TAG TANK Bottom
Plate Thickness Self Wt of plate Distance between Stiffeners Height of Tank Height of Liquid Plate Material Plate yield Stress Density of Liquid Consider width Liquid Load on 1m width Total Load on bottom plate Maximum Bending Moment in plate
12.7 mm 0.997 kN/m 500 mm mm 7400 mm 6216 mm ASTM A240-SS316L 170 Mpa 14.5 kN/m3 1000 mm 90.132 kN/m 91.12895 kN k N/m 3.560 kNm 355972 3559725 5 Nmm Nmm 26881.67 mm m m3 1 3 2 .4 2 2 MPa 0.779 < 1…..HENCE OK
Section Modulous of plate Bending Stress in Plate Utilisation Ratio
Bottom Plate Thickness
0.5 iin n 12. 2.7 7 mm
Assume all Bottom Plate Stiffeners L 100x100x12 All longitudinal stiffeners shall be place at 500 mm c/c All transverse stiffeners shall be place at 3250 mm c/c L 100x100x12
Bottom Plate 5 00 m m
88 12
12
3
2
100
1 500
12.7
NA from bottom MI 1 MI 2 MI 3 Where,
26.521 mm mm
85349.292 mm4 A1*X1^2 = 2583559 mm4 1000000 mm4 A2*X2^2 = 661529.4 mm4 12672 mm4 A3*X3^2 = 8972844 mm4 A1, A2 and A3 are the area of insividual sections specified X1, X2 and X3 are the respective CG distances between the individual section and common NA.
MI of Section Section Modulus
13315954.14 mm4 502095.4091 mm3
Self weight of section per meter Weight of Liquid per meter Total weight on section Length of section Bending Moment Bending Stress Allowable bending Stress Utilisation Ratio
0.676 45.066 45.742 3.25 75.49146 150.353 17 0 0.884
kN/m kN/m kN/m m kN kNm Mpa M Mp pa < 1…..HENCE OK
Length of TANK
3 .2 5 m 0.5 m
0.5 m 0.5 m
0.5 m Bottom Plate of TANK
The purpose of this workbook is the design of Rectangular tanks with Horizontal Stiffeners. Ref : "Pressure Vessel Handbook" (8th and 14th Edition) also "Roarks formulas for Stress and Strain" 7th Edition
RECTANGULAR TANKS Under Hydrostatic Pressure With Horizontal Stiffeners
LEGEND INPUT Notes and additional actions requi Intermidiate results Results
NOTATIONS alpha E G H I L p R S t w
Factor depends of ratio of length and height, (H/L) Table; See Table on page 204 Modulus of elasticity psi, 30000000 fo carbon steel Specific gravity of liquid Height of tank Moment of inertia, in4 Length of tank, in Pressure of liquid, psi Reaction wit subscripts indicating location, lb/in Stress value of plate, psi as tabulated in ASME code Required plate thickness, in Load per unit length, lb/in
Top Stiffener
2 / 1 h
2 / ) 2 h
h1
H1
+ 1 h (
h2 1st Stiffener
H
h3
R1
H2 R2
2nd Stiffener H3
L
When H in inches =
Required Nos of Stiffeners
Spacing of Stiffeners
60 - 84
84 - 120
120 - 156
> 156
1
2
3
4
H1
H2
H3
H4
H5
0.60H 0.45H 0.37H 0.31H
0.40H 0.30H 0.25H 0.21H
0.25H 0.21H 0.18H
0.17H 0.16H
0.14H
1 2 3 4
Load (lb/inch)
w = (0.036 * G * h^2) / 2
Minium Moment of Inertia for Stiffeners
I = (1.25 * R * L^3 )/E
Required Plate Thickness
t = 0.3 * H * SQRT(0.036 * G * H / S)
V= E=
2635 ft^3 30000000 psi
G= H=
1.45 291.34 in
W= L= S= ta =
110 52 24655 0.5
INPUT
in in psi in
where
R = 0.7 * w
Minimum recommanded Thickness t= 0.25 in
Horizontal span between vertical supports ( i.e Stiffeners, stays)
Actual thickness used including corrosion all owance.
