modelo de dimension amen to tanques retangulares

TAG TANK

Bottom

Plate Thickness 12.7 mmSelf Wt of plate 0.997 kN/mDistance between Stiffeners 500 mmHeight of Tank 7400 mmHeight of Liquid 6216 mmPlate Material ASTM A240-SS316LPlate yield Stress 170 MpaDensity of Liquid 14.5 kN/m3Consider width 1000 mmLiquid Load on 1m width 90.132 kN/mTotal Load on bottom plate 91.12895 kN/mMaximum Bending Moment in plate 3.560 kNm

3559725 NmmSection Modulous of plate 26881.67 mm3Bending Stress in Plate 132.422 MPaUtilisation Ratio 0.779 < 1…..HENCE OK

Bottom Plate Thickness 0.5 in12.7 mm

Assume all Bottom Plate Stiffeners L 100x100x12All longitudinal stiffeners shall be place at 500 mm c/cAll transverse stiffeners shall be place at 3250 mm c/c

L 100x100x12

Bottom Plate

500 mm

88 1212

100

12.71

2

3

500

NA from bottom 26.521 mm

MI 1 85349.292 mm4 A1*X1^2 = 2583559 mm4MI 2 1000000 mm4 A2*X2^2 = 661529.4 mm4MI 3 12672 mm4 A3*X3^2 = 8972844 mm4Where, 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 13315954.143 mm4Section Modulus 502095.4091 mm3

Self weight of section per meter 0.676 kN/mWeight of Liquid per meter 45.066 kN/mTotal weight on section 45.742 kN/mLength of section 3.25 mBending Moment 75.49146 kNmBending Stress 150.353 MpaAllowable bending Stress 170 MpaUtilisation Ratio 0.884 < 1…..HENCE OK

Length of TANK

3.25 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 LEGENDUnder Hydrostatic Pressure INPUTWith Horizontal Stiffeners

Intermidiate resultsResults

NOTATIONS

alpha Factor depends of ratio of length and height, (H/L) Table; See Table on page 204E Modulus of elasticity psi, 30000000 fo carbon steelG Specific gravity of liquidH Height of tankI Moment of inertia, in4L Length of tank, inp Pressure of liquid, psiR Reaction wit subscripts indicating location, lb/inS Stress value of plate, psi as tabulated in ASME codet Required plate thickness, inw Load per unit length, lb/in

Notes and additional actions required

H1

H3

H2

H

h1

h3

h2

L

R1

R2

h1 /

2

(h1

+ h2

) / 2

(h2

+ h3

) / 2

Top Stiffener

1st Stiffener

2nd Stiffener

When H in inches =Required Nos of Stiffeners 60 - 84 84 - 120 120 - 156 > 156

1 2 3 4

H1 H2 H3 H4 H5Spacing of Stiffeners 1 0.60H 0.40H

2 0.45H 0.30H 0.25H3 0.37H 0.25H 0.21H 0.17H4 0.31H 0.21H 0.18H 0.16H 0.14H

Load (lb/inch) w = (0.036 * G * h^2) / 2

Minium Moment of Inertia I = (1.25 * R * L^3 )/E where R = 0.7 * wfor Stiffeners

Required Plate Thickness t = 0.3 * H * SQRT(0.036 * G * H / S)

V = 2635 ft^3E = 30000000 psiG = 1.45 Minimum recommanded ThicknessH = 291.34 in INPUT t = 0.25 inW = 110 inL = 52 in Horizontal span between vertical supports ( i.e Stiffeners, stays)S = 24655 psita = 0.5 in Actual thickness used including corrosion allowance.

Calculate minimum recommanded numbers of stiffeners based only on tank height1

Actual numbes of stiffeners used8 INPUT

H1 = 0.18H = 52.44 in Distance between top of tank and 1st stiffenerH2 = 0.15H = 43.70 in Distance between 1st and 2nd stiffenerH3 = 0.15H = 43.70 in Distance between 2nd and 3rd stiffenerH4 = 0.11H = 32.05 in Distance between 3rd and 4th stiffenerH5 = 0.11H = 32.05 in Distance between 4th and 5th stiffener

H6 = 0.085H = 24.76 in Distance between 5th and 6th stiffenerH7 = 0.085H = 24.76 in Distance between 6th and 7th stiffenerH8 = 0.065H = 18.94 in Distance between 7th and 8th stiffenerH9 = 0.065H = 18.94 in Distance between 8th and 9th stiffener

