Notation A = cross-sectional area of brace, in.’
V=base shear, Ib
E = modulus of elasticity, psi W =operating weight of vessel, lb A1 = change in length of brace, lb
F h =horizontal seismic force, Ib F, = vertical seismic force, Ib F, =lateral force at top of vessel, lb Fa = allowable axial stress, psi
Fy = minimum specified yield stress, psi V, =horizontal load on one leg, lb
dl =distance between extreme legs, in.
AI = cross-sectional area of leg, in. 2
f = axial load in brace, lb
n =number of active rods per pane1 = 1 for sway- bracing, 2 for cross-bracing
FL = axial load on leg due to overturning moment, lb FD = axial load on leg due to dead wt, Ib
F, = combined axial load on leg, lb fa =axial stress, psi
y = static deflection, in.
T = maximum period of vibration, sec g = acceleration due to gravity, 386 in./sec2
r = least radius of gyration, in.
M =overturning moment, in.-lb N =number of legs
d =center line diameter of leg circle, in.
C1= chord length between legs, in.
CI, =horizontal seismic factor, see Procedure 3-3 C, = vertical seismic factor
K 1 = end connection coefficient
11 = moment of inertia, cross brace, in.4 SI = slenderness ratio
tan 8 = h ’ C 1
1 = length of cross brace; = h’/sin 8
This procedure is used for calculating the distribution of vertical and horizontal forces due to wind or seismic loadings for vessels, spheres, elevated tanks, and bins supported on cross-braced legs or columns.
To design the legs, base plates, cross-bracing, anchor bolts, ring girder, and foundations, it is necessary for the designer to determine the actual distribution of forces.
The horizontal load due to wind or seismic is distributed to the legs through the cross-bracing or sway rods. The legs, in turn, transfer the forces to the vessel base, ring girder, or support structure. The angle between the applied force and the cross-bracing determines the magnitude of the imposed load at that point.
Large Pressure Vessel
h
I
The c.g. of weld ’
or fastener group
Bin or Elevated Tank
Four legs (for illustration only)
Figure 3-17. Typical dimensional data and forces for a vessel supported on braced legs.
134 Pressure Vessel Design Manual
I
CASE 1 CASE 2
Figure 3-18. Load diagrams for horizontal load distribution.
Horizontal Load Distribution, V,
The horizontal load on any one leg is dependent on the I
direction of the reactions of the leg bracing. The horizontal force, V, is transmitted to the legs through the bracing. Thus, the general equation:
Vsina,
V, =- N and ZV,, = V
Vertical Load Distribution, F,
The vertical load distribution on braced and unbraced legs is identical. The force on any one leg is equal to the dead
I 0
load (weight) plus the live load (greater of wind or seismic) and the angle of that leg to the direction of force, V. The general equation for each case is as follows
For Case 1:
FL = m 4M
F, = FD f FL COS 4,
For Case 2:
F"
FD
CASE 1 CASE 2
Figure 3-19. Load diagrams for vertical load distribution.
Calculations
1. Horizontal seismic force, FJ,.
lJBC design: See Procedure 3-3.
€71, = Ck,, W, or V
2. Sway-bracing. Sway braces are tension only members, not connected at the center. There is one per panel alternating in each adjacent panel.
0 Maximum tension force in sway hrace,f.
LJ,,
f = =
0 Arid stress, tension,%.
f, = f - < 0.66Fy A
3. Cross-bracing. Cross braces are tension and compres- sion members. They may be pinned at the center or not. If the slenderness ratio of the cross brace exceeds 120, then the cross-bracing must be pinned at the center.
0 Maximum jb-ce in cross-bracing, f.
J1=ncOse v,,
0 Required moment of inertia, 11.
Pinned at center
f P
I1 =- 4 2 E
Not pinned at center
f e 2
I , =-
T2E
0 Slenderness ratio, S I . Pinned at center
kl e
SI = - 2r
Not pinned at center k l t
SI = - r
Select size of cross-bracing:
I = A = r =
0 Axial stress, tension. or compression, fa.
c f , = (*$
A
tension: (+) 50.66FV
compression: (-) SF, from AISC Code 4. End connections.
Shear per bolt = 0.5m no. of bolts
0.5Cf) Shear per inch of weld = .
in. of weld 5 . Seismic factors.
e Change in length of brace, Al.
f t A1 1 -
EA
0 Static dejlection, y, y = - A1
cos e
Period of vibration, T .
Bolted * Welded f
Figure 3-20. Typical end connections of leg bracing.
Table 3-1 1 Allowable Load in kips
Bolt Size A-307 A-325
~-
% in. 3.1 6.4
'/8 in. 6.0 12.6
1 in. 7.9 16.5
I'/B in. 9.9 20.9
Weld Size EGOXX* E70XX*
3/16 in. 2.39 2.78
1/4 in. 3.18 3.71
?, in. 4.4 9.3
5/16 in. 3.98 4.64
% in. 4.77 5.57
in. 5.56 6.50
*kipdin. of weld.