Calculate minimum recommanded numbers of stiffeners based only on tank height 1
Actual numbes of stiffeners used 8 H1 = H2 = H3 = H4 = H5 = H6 = H7 =
0.18H = 0.15H = 0.15H = 0.11H = 0.11H = 0.085H = 0.085H =
52.44 43.70 43.70 32.05 32.05 24.76 24.76
INPUT in in in in in in in
Distance between top of tank and 1st stiffener Distance between 1st and 2nd stiffener Distance between 2nd and 3rd stiffener Distance between 3rd and 4th stiffener Distance between 4th and 5th stiffener Distance between 5th and 6th stiffener Distance between 6th and 7th stiffener
H8 = H9 = H10 =
0.065H = 0.065H = 0H =
18.94 in 18.94 in 0.00 in
Distance between 7th and 8th stiffener Distance between 8th and 9th stiffener Distance between bottom stiffener and tank bottom
Calculating distance (X) from tank top to each stiffener (lower case 'n' indicates the stiffener number) X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = X9 = X10 =
52.44 96.14 139.84 171.89 203.94 228.70 253.46 272.40 291.34 0.00
in in in in in in in in in in
…...H1 …..H1+H2 …..H1+H2+H3 …..H1+H2+H3+H4 …..H1+H2+H3+H4+H5 …..H1+H2+H3+H4+H5+H6 …..H1+H2+H3+H4+H5+H6+H7 …..H1+H2+H3+H4+H5+H6+H7+H8 …..H1+H2+H3+H4+H5+H6+H7+H8+H9
Tank Height
Calculating load per inch for each stiffener w1 = w2 = w3 = w4 = w5 = w6 = w7 = w8 = w9 = w10 =
71.78 241.25 510.41 771.15 1085.51 1365.14 1676.78 1936.69 2215.32 0.00
lb/in ib/in lb/in lb/in lb/in lb/in lb/in lb/in lb/in lb/in
Load at Tank Bottom
Calculating reaction at each stiffener R1 = R2 = R3 = R4 = R5 = R6 = R7 = R8 = R9 = R10 =
50.24 168.87 357.29 539.81 759.85 955.59 1173.74 1355.68 1550.72 0.00
lb lb lb lb lb lb lb lb lb lb
wn = 0.036 * G * xn^2 / 2
Rn = 0.7 * wn
Reaction at Bottom
Calculating minimum required moment of inertia for stiffeners In = (1.25 * Rn * L^3)/ E For intermidiate stiffeners
Itop = (0.3 * w1 * L^4) / (192 * E * ta) or Itop = (0.06 * w1 * L^4) / (192 * E * ta)
Required MI of stiffeners Itop = I1 = I2 = I3 = I4 = I5 = I6 = I7 = I8 = I9 = I10 =
0.011 0.294 0.989 2.093 3.163 4.452 5.599 6.877 7.942 9.085 0.000
in^4 in^4 in^4 in^4 in^4 in^4 in^4 in^4 in^4 in^4 in^4
Smallest Angle
For top stiffener Depending on intermidiate stiffeners are used or not.
