following equation and assume
an initial value of Y = A as a first trial.
n = 2 (see Table 3-30)
E, Tension force:

Dimension: ‘1_D - _Y-
f = 0.5d+z
By trial and error, determine Y, effective bearing length, $T = ( - ) P [ b ---+f
utilizing factors K1-3.
Factors: 23
Bearing pressure:
)+:K I = 3(e
f:,f, = Y+B -=z

Design of Vessel Supports 187

t E - t iwv

B -1 B
I

Figure 3-62. Dimensionsfor base plates-beams.

Dimensions for Type 1+2) Bolt Base Plate Dimensions for Type 2-(4) Bolt Base Plate

Column Min Plate Max Column D, 6 , G, E, W, Min Plate Max Bolt
Size Size
D, in. 6 , in. E, in. W, in. Thk, in. Bolt 4, in. in. in. in. in. in. Thk, in. 4, in.
w4
w4 8 8 4 % % % W6 10 10 7 7 2 %1
% 74 W8 %1
W6 8 8 4 % % 74 W10-33thru45 12 12 9 9 5/16
74 W10-49thru112 74 1
W8 10 10 6 '/4 1 W12-40thru50 15 15 11 11 %
74 W12-53thru58 17 15 13 11 YE 78 174
W10-33thru45 12 12 6 1 W12-65thru152
% 17 17 13 13 % 174
W10-49thru 112 13 13 6 5/16 % 1 19 15 15 11
% 1 1 1Y2
W 1 2 - 4 0 t h ~50 14 10 6 5/16 19 17 15 13 YE
1% 19 19 15 15 % 1 1%
W12-53thru58 14 12 6 1 1Y2

W12-65 thru 152 15 15 8 5/16

;w

Angle Legs Pipe Legs

Figure 3-63. Dimensionsfor base plates-angle/pipe.

188 Pressure Vessel Design Manual Dimensions for Pipe Legs
Dimensions for Angle Legs
~~

Lea Size D X m Min. Plate Leg Size D E m Min. Plate
Thk -~ Thk
L2 in. x 2 in. 4 in. 1.5 1 ~~ 4% in. 2.5 in.
L2% in. x 2% in. 5 in. 1.5 1.25 % in. 5% in. 2.7 in. % in.
L3 in. x 3 in. 6 in. 1.75 1.5 % in. 3in. NPS 7% in. 2.7 in. % in.
L4 in. x 4 in. 8 in. 2 2 % in. 7 in. 2.7 in.
L5 in. x 5 in. 9 in. 2.75 2 4in. NPS 8% in. 8% in. 3.2 in. % in.
L6 in. x 6 in. 10 in. 3.5 2 % in. 10 in. 3.5 in. ?, in.
6in. NPS 10 in. 12 in. '/8 in.
Y8 in.
8in. NPS 11% in. 1 in.
% in.
loin. NPS 14 in.

12in. NPS 16 in.

Moment: I where M is greater of MTor M,.

+x = 0.5D f - Y 0 Anchor bolts.

Mt = TX Without uplift: design anchor bolts for shear only.

fl ),(cf= Y - a Ts =&V

Thickness: With uplift: design anchor bolts for full shear and tension
force, T.

PROCEDURE 3-13

DESIGN OF LUG SUPPORTS

Notation w =uniform load on base plate, lbhn.
I =moment of inertia of compression plate, in.4
~~ ~ ~~ E,=modulus of elasticity of vessel shell at design

Q =vertical load per lug, lb temperature, psi
Qa =axial load on gusset, Ib
Q b =bending load on gusset, lb E, = modulus of elasticity of compression plate at design

n = number of gussets per lug temperature, psi
F, = allowable axial stress, psi e =log base 2.71
F1, =allowable bending stress, psi M h =bending moment, in.-lb
f, =axial stress, psi M, = internal bending moment in compression plate,

fb =bending stress, psi in.-lb
A = cross-sectional area of assumed column, i n 2
K = spring constant or foundation modulus
Z =section modulus, in.3
=damping factor

4 = Bolt hole diameter Design of Vessel Supports 189
Single gusset P

Double gusset

--ifb Q, = Q sin 0
Q b = Q COS ti
Base plate
c = - b sin 0
2

m=- h
sin 0

L

Figure 3-64. Dimensions and forces on a lug support.