136 Pressure Vessel Design Manual where g = 386 in./sec2
6. Design of 1eg.Y.
e Force ut top of vessel, Ft (UBC design only).
Ft = 0.07TV or 0.25V whichever is less or
Ft = 0 if T < 0.7sec e Vertical force, F,.
UBC design: F, = W with vertical seismic factor:
F, = UP = (C, - l)W
= down = (1 + C,)W = (-)
e Overturning moment at base, M . UBC design: M = L(Fh - F,) + HFt
Other: M = LFh e Axial stress, fa.
Table 3-12 Summary of Loads V, and F,
Case 1 At Posts Horiz. (V,) Vert. (F,) 1 0.0833V
2 0.2083V 3 0.2083V 4 0.0833V 5 0.2083V 6 0.2083V 1 0.0366V 2 0.125V 3 0.2134V 4 0.125V 5 0.0366V 6 0.125V 7 0.2134v 8 0.125V 1 0.0191v 2 0.0750V 3 0.1655V 4 0.1655V 5 0.0750V 6 0.0191V 7 0.0750V 8 0.1655V 9 0.1655V 10 0.0750V
FD+ FL FO + 0.5F~
FD - 0.5F~
FD - FL FD - 0 . 5 F ~ FD + 0 . 5 F ~ FD + FL FI, + 0.707F~
FD
FD - 0.707F~
FD - FL FD - 0.707F~
FO
FD + 0.707F~
FD + FL FD + 0.809F~
FD + 0.309F~
FD - 0.309F~
FD - 0.809F~
FD - 0.809F~
FD - 0.309F~
FD + 0.309F~
FD + 0.809F~
FD - FL
Case 2 Between Posts Horiz. 01,) Vert. (F,)
0.125V 0.25V 0.125V 0.125V 0.25V 0.125V 0.0625V 0.1875V 0.1875V 0.0625V 0.0625V 0.1875V 0.1 875V 0.0625V 0.0346V 0.125V 0.1809V 0.125V 0.0346V 0.0346V 0.125V 0.1809V 0.125V 0.0346V
FD + 0.866F~
FD
FD - 0.866F~
FD - 0.866F~
FD + 0.866F~
FD + 0.9239F~
FD + 0.3827F~
FD - 0.3827F~
FD - 0.9239F~
FD - 0.9239F~
FD - 0.3827F~
FD + 0.3827F~
FD + 0.9239F~
FD + 0.951 1 FL FD + 0.5878F~
FD
FD - 0.5878F~
FD - 0.951 1 FL FD - 0.951 1 FL FD - 0.5878F~
FD
FD + 0.5878F~
FD + 0.951 1 FL FD
~~ ~ ~
* Case 1
m At Posts
F
Horiz. 01,) Vert. (F,)
-I
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -
-
0.01 12v 0.0472V 0.1194V 0.1 555v 0.1194V 0.0472V 0.01 12v 0.0472V 0.1194V 0.1 555v 0.1 194V 0.0472V 0.0048V 0.021 7 v 0.0625V 0.1 034v 0.1 202v 0.1 034V 0.0625V 0.0217v 0.0048V 0.0217V 0.0625V 0.1034V 0.1202v 0.1034V 0.0625V 0.0217V
FD + FL FD + 0.866F~
FD + 0.5F~
FD
FD - 0.5F~
FD - 0.866F~
FD - 0.866F~
FD - 0.5F~
FD + 0 . 5 F ~ FD + 0.866F~
FD - FL
FD
FD + FL
FD+ 0.9239F~
FD+ 0.7071 FL FD + 0.3827FL FD
FD - 0.3827F~
FD - 0.7071 FL FD - 0.9239F~
FD - 0.9239F~
FD - 0.7071 FL FD - 0.3827F~
FD + 0.3827FL FD + 0.7071 FL FD + 0.9239F~
FD - FL
FD
Case 2 Between Posts Horiz. (V,) Vert. (F,)
0.0209V FD + 0.9659F~
0.0834V FD +0.7071 FL 0.1 458V FD + 0.2588F~
0.1458V FD - 0.2588F~
0.0834V FD - 0.7071 FL 0.0209V FD - 0.9659F~
0.0209V FD - 0.9659F~
0.0834V FD - 0.7071 FL 0.1 458V FD - 0.2588F~
0.1458V FD - 0.2588F~
0.0834V FD - 0.7071 FL 0.0209V FD +0.9659F~
0.0091V FD +0.9808F~
0.0404V FD + 0.831 ~ F L 0.0846V FD + 0.5556F~
0.1 158V FD + 0.1951 FL 0.1 158V FD - 0.1951 FL 0.0846V FD - 0.5556F~
0.0404V FD - 0.831 ~ F L 0.0091V FD - 0.9808F~
0.0091V FD - 0.9808F~
0.0404V FD - 0.831 ~ F L 0.0846V FD - 0.5556F~
0.1158V F ~ - o . 1 9 5 1 F ~ 0.1 158V FD +0.1951 FL 0.0846V FI, + 0.5556F~
0.0404V FD + 0.8315F~
0.0091 v FD + 0.9808F~
e Slenderness ratio for legs, S I .