Smallest Channel
L2x2x1/4 L2x2x1/4 L3x3x1/4 L3x3x1/2 L4x4x7/16 L4x4x7/16 L4x4x3/4 L4x4x3/4 L5x5x3/8
C3x3.5 C3x3.6 C3x3.6
Calculating pressure at each distance (X) P1 = P2 = P3 = P4 = P5 = P6 = P7 = P8 = P9 = P10 =
1.369 3.878 6.159 8.136 9.809 11.292 12.585 13.725 14.714 0.000
Smallest SHS
Smallest Smallest WT,MT,ST W,M,S,HP
2x1x1/8 ST1.5x2.85 2x1x1/8 ST1.5x3.75 2x1x3/16 ST2x4.75
M3x2.9 M3x2.9 M3x2.9
Pn = 0.036 * G * (Xn-1 + Xn) / 2
psi psi psi psi psi psi psi psi psi psi
Calculating required plate thickness at each section tn = 0.3 * Max(Hn,L) * SQRT (0.036 * G * Xn / S) t1 = t2 = t3 = t4 = t5 = t6 = t7 = t8 = t9 = t10 =
0.166 0.223 0.268 0.298 0.324 0.343 0.361 0.375 0.387 0.000
in in in in in in in in in in
Thickness Calculated base on the Pressure at level "n" and the longest dimentions between the line of supports
Tank Bottom
Maximum Thickness =
0.387 in
Maximum deflection of top plate section y(max) = y(max) =
(alpha * 0.036 * G * H1 * L^4) / (E * ta^3) 0.0187 in
Calculating H1/L to find "alpha" H1/L = 1.008 Looking for "alpha" = 0.0035
Stress and deflection calculations below based on the formulas from Roarkes formulas for Stress and Stress, 7th Edition Top section of plate is confirms to Case 10d, table 11.4, page 514 Rectangular plate : 3 edges fixed and one edge free Uniformly descreasing load from fixed to zero at free edge
Z
Z
Free Edge
Free Edge
b
Fixed Edge
Fixed Edge a
a= b= a/b =
Fixed Edge 52 in 52.44 in tr = 0.5 in 0.992 q= 1.369 psi at 1st stiffener location
X
q
Minimum thickness usi solver tool with Roarks formula
(At x=0, z=0) sigma R1 = beta1 * q * b^2 / tr^2 and Rr1 = gamma1 * q * b (At x=+ - a/2, z=b if a>b or z=0.4b if a
0.25
0.5
0.75
1
1.5
2
3
beta1 beta2 gamma1 gamma2
0.018 0.019 0.106 0.075
0.064 0.068 0.195 0.151
0.12 0.125 0.265 0.211
0.195 0.166 0.324 0.242
0.351 0.244 0.406 0.106
0.507 0.387 0.458 0.199
0.758 0.514 0.505 0.313
Calculating Beat's and gamma's
Calculating stress and reaction based on required thickness
beta1 = beta2 = gamma1 = gamma2 =
sigmaR1 = sigmaR2 = Rr1 = Rr2 =
0.429 0.3155 0.432 0.1525
6459.06 4750.194 31.007 10.946
psi psi lb/in lb/in
The remaining section of plate confirms to Case 8a, table 11.4, page 508 Assuming uniform pressure across height of each section Rectangular plate : all edges fixed Uniform load on entire plate a= b1 = b2 = b3 = b4 = b5 = b6 = b7 = b8 = b9 = tr =
52 43.70 43.70 32.05 32.05 24.76 24.76 18.94 18.94 0.00 0.5
in in in in in in in in in in in
Distance between 1st and 2nd stiffener Distance between 2nd and 3rd stiffener Distance between 3rd and 4th stiffener Distance between 4th and 5th stiffener Distance between 5th and 6th stiffener Distance between 6th and 7th stiffener Distance between 7th and 8th stiffener Distance between 8th and 9th stiffener Distance between 9th stiffener and tank bottom Required thickness found above using the solver tool.
a/b
1
1.2
1.4
1.6
1.8
2
3
beta1 beta2 alpha
0.3078 0.1386 0.0138
0.3834 0.1794 0.0188
0.4356 0.2094 0.0226
0.4680 0.2286 0.0251
0.4872 0.2406 0.0267
0.4974 0.2472 0.0277
0.5000 0.2500 0.0284
Calculating beta's and alpha's a/b1 = a/b2 = a/b3 = a/b4 = a/b5 = a/b6 = a/b37= a/b8 = a/b9=
1.190 1.190 1.623 1.623 2.100 2.100 2.746 2.746 #DIV/0!