Design of Gussets Fb = 0.6Fy
6
Assume gusset thickness from Table 3-31.

Qd = Q sin 8

Q, = Q case
c = -b sin8

2
A = t,C
F, = Q.4Fy

190 Pressure Vessel Design Manual eBending
*
Design of Base Plate 9Bearing
Iblin
Single Gusset
e Bending. Assume to be a simply supported beam. Figure 3-66.Loading diagram of base plate with two gussets.

e Bearing.

w = -Q

a1
Wd'

Mb =-
2

e Thickness required base plate.

e Bearing.

where Mk, is greater moment from bending or bearing.

e Thickness required base plate.

(b - 4)Fb

Bearing - 4w -Ib/in where Mb is greater moment from bending or bearing.

Compression Plate

Single Gusset

I'

Figure 3-65.Loading diagram of base plate with one gusset.

Double Gusset \R

e Bending. Assume to be between simply supported and Figure 3-67.Loading diagram of compression plate with one gusset.
fixed.

Design of Vessel Supports 191

Assume thickness t, and calculate I and Z: f = -Qe
I=--.tcy3 2h

12 K = - E,,t
H2
2
I = -tc-y3
Z=t'Y 12

6

Mx = qf p+ 4E,I

fb = -Mx < 0.6FY f
Z
-[l
Note: These calculations are based on a beam on elastic +M - (e-Bx(cosBx - sin Bx))]
foundation methods. -48

Double Gusset Bx is in radians. See Procedure 5-2.

f b = -Mx < 0.6FY

Z

AR

Figure 3-68. Loading diagram of compression plate with two gussets.

Table 3-31

Standard Lug Dimensions

Type e b Y X h t, = tb Capacity (b)

1 462 66 % 23,500

2 462 69 7/16 45,000

3 462 6 12 Yi 45,000

4 5 7 2.5 7 15 9/16 70,000

5 5 7 2.5 7 18 % 70,000

6 5 7 2.5 7 21 I1 70,000
46
a 24 %
7 683 100,000

192 Pressure Vessel Design Manual

PROCEDURE 3-14

DESIGN OF BASE DETAILS FOR VERTICAL VESSELS #1
[5, 10, 14, 18, 191

Notation 6 =vessel deflection, in. (see Procedure 4-4)
M, =bending moment per unit length in.-lb/in.
Ab = required area of anchor bolts,
Bd =anchor bolt diameter, in. N =number of anchor bolts
B, =allowable bearing pressure, psi (see n = ratio of modulus of elasticity of steel to con-

Table 3-35) crete (see Table 3-35)
b, =bearing stress, psi P = maximum anchor bolt force, Ib
C = compressive load on concrete, lb PI =maximum axial force in gusset, lb
d = diameter of bolt circle, in. E =joint efficiency of skirt-head attachment
db =hameter of hole in base plate of compres-
weld
sion plate or ring, in. R,=root area of anchor bolt, i n 2 (see
FLT=longitudinal tension load, lb/in.
F L C =longitudinal compression load, lb/in. Table 3-32)
r = radius of bolt circle, in.
F b =allowable bending stress, psi Wb =weight of vessel at base, lb
F, =allowable compressive stress, concrete, psi W, =weight of vessel at tangent line, lb
w =width of base plate, in.
(see Table 3-35) Z1 =section modulus of skirt, in.3
F, =allowable tension stress, anchor bolts, psi S, =allowable stress (tension) of skirt, psi
S, = allowable stress (compression)of skirt, psi
(see Table 3-33) G =width of unreinforced opening in skirt, in.
F, =minimum specified yield strength, psi C,,CT,J,Z,K =coefficients (see Table 3-38)
fb =bending stress, psi y1,yz =coefficients for moment calculation in com-
f, =compressive stress, concrete, psi
f, =equivalent tension stress in anchor bolts, pression ring
S =code allowable stress, tension, psi
psi E l = modulus of elasticity, psi
Mb =overturning moment at base, in.-lb t, =equivalent thickness of steel shell which
M, =overturning moment at tangent line, in.-lb
M, =unit bending moment in base plate, represents the anchor bolts in tension, in.
T =tensile load in steel, lb
circumferential, in.-lb/in. u =Poisson’s ratio, 0.3 for steel
My =unit bending moment in base plate, radial, B = code allowable longitudinal compressive