H10 = 0H = 0.00 in Distance between bottom stiffener and tank bottom

Calculating distance (X) from tank top to each stiffener (lower case 'n' indicates the stiffener number)

X1 = 52.44 in …...H1X2 = 96.14 in …..H1+H2X3 = 139.84 in …..H1+H2+H3X4 = 171.89 in …..H1+H2+H3+H4X5 = 203.94 in …..H1+H2+H3+H4+H5X6 = 228.70 in …..H1+H2+H3+H4+H5+H6X7 = 253.46 in …..H1+H2+H3+H4+H5+H6+H7X8 = 272.40 in …..H1+H2+H3+H4+H5+H6+H7+H8X9 = 291.34 in …..H1+H2+H3+H4+H5+H6+H7+H8+H9X10 = 0.00 in Tank Height

Calculating load per inch for each stiffener wn = 0.036 * G * xn^2 / 2

w1 = 71.78 lb/inw2 = 241.25 ib/in w3 = 510.41 lb/inw4 = 771.15 lb/inw5 = 1085.51 lb/inw6 = 1365.14 lb/inw7 = 1676.78 lb/inw8 = 1936.69 lb/inw9 = 2215.32 lb/inw10 = 0.00 lb/in Load at Tank Bottom

Calculating reaction at each stiffener Rn = 0.7 * wn

R1 = 50.24 lbR2 = 168.87 lbR3 = 357.29 lbR4 = 539.81 lbR5 = 759.85 lbR6 = 955.59 lbR7 = 1173.74 lbR8 = 1355.68 lbR9 = 1550.72 lb

R10 = 0.00 lb Reaction at Bottom

Calculating minimum required moment of inertia for stiffenersIn = (1.25 * Rn * L^3)/ E For intermidiate stiffenersItop = (0.3 * w1 * L^4) / (192 * E * ta) For top stiffener

or Depending on intermidiate stiffeners are used or not.Itop = (0.06 * w1 * L^4) / (192 * E * ta)

Smallest Smallest Smallest Smallest SmallestRequired MI of stiffeners Angle Channel SHS WT,MT,ST W,M,S,HP

Itop = 0.011 in^4 L2x2x1/4 C3x3.5 2x1x1/8 ST1.5x2.85 M3x2.9I1 = 0.294 in^4 L2x2x1/4 C3x3.6 2x1x1/8 ST1.5x3.75 M3x2.9I2 = 0.989 in^4 L3x3x1/4 C3x3.6 2x1x3/16 ST2x4.75 M3x2.9I3 = 2.093 in^4 L3x3x1/2I4 = 3.163 in^4 L4x4x7/16I5 = 4.452 in^4 L4x4x7/16I6 = 5.599 in^4 L4x4x3/4I7 = 6.877 in^4 L4x4x3/4I8 = 7.942 in^4 L5x5x3/8I9 = 9.085 in^4I10 = 0.000 in^4

Calculating pressure at each distance (X) Pn = 0.036 * G * (Xn-1 + Xn) / 2

P1 = 1.369 psiP2 = 3.878 psiP3 = 6.159 psiP4 = 8.136 psiP5 = 9.809 psiP6 = 11.292 psiP7 = 12.585 psiP8 = 13.725 psiP9 = 14.714 psiP10 = 0.000 psi

Calculating required plate thickness at each sectiontn = 0.3 * Max(Hn,L) * SQRT (0.036 * G * Xn / S)

t1 = 0.166 in Thickness Calculated base on the Pressure at level "n"t2 = 0.223 in and the longest dimentions between the line of supportst3 = 0.268 int4 = 0.298 int5 = 0.324 in

t6 = 0.343 int7 = 0.361 int8 = 0.375 int9 = 0.387 int10 = 0.000 in Tank Bottom

Maximum Thickness = 0.387 in

Maximum deflection of top plate section

y(max) = (alpha * 0.036 * G * H1 * L^4) / (E * ta^3) Calculating H1/L to find "alpha"y(max) = 0.0187 in 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 EditionTop section of plate is confirms to Case 10d, table 11.4, page 514Rectangular plate : 3 edges fixed and one edge freeUniformly descreasing load from fixed to zero at free edge

Z ZFree Edge Free Edge

Fixed FixedEdge Edge

Fixed Edge X qa = 52 inb = 52.44 in tr = 0.5 in Minimum thickness using thea/b = 0.992 q = 1.369 psi solver tool with Roarks

at 1st stiffener location 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<b) sigmaR2 = beta2 * q * b^2 / tr^2 and Rr2 = gamma2 * q * b

a

b

a/b 0.25 0.5 0.75 1 1.5 2 3beta1 0.018 0.064 0.12 0.195 0.351 0.507 0.758beta2 0.019 0.068 0.125 0.166 0.244 0.387 0.514

gamma1 0.106 0.195 0.265 0.324 0.406 0.458 0.505gamma2 0.075 0.151 0.211 0.242 0.106 0.199 0.313