beta1(b1)= beta1(b2)= beta1(b3)= beta1(b4)= beta1(b5)= beta1(b6)= beta1(b7)= beta1(b8)= beta1(b9)=
0.3834 0.3834 0.4680 0.4680 0.4974 0.4974 0.5000 0.5000 0.0000
beta2(b1)= beta2(b2)= beta2(b3)= beta2(b4)= beta2(b5)= beta2(b6)= beta2(b7)= beta2(b8)= beta2(b9)=
0.1794 0.1794 0.2286 0.2286 0.2472 0.2472 0.2500 0.2500 0.0000
alpha(b1)= alpha(b2)= alpha(b3)= alpha(b4)= alpha(b5)= alpha(b6)= alpha(b7)= alpha(b8)= alpha(b9)=
0.0188 0.0188 0.0251 0.0251 0.0277 0.0277 0.0284 0.0284 0.0000
Calculating stress and deflection based on required thickness tr (At center of long edge ), sigma(max) = beta1 * Pn+1 * bn^2 / tr^2 sigma(max)b1 = sigma(max)b2 = sigma(max)b3 = sigma(max)b4 = sigma(max)b5 = sigma(max)b6 = sigma(max)b7 = sigma(max)b8 = sigma(max)b9 =
11357.933 18039.070 15642.620 18858.860 13777.315 15354.516 9843.928 10552.909 0.000
psi psi psi psi psi psi psi psi psi
(At center) sigmac = ( beta2 * Pn+1 * bn^2) / tr^2 delta(max) = (alpha * Pn+1 * bn^4) / (E * tr^3)
and
sigmac(b1) = sigmac(b2) = sigmac(b3) = sigmac(b4) = sigmac(b5) = sigmac(b6) = sigmac(b7) = sigmac(b8) = sigmac(b9) =
delta(max)b1 = delta(max)b2 = delta(max)b3 = delta(max)b4 = delta(max)b5 = delta(max)b6 = delta(max)b7 = delta(max)b8 = delta(max)b9 =
Max Stress =
5314.588 8440.817 7640.818 9211.828 6847.110 7630.954 4921.964 5276.455 0.000
psi psi psi psi psi psi psi psi psi
18858.860 psi
Max Deflection =
0.071 0.113 0.057 0.069 0.031 0.035 0.013 0.014 0.000
in in in in in in in in in
0.1126 in
Minimum recommanded plate thickness is 0.25 in, which is greater that of found by using "Pressure Vessel Handbook" and "Roarks formula for stress and strain" rounded upto the nearest 1/16th
1.32 m or less Top Stiffener 1.332 m 1st Stiffener 1.11 m 2nd Stiffener 1.11 m
3rd Stiffener 0.814 m 7.4
Vertical Stiffeners
m
4th Stiffener 0.814 m 5th Stiffener 0.629 m 6th Stiffener 0.629 m
7th Stiffener 0.481 m 8th Stiffener 0.481 m TANK Wall Horizontal Stiffeners Top Stiffener 1st Stiffener 2nd Stiffener 3rd Stiffener 4th Stiffener 5th Stiffener 6th Stiffener 7th Stiffener 8th Stiffener Vertical Stiffeners L 120x120x12
L L L L L L L L L
50x50x6 50x50x6 70x70x8 90x90x8 100x100x12 100x100x12 120x120x10 120x120x10 120x120x12
(Tank Wall plate Thickness is 0.5 in = 12.7 mm)
(All Vertical stiffeners shall be placed at a distance of 1.32 m or Less c
ed
2 / ) 3 h + 2 h (
ng the
r
Utilisation =
in.