Klh’
s1 =- r KI = 0.5 to 1.0
e Allowable compressive stress, Fa.
Fa = from AISC (see App. L)
Table 3-13 Dimension, d,
No. of Legs dl
3 4 6 10 12 16
a
0.75d 0.705d 0.865d 0.925d 0.95d 0.9654 0.98d
Table 3-14
Suggested Sizes of Legs and Cross-Bracing
Tan to Tan SUPPOfi Leg Base Plate Bracing Angle Bolt Size Y
Vessel O.D. (in.) Length (in.) Angle Sizes (in.) Size (in.) Size (in.) (in.) (in.)
Up to 30 30 to 42
Up to 240 121 to 169 170 to 240 121 to 169 170 to 240 up to 120 121 to 169 170 to 240 121 to 169 170 to 240 121 to 169 170 to 240 121 to 169 170 to 240 u p to 120
u p to 120 43 to 54
55 to 56
up to 120 67 to 78
up to 120 79 to 80
up to 120 91 to 102
(3) 3 x 3 x k
(4) 3 x 3 x %
(4) 3 x 3 x %
(4) 3 x 3 x %
(4) 3 x 3 x %
(4) 3 x 3 x %
(4) 4 x 4 x %
(4) 4 x 4 x %
(4) 4 x 4 x % (4) 4 x 4 x ?h (4) 5 x 5 x %
( 4 ) 5 X 5 X % (4) 6 x 6 x % (4) 6 x 6 x Yz (4) 6 x 6 x % (4) 6 x 6 x % (4) 6 x 6 x % (6) 6 x 6 x % (6) 6 x 6 x
6 x 6 x % 6 x 6 x % 6 x 6 x X 6 x 6 x % 6 x 6 x % 6 x 6 x % 8 X 8 X % 8 X 8 X % 8X8XY2 8X8XYZ 9 X 9 X % 9 X 9 X % 1OX1OX%
10 x 10 x Y2
10 x 10 x Y2
l o x l o x % 1OX1OX%
1OX1OX%
1 o x 1 o x ~
2 X 2 X ? 4
2 X 2 X % %
% %
L
2% x 2% x ‘/4
3 X 3 X ’ / 4 1%
1%
1%
3 X 3 X 3 1%
178 1%
3 X 3 X 7 * 1 78
1%
1%
1 1 1
12 8 10 12 8 10 12 8 10 12 8 10 12 10 12 12 12 12 12
1. Cross-bracing the legs will conveniently reduce bend- ing in legs due to overturning moments (wind and equipment) normally associated with unbraced legs.
The lateral bracing of the legs must be sized to take lateral loads induced in the frame that would other- wise came the legs to bend.
2 . Legs may be made from angles, pipes, channels, beam sections, o r rectangular tubing.
3. Legs longer than about 7ft should be cross-braced.
4. Check to see if the cross-bracing interferes with piping 5. Shell stresses at the leg attachment should be investi- gated for local loads. For thin shells, extend “Y.” Legs should be avoided as a support method for vessels with high shock loads or vibration service.
from bottom head.
138 Pressure Vessel Design Manual
Flow chart for design of vertical vessels on legs
Determine preliminary design details
legs
YES
Cross-braced
Q Sway-braced
1. Qty of legs: 3,4,6, etc.
2. Types of legs: pipe, angle, 3. Size of legs: 4", 6", 8",etc.
4. Leg attachment type tube, or beam
r I 0 -:-- -1 _ _ _ ^ ^
3. I ype Q 3 1 ~ 6 U I ~ ~ w s a - u r a ~ ~ i i y 6. Method of attachment of
cross-bracing to columns
n anchor bolts &
Figure 3-21. Flow chart for design of vertical vessels on legs.
-
Types of Leg Attachment
Souare or Rectanalar Tube Beam Section Angle / I T I
I
Bottled Legs
Legs with rings
I
Pipe
\ Doubleclip fl
- 1 1
i ' I '
Beam Legs - Not Coped
I _.
Beam-flange out Pedestal
I
Beam I Angle
140 Pressure Vessel Design Manual
PROCEDURE 3-6