ASME STS-1,2006

Input values Reference

3 sec gust basic wind speed, V 34 m/s 76.011 mph SP-1275

Importance factor, I 1.15 1.15 Table I-3, ASME

Exposure category C C Cl 4.3.3.4 ASME

Structural Category IV IV Table I-2, ASME

Stack height, h 40 m 131.23 ft

stack outer dia, D 3.5 m 11.48 ft

plate thickness

Minimum thickness 4.76 mm 0.1875 in Table 4.4.7, ASME

Corrosion allowance, Internal 3.00 mm

Corrosion allowance, external 0.00 mm

Minimum thickness required 7.76 mm

16-40m 8 mm 0.315 in

4.3-16m 10 mm 0.394 in

Adopted thickness 0-4.3m 12 mm 0.472 in

first mode frequency, n1 1.898 Hz

621.2 kg/m 417.7 lb/ft

Air density ρ 1.225 kg/cum 0.076 lbm/ft3

Moment of Inertia, Iz

Damping calculaton

0.002 Table 5.1, ASME

Stack dia at top 1/3h, D_ 3.500 m 11.48 ft

Vel.pr expo. Coeff, Kz 1.340 Table I-4, ASME

Topographic factor, Kzt 1.000 Fig I-2, ASME

Velocity pressure at h, qz 1.1 kN/m2 22.793 psf Eq 4.4, ASME

D*(qz)^0.5 3.66 54.82

h/D 11.43

0.7 Force coefficient, cf 0.62 (upto 24m) Table I-5, ASME

1.4 Force coefficient, cf 1.05 (upto 40m) Table I-5, ASME

b_ 0.65 Table I-1, ASME

0.154 Table I-1, ASME

Mean hourly wind speed, Vz_ 25.27 m/s 82.838 ft/secAero dynamic damping, βa 0.0045

0.007 βs+βa

Gust effect calculationZmin 4.572 m 15 ft Table I-1, ASME

c 0.2 0.2 Table I-1, ASME

Equi.str ht, z_ 24 m 78.740 ftIntensity of turbulence, Iz_ 0.173

l 500 ft Table I-1, ASME

0.200 Table I-1, ASME

594.986Background response, Q 0.892

Mass/unit length of top 1/3 stack, ma

Structural damping, βs

α_

total damping, β

ε_Intergral length scale of turbulence, Lz

factor gq 3.400 App I, ASME

factor gv 3.400 App I, ASME

gr 4.340 App I, ASME

N1 13.632Rn 0.0265Rh 0.06972 13.832RB 0.51541 ηb 1.210Rd 0.21647 ηd 4.052

Resonant Response factor, R 0.304Calculated Gust factor, Gf 0.912

Assumed Gust factor, Gf 1.0

GEOMETRY

0 3500 12 3 0 10.322 1314.95 2.00E+07 1142712000 3500 12 3 0 10.322 1314.95 2.00E+07 1142714300 3500 10 3 0 8.607 1096.42 1.67E+07 953906000 3500 10 3 0 8.607 1096.42 1.67E+07 953908000 3500 10 3 0 8.607 1096.42 1.67E+07 95390

10000 3500 10 3 0 8.607 1096.42 1.67E+07 9539012000 3500 10 3 0 8.607 1096.42 1.67E+07 9539014000 3500 10 3 0 8.607 1096.42 1.67E+07 9539016000 3500 8 3 0 6.889 877.64 1.34E+07 7644318000 3500 8 3 0 6.889 877.64 1.34E+07 7644320000 3500 8 3 0 6.889 877.64 1.34E+07 7644321300 3500 8 3 0 6.889 877.64 1.34E+07 7644324000 3500 8 3 0 6.889 877.64 1.34E+07 7644326000 3500 8 3 0 6.889 877.64 1.34E+07 7644328000 3500 8 3 0 6.889 877.64 1.34E+07 7644330000 3500 8 3 0 6.889 877.64 1.34E+07 7644332000 3500 8 3 0 6.889 877.64 1.34E+07 7644334000 3500 8 3 0 6.889 877.64 1.34E+07 7644336000 3500 8 3 0 6.889 877.64 1.34E+07 7644338000 3500 8 3 0 6.889 877.64 1.34E+07 7644340000 3500 8 3 0 6.889 877.64 1.34E+07 76443