Calculating Beat's and gamma's Calculating stress and reaction based on required thickness tr

beta1 = 0.429 sigmaR1 = 6459.06 psibeta2 = 0.3155 sigmaR2 = 4750.1944 psigamma1 = 0.432 Rr1 = 31.007 lb/ingamma2 = 0.1525 Rr2 = 10.946 lb/in

The remaining section of plate confirms to Case 8a, table 11.4, page 508Assuming uniform pressure across height of each sectionRectangular plate : all edges fixedUniform load on entire plate

a = 52 inb1 = 43.70 in Distance between 1st and 2nd stiffenerb2 = 43.70 in Distance between 2nd and 3rd stiffenerb3 = 32.05 in Distance between 3rd and 4th stiffenerb4 = 32.05 in Distance between 4th and 5th stiffenerb5 = 24.76 in Distance between 5th and 6th stiffenerb6 = 24.76 in Distance between 6th and 7th stiffenerb7 = 18.94 in Distance between 7th and 8th stiffenerb8 = 18.94 in Distance between 8th and 9th stiffenerb9 = 0.00 in Distance between 9th stiffener and tank bottomtr = 0.5 in Required thickness found above using the solver tool.

a/b 1 1.2 1.4 1.6 1.8 2 3beta1 0.3078 0.3834 0.4356 0.4680 0.4872 0.4974 0.5000beta2 0.1386 0.1794 0.2094 0.2286 0.2406 0.2472 0.2500alpha 0.0138 0.0188 0.0226 0.0251 0.0267 0.0277 0.0284

Calculating beta's and alpha's

a/b1 = 1.190 beta1(b1)= 0.3834 beta2(b1)= 0.1794 alpha(b1)= 0.0188a/b2 = 1.190 beta1(b2)= 0.3834 beta2(b2)= 0.1794 alpha(b2)= 0.0188a/b3 = 1.623 beta1(b3)= 0.4680 beta2(b3)= 0.2286 alpha(b3)= 0.0251a/b4 = 1.623 beta1(b4)= 0.4680 beta2(b4)= 0.2286 alpha(b4)= 0.0251a/b5 = 2.100 beta1(b5)= 0.4974 beta2(b5)= 0.2472 alpha(b5)= 0.0277a/b6 = 2.100 beta1(b6)= 0.4974 beta2(b6)= 0.2472 alpha(b6)= 0.0277

a/b37= 2.746 beta1(b7)= 0.5000 beta2(b7)= 0.2500 alpha(b7)= 0.0284a/b8 = 2.746 beta1(b8)= 0.5000 beta2(b8)= 0.2500 alpha(b8)= 0.0284a/b9= #DIV/0! beta1(b9)= 0.0000 beta2(b9)= 0.0000 alpha(b9)= 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 = 11357.933 psisigma(max)b2 = 18039.070 psisigma(max)b3 = 15642.620 psisigma(max)b4 = 18858.860 psisigma(max)b5 = 13777.315 psisigma(max)b6 = 15354.516 psisigma(max)b7 = 9843.928 psisigma(max)b8 = 10552.909 psisigma(max)b9 = 0.000 psi

(At center) sigmac = ( beta2 * Pn+1 * bn^2) / tr^2 anddelta(max) = (alpha * Pn+1 * bn^4) / (E * tr^3)

sigmac(b1) = 5314.588 psi delta(max)b1 = 0.071 insigmac(b2) = 8440.817 psi delta(max)b2 = 0.113 insigmac(b3) = 7640.818 psi delta(max)b3 = 0.057 insigmac(b4) = 9211.828 psi delta(max)b4 = 0.069 insigmac(b5) = 6847.110 psi delta(max)b5 = 0.031 insigmac(b6) = 7630.954 psi delta(max)b6 = 0.035 insigmac(b7) = 4921.964 psi delta(max)b7 = 0.013 insigmac(b8) = 5276.455 psi delta(max)b8 = 0.014 insigmac(b9) = 0.000 psi delta(max)b9 = 0.000 in

Max Stress = 18858.860 psi Max Deflection = 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 in.