0.76491
< 1…..HENCE OK
c)
Density of Steel Weight of angle L 50x50x6 Weight of angle L 70x70x8 Weight of angle L 90x90x8 Weight of angle L 100x100x12 Weight of angle L 120x120x10 Weight of angle L 120x120x12 Weight of Base Profile W200x31.3 ASTM A-36
2 Tag
7850 4.6 8.4 10.9 17.9 18.3 21.7 31.3
kg/m3 kg/m kg/m kg/m kg/m kg/m kg/m kg/m
TANK
Length Width Height Compartments Volume of one Compartment Total Volume
3600 2800 7400 1 74.59 74.59
Tank Bottom Plate Thickness Weight of Plate Spacing of Longitudinal stiffeners (L 100x100x12) Total longitudinal stiffeners Weight of longitudinal stiffeners Spacing of transverse stiffeners (L 100x100x12) Total transverse stiffeners Weight of Transverse stiffeners
Longitudinal Tank Wall Plate Thickness Nos of Longitudinal walls Weight of Plate Spacing of vertical Stiffener (L 120x120x12) Total Vertical stiffeners Weight of Vertical stiffeners
mm mm mm m3 m3 3600
x
2800
x
7400
12.7 mm 1004.926 kg 500 mm 6 Nos 468.72 kg 3250 mm 1.00 Nos 60.76 kg 3600 12.7 mm 2 Nos 5311.75 kg 1320 mm 6.00 Nos 963.48 kg
Total intermidiate horizontal stiffeners (L50x50x6) Weight of intermidiate horizontal stiffeners
2.00 Nos 33.12 kg
Total intermidiate horizontal stiffeners (L70x70x8) Weight of intermidiate horizontal stiffeners
2.00 Nos 60.48 kg
Total intermidiate horizontal stiffeners (L90x90x8) Weight of intermidiate horizontal stiffeners
2.00 Nos 78.48 kg
Total intermidiate horizontal stiffeners (L100x100x12) Weight of intermidiate horizontal stiffeners
4.00 Nos 257.76 kg
Total intermidiate horizontal stiffeners (L120x120x10) Weight of intermidiate horizontal stiffeners
4.00 Nos 263.52 kg
Total intermidiate horizontal stiffeners (L120x120x12) Weight of intermidiate horizontal stiffeners
2.00 Nos 156.24 kg
Total top horizontal stiffeners (L50x50x6) Weight of top horizontal stiffeners
Transverse Tank Wall Plate Thickness Nos of transverse walls Weight of Plate Spacing of vertical Stiffener (L 120x120x12) Total Vertical stiffeners Weight of Vertical stiffeners
2.00 Nos 33.12 kg 2800 12.7 mm 2 Nos 4131.361 kg 1320 mm 4.00 Nos 642.32 kg
Total intermidiate horizontal stiffeners (L50x50x6) Weight of intermidiate horizontal stiffeners
2.00 Nos 25.76 kg
Total intermidiate horizontal stiffeners (L70x70x8) Weight of intermidiate horizontal stiffeners
2.00 Nos 47.04 kg
Total intermidiate horizontal stiffeners (L90x90x8) Weight of intermidiate horizontal stiffeners
2.00 Nos 61.04 kg
Total intermidiate horizontal stiffeners (L100x100x12) Weight of intermidiate horizontal stiffeners
4.00 Nos 200.48 kg
Total intermidiate horizontal stiffeners (L120x120x10) Weight of intermidiate horizontal stiffeners
4.00 Nos 204.96 kg
Total intermidiate horizontal stiffeners (L120x120x12) Weight of intermidiate horizontal stiffeners
2.00 Nos 121.52 kg
Total top horizontal stiffeners (L50x50x6) Weight of top horizontal stiffeners
2.00 Nos 25.76 kg
x
7400
Nos of corner angles (L90x90x8) weight of corner angles
Tank Top Plate Thickness Weight of Plate
4.00 Nos 322.64 kg 3600
2800
= =
15.384 Ton 18.461 Ton
5 mm 395.64 kg
Spacing of Longitudinal stiffeners (L50x50x6) Total longitudinal stiffeners Weight of longitudinal stiffeners
500 mm 6 Nos 99.36 kg
Spacing of transverse stiffeners (L50x50x6) Total transverse stiffeners Weight of Transverse stiffeners
3250 mm 1.00 Nos 12.88 kg
Total Length of Base Profile W200x31.3 ASTM A-36 Weight of Base Profile
x
12.80 m 400.64 kg
Tank Tag : Total Weight of Plate (12.7 mm) ASME A240, SS316 Total Weight of Plate (5 mm) ASME A240, SS316 Total Weight of Angle L 50x50x6 Total Weight of Angle L 70x70x8 Total weight of Angle L 90x90x8 Total weight of Angle L 100x100x12 Total weight of Angle L 120x120x10 Total weight of Angle L 120x120x12 Total Weight of Base Profile W200x31.3 ASTM A-36
10448.04 395.64 230 107.52 462.16 987.72 468.48 1883.56 400.64
kg kg kg kg kg kg kg kg kg
Total weight of tank without fabrication loss = Total weight of tank with fabrication loss (20%) =
15383.76 kg 18460.51 kg