LOAD CALCULATIONS

0 3500 0.85 0.7 0.692 0.065 5.041 50.411 20.5112000 3500 0.85 0.7 0.692 0.065 4.911 49.112 20.6484300 3500 0.85 0.7 0.692 0.065 4.762 47.619 16.5896000 3500 0.9 0.7 0.733 0.069 4.645 46.450 18.1458000 3500 0.95 0.7 0.774 0.073 4.500 44.998 17.541

10000 3500 1 0.7 0.814 0.076 4.347 43.470 16.91112000 3500 1.04 0.7 0.847 0.079 4.188 41.881 16.26214000 3500 1.07 0.7 0.871 0.082 4.025 40.247 15.59016000 3500 1.11 0.7 0.904 0.085 3.855 38.551 14.90218000 3500 1.13 0.7 0.920 0.086 3.682 36.824 12.971

ηh

Elevation (mm)

External Dia (mm)

Shell thickness (mm)

Inernal corrosion

(mm)

External corrosion

(mm)Full weight

(kN/m)

Sectional area

(cm2)Full inertia

J (cm4)

Section modulus W (cm3)

Elevation (mm)

External Dia (mm)

Velocity pressure coefficie

nt, Kz

Force coefficient

(Cf)

Wind pressure, qz (kN/m2)

wind load along wind

dir wz_(kN/m)

Shear due to wind

wz_(kN)

Shear due to wind wz_(kN)

Moment due to

wind wz_ (kNm)

20000 3500 1.16 0.7 0.945 0.089 3.505 35.052 11.25921300 3500 1.17 0.7 0.953 0.089 3.389 33.890 16.19824000 3500 1.2 0.7 0.977 0.092 3.141 31.414 11.44726000 3500 1.22 1.4 0.994 0.186 2.769 27.686 9.93828000 3500 1.24 1.4 1.010 0.189 2.390 23.897 8.40430000 3500 1.26 1.4 1.026 0.193 2.005 20.046 6.84532000 3500 1.28 1.4 1.042 0.196 1.613 16.135 5.26234000 3500 1.3 1.4 1.059 0.199 1.216 12.162 3.66436000 3500 1.31 1.4 1.067 0.200 0.816 8.159 2.04438000 3500 1.33 1.4 1.083 0.203 0.409 4.095 0.40940000 3500 1.34 1.4 1.091 0.205 0 0.000 0

STRESS VERIFICATIONS

Material propertiesSteel for shell S275JR

fy 275 N/mm2Mean temperature of shell 150 degC

Fy, op 200 N/mm2 29.00653 ksiE, op 203000 N/mm2 29441624 psiparameters2.8Fy/E 0.00287.2Fy/E 0.007110Fy/E 0.0099Le = 2h 80000 mm

Factor of safety 1.5Maximum stiffener spacing 7000 mm 22.96588 ft Table 4.4.7, ASME

Design stiffener offset 3000 mm

t/D0 772.15 167 4045 0.0026 OK 7.82 47.08 0.001

2000 746.83 165 3708 0.0026 OK 7.57 43.15 0.0014300 722.36 163 3325 0.0020 OK 9.40 49.67 0.0016000 699.06 161 3046 0.0020 OK 9.10 45.50 0.0018000 666.17 155 2728 0.0020 OK 8.67 40.75 0.001