in.-1b/in . stress, psi

H =overall vessel height, ft

Lap welded Butt welded Pedestal Design of Vessel Supports 193

Conical

m

T Small-diameter
E = 0.7 vessels only

E = 0.5 Figure 3-69. Skirt types. Shear ring or
slip band
Type 1: Without gussets Type 2: With gussets
-hh 2 in.
Type 3: Chairs h.= 2 in.
c,= 1‘h in. cmn e 1 % in.

b

lbylType4:Topring Bond+ 1in.

Bolt 6 + %in. &Washer
Boll + 1 in.
7
Ship loose
and attach
in field

bolt 0 + 1 in 5 in. minimum

Figure 3-70. Base details of various types of skirt-supported vessels.

194 Pressure Vessel Design Manual

Table 3-32 Table 3-35

Bolt Chair Data Average Properties of Concrete

Y4-1 o 5.50 0.302 2 3.50 1.5 Water Ult Allowable Allowable Coefficient,
5.50 0.419 2 3.50 1.5 ContenVBag 28-Day Compression, Fc B, (Psi) n
7/8-9 5.50 0.551 2 3.50 1.5
1-8 5.50 0.693 2 3.50 1.5 Str (Psi)
5.50 0.890 2 3.50 1.5 (psi)
1Ye-7 5.50 1.054 2.13 3.50 1.75
11/4-7 5.75 1.294 2.25 3.50 7.5 2000 800 500 15
5.75 1.515 2.38 4.00 2 6.75 2500 1000 625 12
17*+ 6.00 1.744 2.5 4.00 2 6 3000 1200 750 10
6.25 2.049 2.63 4.00 2.25 5 3750 1400 938 8
1Y2-6 6.50 2.300 2.75 4.00 2.5
15/8-5'/2 7.00 3.020 3 4.50 2.5 Reprinted by permission of John Wiley & Sons, Inc.
7.25 3.715 3.25 4.50 2.75
174-5 7.50 4.618 3.50 4.75 3 Table 3-36
1%-5 8.00 5.621 3.75 5.00 3.25
3.50 Bending Moment Unit Length
24%

2'/,4'/2
2Y2-4

~7~4-4

34

~ ~___________

Table 3-33 0 0 -o.5fce2
0.333 0.0078fcb2 -o.428fce2
Number of Anchor Bolts, N 0.5 0.0293fcb2 -0.31 9fct2
0.667 0.0558fcb2 -o.227fce2
Skirt Diameter (in.) Minimum Maximum 0.0972fcb2 -0.1 19fC@
1.o 0.123fcb2 -0.1 24fce2
24-36 4 4 0.131fcb2 -0.1 25fce2
42-54 4 8 1.5 0.133fcb2 -o.125fce2
6C-78 8 12 2.0 0.133fcb2 -o.i25fcez
84-1 02 12 16 3.0
108-1 26 16 20
132-1 44 20 24 cy,

Reprinted by permission of John Wiiey & Sons, Inc.