1.32 m or less

1.332 m

1.11 m

1.11 m

0.814 m7.4

m

0.814 m

0.629 m

0.629 m

0.481 m

0.481 mTANK Wall

Horizontal Stiffeners

Top Stiffener L 50x50x61st Stiffener L 50x50x6 (Tank Wall plate Thickness is 0.5 in = 12.7 mm)2nd Stiffener L 70x70x83rd Stiffener L 90x90x84th Stiffener L 100x100x125th Stiffener L 100x100x126th Stiffener L 120x120x107th Stiffener L 120x120x108th Stiffener L 120x120x12

Vertical Stiffeners

L 120x120x12 (All Vertical stiffeners shall be placed at a distance of 1.32 m or Less c/c)

Top Stiffener

1st Stiffener

2nd Stiffener

Vertical Stiffeners

7th Stiffener

6th Stiffener

5th Stiffener

4th Stiffener

3rd Stiffener

8th Stiffener

Utilisation = 0.76491 < 1…..HENCE OK

Density of Steel 7850 kg/m3Weight of angle L 50x50x6 4.6 kg/mWeight of angle L 70x70x8 8.4 kg/mWeight of angle L 90x90x8 10.9 kg/mWeight of angle L 100x100x12 17.9 kg/mWeight of angle L 120x120x10 18.3 kg/mWeight of angle L 120x120x12 21.7 kg/mWeight of Base Profile W200x31.3 ASTM A-36 31.3 kg/m

2 Tag TANK

Length 3600 mmWidth 2800 mmHeight 7400 mmCompartments 1Volume of one Compartment 74.59 m3Total Volume 74.59 m3

Tank Bottom 3600 x 2800Plate Thickness 12.7 mmWeight of Plate 1004.926 kg

Spacing of Longitudinal stiffeners (L 100x100x12) 500 mmTotal longitudinal stiffeners 6 NosWeight of longitudinal stiffeners 468.72 kg

Spacing of transverse stiffeners (L 100x100x12) 3250 mmTotal transverse stiffeners 1.00 NosWeight of Transverse stiffeners 60.76 kg

Longitudinal Tank Wall 3600 x 7400Plate Thickness 12.7 mmNos of Longitudinal walls 2 NosWeight of Plate 5311.75 kg

Spacing of vertical Stiffener (L 120x120x12) 1320 mmTotal Vertical stiffeners 6.00 NosWeight of Vertical stiffeners 963.48 kg

Total intermidiate horizontal stiffeners (L50x50x6) 2.00 NosWeight of intermidiate horizontal stiffeners 33.12 kg






Total top horizontal stiffeners (L50x50x6) 2.00 NosWeight of top horizontal stiffeners 33.12 kg

Transverse Tank Wall 2800 x 7400Plate Thickness 12.7 mmNos of transverse walls 2 NosWeight of Plate 4131.361 kg

Spacing of vertical Stiffener (L 120x120x12) 1320 mmTotal Vertical stiffeners 4.00 NosWeight of Vertical stiffeners 642.32 kg







Total top horizontal stiffeners (L50x50x6) 2.00 NosWeight of top horizontal stiffeners 25.76 kg

Nos of corner angles (L90x90x8) 4.00 Nosweight of corner angles 322.64 kg

Tank Top 3600 x 2800Plate Thickness 5 mmWeight of Plate 395.64 kg

Spacing of Longitudinal stiffeners (L50x50x6) 500 mmTotal longitudinal stiffeners 6 NosWeight of longitudinal stiffeners 99.36 kg

Spacing of transverse stiffeners (L50x50x6) 3250 mmTotal transverse stiffeners 1.00 NosWeight of Transverse stiffeners 12.88 kg

Total Length of Base Profile W200x31.3 ASTM A-36 12.80 mWeight of Base Profile 400.64 kg

Tank Tag :

Total Weight of Plate (12.7 mm) ASME A240, SS316 10448.04 kgTotal Weight of Plate (5 mm) ASME A240, SS316 395.64 kgTotal Weight of Angle L 50x50x6 230 kgTotal Weight of Angle L 70x70x8 107.52 kgTotal weight of Angle L 90x90x8 462.16 kgTotal weight of Angle L 100x100x12 987.72 kgTotal weight of Angle L 120x120x10 468.48 kgTotal weight of Angle L 120x120x12 1883.56 kgTotal Weight of Base Profile W200x31.3 ASTM A-36 400.64 kg

Total weight of tank without fabrication loss = 15383.76 kg = 15.384 TonTotal weight of tank with fabrication loss (20%) = 18460.51 kg = 18.461 Ton

modelo de dimension amen to tanques retangulares

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