10000 631.28 148 2424 0.0020 OK 8.22 36.21 0.00112000 596.39 140 2135 0.0020 OK 7.76 31.89 0.00114000 561.50 132 1862 0.0020 OK 7.31 27.81 0.00116000 530.05 123 1605 0.0014 OK 9.65 33.51 0.00118000 498.59 114 1366 0.0014 OK 9.08 28.52 0.00120000 467.14 105 1146 0.0014 OK 8.51 23.92 0.00121300 440.51 97 1014 0.0014 OK 8.02 21.17 0.00124000 400.23 86 762 0.0014 OK 7.29 15.91 0.00126000 360.45 76 594 0.0014 OK 6.57 12.40 0.00228000 343.17 68 442 0.0014 OK 6.25 9.23 0.00230000 326.39 58 309 0.0014 OK 5.95 6.45 0.00232000 185.12 45 204 0.0014 OK 3.37 4.26 0.00234000 169.34 35 117 0.0014 OK 3.08 2.44 0.00236000 154.06 25 53 0.0014 OK 2.81 1.11 0.00238000 139.28 15 11 0.0014 OK 2.54 0.23 0.00240000 0.00 0 0 0.0014 OK 0.00 0.00 0.002

STIFFENER VERIFICATIONS

Elevation (mm)

Axial force (kN)

Shear force (kN)

Bending moment (kNm)

Complied? (t/D <=10Fy/E)

σ1 N/A

(N/mm2)

σ2 M/W

(N/mm2)

σ3 fc

(N/mm2)

Stiffener considered L 150*10Moment of Inertia 258 cm4

Area 29.3 cm2Section modulus 64.02 cm3

Elastic modulus, E 203000 N/mm2

0 3000 0.692 2.74 9.728 3.74 10.0 OK2000 3000 0.692 2.74 9.728 3.74 10.0 OK4300 3000 0.692 2.74 9.728 3.74 10.0 OK6000 3000 0.733 2.90 9.728 3.96 10.6 OK8000 3000 0.774 3.06 9.728 4.18 11.2 OK

10000 3000 0.814 3.23 9.728 4.40 11.8 OK12000 3000 0.847 3.35 9.728 4.57 12.2 OK14000 3000 0.871 3.45 9.728 4.70 12.6 OK16000 3000 0.904 3.58 9.728 4.88 13.1 OK18000 3000 0.920 3.64 9.728 4.97 13.3 OK20000 3000 0.945 3.74 9.728 5.10 13.7 OK21300 3000 0.953 3.77 9.728 5.14 13.8 OK24000 3000 0.977 3.87 9.728 5.27 14.1 OK26000 3000 0.994 3.93 9.728 5.36 14.4 OK28000 3000 1.010 4.00 9.728 5.45 14.6 OK30000 3000 1.026 4.06 9.728 5.54 14.8 OK32000 3000 1.042 4.13 9.728 5.63 15.1 OK34000 3000 1.059 4.19 9.728 5.71 15.3 OK36000 3000 1.067 4.23 9.728 5.76 15.4 OK38000 3000 1.083 4.29 9.728 5.85 15.7 OK40000 3000 1.091 4.32 9.728 5.89 15.8 OK

Elevation (mm)

Stiffener spacing, ls (mm)

Wind pressure coeff, q (kN/m2)

Min. Stiffener inertia (cm4)