Table 3-34 Table 3-37

Allowable Stress for Bolts, F, Constant for Moment Calculation, y1 and y2

Spec Diameter Allowable Stress ble Y1 Y2
(in.) (KSO
A-307 1.o 0.565 0.135
A-36 All 20.0 0.115
A-325 All 19.0 1.2 0.350 0.085
A-449 c1-1/2" 44.0 1.4 0.211 0.057
c1" 39.6 1.6 0.125 0.037
1-1/8 to 1-112" 34.7 1.8 0.073 0.023
1-5/8 to 3 ' 29.7 2.0 0.042
cy, 0 0

Reprinted by permission of John Wiley & Sons, Inc.

Table 3-38

Values of Constants as a Function of K

K CC ct J z K cc ct J z

0.1 0.852 2.887 0.766 0.480 0.55 2.113 1.884 0.785 0.381
0.15 1.049 2.772 0.771 0.469 0.6 2.224 1.765 0.784 0.369
0.2 1.218 2.661 0.776 0.459 0.65 2.333 1.640 0.783 0.357
0.25 1.370 2.551 0.779 0.448 0.7 2.442 1.510 0.781 0.344
0.3 1.510 2.442 0.781 0.438 0.75 2.551 1.370 0.779 0.331
0.35 1.640 2.333 0.783 0.427 0.8 2.661 1.218 0.776 0.316
0.4 1.765 2.224 0.784 0.416 0.85 2.772 1.049 0.771 0.302
0.45 1.884 2.113 0.785 0.404 0.9 2.887 0.852 0.766 0.286
0.5 2.000 2.000 0.785 0.393 0.95 3.008 0.600 0.760 0.270

Reprinted by permission of John Wiley & Sons, Inc.

ANCHOR BOLTS: EQUIVALENT AREA METHOD Design of Vessel Supports 195
1. Cakulrte rellmlna K valuo budon a l h b k r .
2. Make p r d k l n r r y &tion of anchor bdtr and width of baw

d.tr

3. &k&e h d S and w-.
4. Cakukto K baaed on actual *oases and compare wlth valuo

EGod In Stop 2.

5. encr excoeds .01, aoloct a new K batweon bothvahm and
rOPO.1 S t v 2-6. (W Note 6.)

1 - TRIAL 1 I TRIAL 2

I1 Data

wb I I 12 Approxlmate K UJng Alkwabba

2 Approximate K Udng Alkrrrbba Coefflclents I

IK-- 1 cc 3 Tendk Load In Steel
Ct
I 1 +I?. 4 Number of Anchor B o b Required
nFc J in.2
2 bolts
Jd
I 5 Stress In Equlvaknt Steal Band
4 Number of Anchor Bohr Rwulrsd
R, (Table3-33) 6 Compre8dvo Load In Concrete
%-- Td
F.G Use( ) I

%IN I 7 Strem In Concrete

I I

8 Cunprowtve Lo8d In Concrete
I
C=T+Wb

7 Stroaa In Comrete

8 Fiecheck K UJng Actual f.8nd 1,
K-- 1

1+L

See example of completed form on nexl page.

196 Pressure Vessel Design Manual

ANCHOR BOLTS: EQUIVALENT AREA METHOD EXAMPLE

PROCEDURE
1. Calculate reihinar K value bsmd on aikwabks.
2. Make p r e l h f w y w L k n of anchor bolts and width of bsse
3. %%ate loads and stresses.
4. Calculate K based on actucrl stresses and compare with vrlue

iT~enceed In Step 2.

5. ex- .o1, wlsct a new K between both valuer and
repeat Steps 2-8. (See Note 6.)

TRIAL 1 I TRIAL 2

I I12 Approxinuto K Udng A l k w a M r

I p c = Mi64 I

I I
I3 Tmdb Load in Steel
I Tendk Load In Steal
33b.7
. - . -.
4 Number of Anchor Bdtr Required
r--

I Numkr of Anchor Bolts Raaulrod

bIfcf Designof Vessel Supports 197
x .E

M Maximum
bearing load

fc P1
Figure 3-71. Loading diagram of base plate with gussets and chairs.

Type 1: Without Chairs or Gussets

K =from “Anchor Bolts.”

e=

f, =from “Anchor Bolts.”
d=

e Bending moment per unit length.