Allowable compress. stress in stiffeners Sccs N/mm2

Min. sectional area of stiffener

cm2

Min. sectional modulus

of stiffener Ss cm3

Stiffener verification

ASME STS-1,2006

Table I-3, ASME

Cl 4.3.3.4 ASME

Table I-2, ASME

120 1.31 7 1

131.23 1.34 11.43 1.05

140 1.36 25 1.2

Table 4.4.7, ASME

Table 5.1, ASME

k1 0

Table I-4, ASME k2 1

k3 1

kzt 1.0

Table I-5, ASME

Table I-5, ASME

Table I-1, ASME

Table I-1, ASME

Table I-1, ASME 0.6h or zminTable I-1, ASME

Table I-1, ASME

Table I-1, ASME

9.0 987.06 1.50E+07 85924 123.43 0 0 303.05 4.689.0 987.06 1.50E+07 85924 123.43 0 0 282.41 4.687.0 768.15 1.17E+07 66945 123.50 0 0 262.61 4.687.0 768.15 1.17E+07 66945 123.50 0 0 247.98 4.687.0 768.15 1.17E+07 66945 123.50 0 0 230.77 4.687.0 768.15 1.17E+07 66945 123.50 0 0 213.55 4.687.0 768.15 1.17E+07 66945 123.50 0 0 196.34 4.687.0 768.15 1.17E+07 66945 123.50 0 0 179.13 4.685.0 548.99 8.38E+06 47900 123.57 0 0 165.35 4.685.0 548.99 8.38E+06 47900 123.57 0 0 151.57 4.685.0 548.99 8.38E+06 47900 123.57 0 0 137.79 4.685.0 548.99 8.38E+06 47900 123.57 1 0 128.83 4.685.0 548.99 8.38E+06 47900 123.57 1 0 110.23 4.005.0 548.99 8.38E+06 47900 123.57 1 0 96.45 3.505.0 548.99 8.38E+06 47900 123.57 1 0 82.67 3.005.0 548.99 8.38E+06 47900 123.57 1 1 68.89 2.505.0 548.99 8.38E+06 47900 123.57 1 0 55.12 2.005.0 548.99 8.38E+06 47900 123.57 1 0 41.34 1.505.0 548.99 8.38E+06 47900 123.57 1 0 27.56 1.005.0 548.99 8.38E+06 47900 123.57 1 1 13.78 0.505.0 548.99 8.38E+06 47900 123.57 1 0 0 0.00

Additional loads (wind load on ladders + horizontal thrust loads)

1455 0.00 67.45 1649 117.860 3104.00 4.68 169 44.21340 0.16 67.13 1527 116.240 2867.00 4.68 158 44.21211 0.35 66.33 1387 113.953 2598.00 4.68 145 44.21119 0.48 65.52 1284 111.966 2403.00 4.68 136 44.21014 0.64 64.23 1165 109.230 2179.00 4.68 125 41.4912 0.80 62.63 1048 106.098 1960.00 4.68 114 37.1814 0.96 60.70 934 102.583 1748.00 4.68 103 32.8719 1.12 58.45 824 98.701 1543.00 4.68 92 28.5628 1.28 55.89 717 94.438 1345.00 4.68 81 24.2542 1.44 53.00 616 89.822 1158.00 4.68 69 19.9

Corroded thickness

(mm)

Sectional area (cm2)

Full inertia J

(cm4)

Section modulus W (cm3)

Radius of gyration

(cm)Ladder

presenceWalkway presence

Shell weight

(kN)Ladder wt

(kN)

Moment due to

wind wz_ (kNm)

Fluctuating Wind load Wd

(kN)

Shear due to wind

wd(kN)

Moment due to

wind wd (kNm)

Total V on

cylinder (kN)

Total M on

cylinder (kNm)

Shear due to

wind on ladders

(kN)

Moment due to

wind on ladders (kNm)

Shear due to thrust

loads (kN)

460 1.60 49.79 520 84.840 980.00 4.68 58 15.6409 1.71 47.57 461 81.456 870.00 4.68 51 11.3308 1.93 42.37 347 73.782 655.00 4.00 37 8.5238 2.09 38.19 271 65.881 509.00 3.50 29 7176 2.25 33.70 203 57.598 379.00 3.00 21 7122 2.41 28.89 144 48.933 266.00 2.50 15 779 2.57 23.75 94 39.886 173.00 2.00 10 3.544 2.73 18.29 54 30.457 98.00 1.50 5 3.520 2.89 12.52 24 20.677 44.00 1.00 2 3.55 3.05 6.42 6 10.514 11.00 0.50 0 3.50 3.21 0 0 0.000 0.00 0.00 0 0

Table 4.4.7, ASME

1.69 54.90 54.90 1.053 1.00 87.00 OK 87.00 OK1.67 50.72 50.72 1.053 1.00 87.00 OK 87.00 OK2.12 59.07 59.07 1.225 1.00 67.67 OK 67.67 OK2.09 54.60 54.60 1.225 1.00 67.67 OK 67.67 OK2.02 49.42 49.42 1.225 1.00 67.67 OK 67.67 OK1.93 44.43 44.43 1.225 1.00 67.67 OK 67.67 OK1.82 39.66 39.66 1.225 1.00 67.67 OK 67.67 OK1.72 35.12 35.12 1.225 1.00 67.67 OK 67.67 OK2.25 43.16 43.16 1.410 1.00 48.33 OK 48.33 OK2.08 37.60 37.60 1.410 1.00 48.33 OK 48.33 OK1.91 32.43 32.44 1.410 1.00 48.33 OK 48.33 OK1.77 29.19 29.19 1.410 1.00 48.33 OK 48.33 OK1.57 23.20 23.20 1.410 1.00 48.33 OK 48.33 OK1.39 18.97 18.97 1.410 1.00 48.33 OK 48.33 OK1.23 15.48 15.48 1.410 1.00 48.33 OK 48.33 OK1.06 12.40 12.40 1.410 1.00 48.33 OK 48.33 OK0.83 7.63 7.63 1.410 1.00 48.33 OK 48.33 OK0.65 5.53 5.53 1.410 1.00 48.33 OK 48.33 OK0.46 3.91 3.91 1.410 1.00 48.33 OK 48.33 OK0.26 2.77 2.77 1.410 1.00 48.33 OK 48.33 OK0.00 0.00 0.00 1.410 1.00 48.33 OK 48.33 OK

τ T/A

(N/mm2)

σ1 + σ2

(N/mm2)Vonmises (N/mm2)

Parameter Ks

Parameter Y

Allow. Compressive stress

Scl (N/mm2)

Verify N/A < Scl

Allowable bending

stress Sbl (N/mm2)

Verify N/A +M/W< Sbl

0 0 562.15 772.150 0 536.83 746.830 4 512.36 722.360 11 489.06 699.060 13 456.17 666.170 13 421.28 631.280 13 386.39 596.390 13 351.50 561.500 13 320.05 530.050 13 288.59 498.590 13 257.14 467.140 17 230.51 440.510 12 10 190.23 400.230 0 160.45 360.450 0 143.17 343.170 25 100 126.39 326.390 0 85.12 185.120 0 69.34 169.340 0 54.06 154.060 25 100 39.28 139.280 0 0 0.00

Additional loads (wind load on ladders + horizontal thrust loads)

772 166.74 4045683 165.12 3708582 162.83 3325507 160.84 3046424 155.31 2728350 147.87 2424284 140.06 2135227 131.88 1862179 123.31 1605139 114.40 1366

Insulation wt (kN)

Additional dead

load (kN)

Live loads (kN)

Total Dead

load (kN)Total wt

(kN)

Moment due to thrust loads (kNm)

Total shear (kN)

Total Moment (kNm)

108 105.12 114693 97.43 101470 86.28 76256 76.38 59442 67.60 44228 58.43 30921 45.39 20414 35.46 1177 25.18 530 14.51 110 0.00 0

1.0 26.76 OK 0.63 OK1.0 26.76 OK 0.58 OK1.0 18.36 OK 0.87 OK1.0 18.36 OK 0.81 OK1.0 18.36 OK 0.73 OK1.0 18.36 OK 0.66 OK1.0 18.36 OK 0.59 OK1.0 18.36 OK 0.52 OK1.0 11.08 OK 0.89 OK1.0 11.08 OK 0.78 OK1.0 11.08 OK 0.67 OK1.0 11.08 OK 0.60 OK1.0 11.08 OK 0.48 OK1.0 11.08 OK 0.39 OK1.0 11.08 OK 0.32 OK1.0 11.08 OK 0.26 OK1.0 11.08 OK 0.16 OK1.0 11.08 OK 0.11 OK1.0 11.08 OK 0.08 OK1.0 11.08 OK 0.06 OK1.0 11.08 OK 0.00 OK

Parameter K (for Scc)

Allowable circumferential stress

Scc (N/mm2)

Verify fc < Scc

Combined Scl and Scc

Verify combined Scl

and Scc <1