M, = 0.5f,12

e Maximum bearing load. Figure 3-72. Dimensions of various base plate configurations.

+ )b, e With twice as many gussets as anchor bolts.
= f c ( 2Kd w iB, (see Table 3-35) b =-nd
2Kd 2N

e Thickness required. -c

b

M, =greater of M, or My from Table 3-36

Type 2: With Gussets Equally Spaced, Straddling
Anchor Bolts

e With same number as anchor bolts Type 3 or 4: With Anchor Chairs or Full Ring

b = -nd e Between gussets.
N
P = F,R,
-c Pb

b M”=8

M,=greater of M, or M yfrom Table 3-36

/6M,

tb = \ig

198 Pressure Vessel Design Manual

0 Between chairs

M, =greater of M, or M yfrom Table 3-36

Top Plate or Ring (Type 3 or 4) Figure 3-73.Top plate dimensions and loadings.

e Minimum required height of unchor chair (Type 3 or 4 ) . Washers

hlllin= 7.296d < 18in. X
H
0 Minimum required thickness of top plate of unchor chair.

Top plate is assumed as a beam, e x A with partially ftved Figure 3-74.Compression plate dimensions.
ends and a portion of the total anchor bolt force P/3,
distributed along part of the span. (See Figure 3-73.) 0 Minimum required thickness of top ring (Type 4).
0 Bending moment, M,, in top ring (Type 4).

-be

y1= (see Table 3-37)
y2 = (see Table 3-37)
1. If a = t / 2 and b/e > 1, My governs

Gussets

+pM, = 4n [(1+ u)log@ (1 - n)] e Type 2. Assume each gusset shares load with each adjoin-
ing gusset. The uniform load on the base is fc, and the area
2 . If a # U 2 but b/e > 1, My governs supported by each gusset is x b. Therefore the load on
the gusset is
3. If b/e < 1. invert b/e and rotate axis X-X and Y-Y 90"
PI=f,Cb
4n
Thickness required is
r D1
Pi(6a - 2e)

tg = Fhe2

e Type 3 or 4 .

'P 3 > - in.
t --
- 18,000e 8

Skirt Design of Vessel Supports 199

0 Thickness required in skirt at compression plate or ring Skirt thickness required:
due to muximum bolt load reaction.
For Type 3: f b fl,

- 1.0 4,640,000

whichever is greater
Determine allowable longitudinal stresses.
Tension
St =lesser of 0.6F, or 1.33s
Compression

For Type 4: S, = 0.333 F,
= 1.33x factor “B”
Consider the top compression ring as a uniform ring with
N number of equally spaced loads of magnitude. --tskEl
16 R
-Pa
h = 1.33s
whichever is less.
See Procedure 5-1 for details. Longitudinal forces
The moment of inertia of the ring may include a portion of
the skirt equal to 16t,k on either side of the ring (see Skirt thickness required
Figure 3-75).
whichever is greater.
0 Thickness required at opening of skirt. 0 Thickness required at skirt-head attachment due to Mt.
Note: If skirt is stiffened locally at the opening to compen-
sate for lost moment of inertia of skirt cross section, this Longitudinal forces
portion may be disregarded.
G = width of opening, in.

1 48Mh

]+f b = n D - 3 G [ o Wh

Actual weights and moments at the elevation of the open-
ing may be substituted in the foregoing equation if
desired.

-Pa P[a,,
h
Skirt thickness required
I 1I-Pa h /
h FLT F L C
tsk = 0.707 StE or 0.707SCE
Figure 3-75. Dimensions and loadings on skirt due to load P.
whichever is greater.

200 Pressure Vessel Design Manual 6. The value of K represents the location of the neutral
axis between the anchor bolts in tension and the con-
Notes crete in compression. A preliminary value of K is esti-
mated based on a ratio of the “allowable” stresses of the
~~
anchor bolts and concrete. From this preliminary value,
1. Base plate thickness: anchor bolt sizes and numbers are determined and
actual stresses computed. Using these actual stresses,
0 If t 5 & in., use Type 1. the location of the neutral axis is found and thus an
actual corresponding K value. A comparison of these
30 If in. < t 5 in., use Type 2. K values tells the designer whether the location of the
30 If t > in., use Type 3 or 4.
neutral axis he assumed for selection of anchor bolts
2 . To reduce sizes of anchor bolts:
was accurate. In successive trials, vary the anchor bolt
0 Increase number of anchor bolts. sizes and quantity and width of base plate to obtain an
0 Use higher-strength bolts. optimum design. At each trial a new K is estimated and
0 Increase width of base plate.
calculations repeated until the estimated K and actual
3. Number of anchor bolts should always be a multiple of K are approximately equal. This indicates both a
4. If more anchor bolts are required than spacing
allows, the skirt may be angled to provide a larger balanced design and accurate calculations.
bolt circle or bolts may be used inside and outside of 7 . The maximum compressive stress between base plate
the skirt. Arc spacing should be kept to a minimum if
possible. and the concrete occurs at the outer periphery of the
base plate.
4. The base plate is not made thinner by the addition of a 8. For heavy-wall vessels, it is advantageous to have the
center lines of the skirt and shell coincide if possible.
compression ring. th would be the same as required for For average applications, the O.D. of the vessel and
chair-type design. Use a compression ring to reduce O.D. of the skirt should be the same.
induced stresses in the skirt or for ease of fabrication 9. Skirt thickness should be a minimum of R/200.
when chairs become too close.
5 . Dimension “a” should be kept to a minimum to reduce
induced stresses in the skirt. This will provide a more
economical design for base plate, chairs, and anchor
bolts.

PROCEDURE 3-15
DESIGN OF BASE DETAILS FOR VERTICAL VESSELS #2

Notation f, =tension force per bolt, lb
f, =bearing pressure on foundation, psi
~ Mb =overturning moment at base, ft-lb
MT =overturning moment at tangent line, ft-lb
E =joint efficiency
E 1 = modulus of elasticity at design temperature, psi Allowable Stresses
AI, =cross-sectional area of bolts, in.2
d = diameter of bolt circle, in. FT = lesser of *0.6F, =
Wl, =weight of vessel at base, lb 1.33s=
WT =weight of vessel at tangent line, Ib
w =width of base plate, in. *0.333FY=

S = code allowable stress, tension, psi 1.33Factor B =
N =number of anchor bolts
F: =allowable bearing pressure, concrete, psi F, = lesser of tskEl --
F, = minimum specified yield stress, skirt, psi
F, =allowable stress, anchor bolts, psi 0 -
fLT =axial load, tension, Ib/in.-circumference
fIdc = axial load, compression, lb/in.-circumference 16R
FT= allowable stress, tension, skirt, psi
F, = allowable stress, compression, skirt, psi 1.33s =
Fl, = allowable stress, bending, psi

Design of Vessel Supports 201

Factor A = O.125tsk --
R~

Factor B = from applicable material
chart of ASME Code, Section 11,
Part D, Subpart 3

Anchor Bolts
a Force per bolt due to uplift.

e Required bolt area, Ah.

A b = - f=S
Fs

Use ( ) diameter bolts

Note: Use four %-in.-diameter bolts as a minimum.

-at=Bunwelded Lap welded Base Plate
E = 0.7 a Bearing pressure, fc (average at bolt circle).
E = 0.5
e Required thickness of base plate. th.

IT/, in. 2 in. llh in.? Minimums

Skirt

3 x 3 x % in. 1% = YIS in. minimum e Longitudinal forces, f L T and fLc.
minimum Ih-1 in.
fLT= -48Mb - -Wb
rD2 XD

fLC = ( - 4r18DM7b - W-TDb

Figure 3-76. Typical dimensional data and forces for a vertical vessel Notes
supported on a skirt.

Fk =500 psi for 2000 lb concrete 1. This procedure is based on the “neutral axis” method
750 psi for 3000 lb concrete and should be used for relatively small or simple ver-
tical vessels supported on skirts.

2. If moment ML is from seismic, assume Wb as the oper-
ating weight at the base. If Mb is due to wind, assume
empty weight for computing the maximum value of fLT
and operating weight for fLc.

202 Pressure Vessel Design Manual

e Thicknew required of skirt at base plate, t&. I Thickness required:

t,k = greater of f LT = t,k = greater of ~LT -
-
FT 0.707 FTE -

or -f1,C = or 0.707 FcE -
FC

e Tliickries~reyiiiretl of skirt at skirt-head attachment.
Longitudinal forces:

REFERENCES

1. ASCE 7-95, “Minimum Design Loads for Buildings Welding Journal Research Supplement, December
and Other Structures,” American Society of Civil 1955, pp. 608-617.
Engineers. 13. Bijlaard, P. P., “Stresses from Radial Loads and
External Moments in Cylindrical Pressure Vessels.”
2 . “Recommended Practice #11, Wind and Earthquake Welding Journal Research Supplement, December
Design Standards,” Chevron Corp., San Francisco, 1954, pp. 615-623.
CA, March 1985. 14. Megyesy, E. F., Pressure Vessel Handbook, 3rd Edition,
Pressure Vessel Handbook Publishing Co., 1975, pp.
3. Unqororni Building Code, 1997 Edition, International 72-85.
Conference of Building Officials, Whittier, CA, 1997. 15. Zick, L. P., “Stresses in Large Horizontal Cylindrical
Pressure Vessels on Two Saddle Supports,” Welding
4. Bednar, H. H., Pressure Vessel Design Handbook, Van Research Journal Supplement, September 1951.
Nostrand Reinhold Co., 1981, Section 5.1. 16. Moody, G. B., “How to Design Saddle Supports,”
Hydrocarbon Procesing, November 1972.
5. Brownell, L. E., and Young, E. H., Process Equipment 17. Wolters, B. J,, “Saddle Design-Horizontal Vessels
Verign, Tohn Wiley and Sons, Inc., 1959, Section 1 0 . 2 ~ . over 13 Feet Diameter,” Fluor Engineers, Inc.,
Irvine, CA, 1978.
6. Fowler, D. W., “New Analysis Method for Pressure 18. Committee of Steel Plate Producers, Steel Plate
Vessel Column Supports,” Hydrocarbon Processing, Engineering Datu, Volume 2, Useful Information on
the Design of Plate Structures, American Iron and
- May 1969. Steel Institute, Part VII.
19. Gartner, A. I., “Nomographs for the Solution of Anchor
1 . Manual of Steel Construction, 8th Edition, American Bolt Problems,” Petroleum Refiner, July 1951, pp.
Institute of Steel Construction, Inc., 1980, Tables 101-106.
C1.8.1 and 3-36. 20. Manual of Steel Construction, 8th Edition, American
Institute of Steel Construction, Inc., 1980, Part 3.
8 . h a r k , R. J., Fomnulns fi)r Stress and Strain, 4th 21. Blodgett, O., Design of Welded Structures, The James
Edition, McGraw Hill, 1971, Table VIII, Cases 1, 8, 9 F. Lincoln Arc Welding Foundation, 7th printing, 1975,
and 18. Section 3.3.

9. Wolosewick, F. E., “Support for Vertical Pressure
Vessels,’’ Petroleum Refiner, July 1981, pp. 137-140,
August 1981, pp. 101-108.

10. Blodgett, O., Design of Weldments, The James F.
Lincoln Arc Welding Foundation, 1963, Section 4.7.

11. “Local Stresses in Spherical and Cylindrical Shells Due
to External Loadings,” WRC Bulletin #107, 3rd revised
printing, April 1972.

12. Bijlaard, P. P., “Stresses from Radial Loads and
External Moments in Cylindrical Pressure Vessels,”