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
Mass/unit length of top 1/3 stack, ma 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
Structural damping, βs 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
α_ 0.154 Table I-1, ASME
Mean hourly wind speed, Vz_ 25.27 m/s 82.838 ft/sec Aero dynamic damping, βa 0.0045
total damping, β 0.007βs+βa
Gust effect calculation
Zmin 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 ft
Intensity of turbulence, Iz_ 0.173
l 500 ft Table I-1, ASME
ε_ 0.200 Table I-1, ASME
Intergral length scale of turbulence, Lz 594.986
Background response, Q 0.892
factor gq 3.400 App I, ASME
gr 4.340 App I, ASME N1 13.632 Rn 0.0265 Rh 0.06972 ηh 13.832 RB 0.51541 ηb 1.210 Rd 0.21647 ηd 4.052
Resonant Response factor, R 0.304 Calculated Gust factor, Gf 0.912 Assumed Gust factor, Gf 1.0
GEOMETRY 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) 0 3500 12 3 0 10.322 1314.95 2.00E+07 114271 2000 3500 12 3 0 10.322 1314.95 2.00E+07 114271 4300 3500 10 3 0 8.607 1096.42 1.67E+07 95390 6000 3500 10 3 0 8.607 1096.42 1.67E+07 95390 8000 3500 10 3 0 8.607 1096.42 1.67E+07 95390 10000 3500 10 3 0 8.607 1096.42 1.67E+07 95390 12000 3500 10 3 0 8.607 1096.42 1.67E+07 95390 14000 3500 10 3 0 8.607 1096.42 1.67E+07 95390 16000 3500 8 3 0 6.889 877.64 1.34E+07 76443 18000 3500 8 3 0 6.889 877.64 1.34E+07 76443 20000 3500 8 3 0 6.889 877.64 1.34E+07 76443 21300 3500 8 3 0 6.889 877.64 1.34E+07 76443 24000 3500 8 3 0 6.889 877.64 1.34E+07 76443 26000 3500 8 3 0 6.889 877.64 1.34E+07 76443 28000 3500 8 3 0 6.889 877.64 1.34E+07 76443 30000 3500 8 3 0 6.889 877.64 1.34E+07 76443 32000 3500 8 3 0 6.889 877.64 1.34E+07 76443 34000 3500 8 3 0 6.889 877.64 1.34E+07 76443 36000 3500 8 3 0 6.889 877.64 1.34E+07 76443 38000 3500 8 3 0 6.889 877.64 1.34E+07 76443 40000 3500 8 3 0 6.889 877.64 1.34E+07 76443 LOAD CALCULATIONS 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) 0 3500 0.85 0.7 0.692 0.065 5.041 50.411 20.511 2000 3500 0.85 0.7 0.692 0.065 4.911 49.112 20.648 4300 3500 0.85 0.7 0.692 0.065 4.762 47.619 16.589 6000 3500 0.9 0.7 0.733 0.069 4.645 46.450 18.145 8000 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 16.911 12000 3500 1.04 0.7 0.847 0.079 4.188 41.881 16.262 14000 3500 1.07 0.7 0.871 0.082 4.025 40.247 15.590 16000 3500 1.11 0.7 0.904 0.085 3.855 38.551 14.902 18000 3500 1.13 0.7 0.920 0.086 3.682 36.824 12.971 20000 3500 1.16 0.7 0.945 0.089 3.505 35.052 11.259 21300 3500 1.17 0.7 0.953 0.089 3.389 33.890 16.198 24000 3500 1.2 0.7 0.977 0.092 3.141 31.414 11.447 26000 3500 1.22 1.4 0.994 0.186 2.769 27.686 9.938
28000 3500 1.24 1.4 1.010 0.189 2.390 23.897 8.404 30000 3500 1.26 1.4 1.026 0.193 2.005 20.046 6.845 32000 3500 1.28 1.4 1.042 0.196 1.613 16.135 5.262 34000 3500 1.3 1.4 1.059 0.199 1.216 12.162 3.664 36000 3500 1.31 1.4 1.067 0.200 0.816 8.159 2.044 38000 3500 1.33 1.4 1.083 0.203 0.409 4.095 0.409 40000 3500 1.34 1.4 1.091 0.205 0 0.000 0 STRESS VERIFICATIONS Material properties
Steel for shell S275JR
fy 275 N/mm2
Mean temperature of shell 150 degC
Fy, op 200 N/mm2 29.00653 ksi E, op 203000 N/mm2 29441624 psi parameters 2.8Fy/E 0.0028 7.2Fy/E 0.0071 10Fy/E 0.0099 Le = 2h 80000 mm Factor of safety 1.5
Maximum stiffener spacing 7000 mm 22.96588 ft Table 4.4.7, ASME
Design stiffener offset 3000 mm
Elevation (mm) Axial force (kN) Shear force (kN) Bending moment (kNm) t/D Complied? (t/D <=10Fy/E) σ1 N/A (N/mm2) σ2 M/W (N/mm2) σ3 fc (N/mm2) 0 772.15 167 4045 0.0026 OK 7.82 47.08 0.001 2000 746.83 165 3708 0.0026 OK 7.57 43.15 0.001 4300 722.36 163 3325 0.0020 OK 9.40 49.67 0.001 6000 699.06 161 3046 0.0020 OK 9.10 45.50 0.001 8000 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 0.001 12000 596.39 140 2135 0.0020 OK 7.76 31.89 0.001 14000 561.50 132 1862 0.0020 OK 7.31 27.81 0.001 16000 530.05 123 1605 0.0014 OK 9.65 33.51 0.001 18000 498.59 114 1366 0.0014 OK 9.08 28.52 0.001 20000 467.14 105 1146 0.0014 OK 8.51 23.92 0.001 21300 440.51 97 1014 0.0014 OK 8.02 21.17 0.001 24000 400.23 86 762 0.0014 OK 7.29 15.91 0.001 26000 360.45 76 594 0.0014 OK 6.57 12.40 0.002 28000 343.17 68 442 0.0014 OK 6.25 9.23 0.002 30000 326.39 58 309 0.0014 OK 5.95 6.45 0.002 32000 185.12 45 204 0.0014 OK 3.37 4.26 0.002 34000 169.34 35 117 0.0014 OK 3.08 2.44 0.002 36000 154.06 25 53 0.0014 OK 2.81 1.11 0.002 38000 139.28 15 11 0.0014 OK 2.54 0.23 0.002 40000 0.00 0 0 0.0014 OK 0.00 0.00 0.002 STIFFENER VERIFICATIONS Stiffener considered L 150*10 Moment of Inertia 258 cm4 Area 29.3 cm2 Section modulus 64.02 cm3 Elastic modulus, E 203000 N/mm2
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 0 3000 0.692 2.74 9.728 3.74 10.0 OK 2000 3000 0.692 2.74 9.728 3.74 10.0 OK 4300 3000 0.692 2.74 9.728 3.74 10.0 OK 6000 3000 0.733 2.90 9.728 3.96 10.6 OK 8000 3000 0.774 3.06 9.728 4.18 11.2 OK 10000 3000 0.814 3.23 9.728 4.40 11.8 OK 12000 3000 0.847 3.35 9.728 4.57 12.2 OK 14000 3000 0.871 3.45 9.728 4.70 12.6 OK 16000 3000 0.904 3.58 9.728 4.88 13.1 OK 18000 3000 0.920 3.64 9.728 4.97 13.3 OK 20000 3000 0.945 3.74 9.728 5.10 13.7 OK 21300 3000 0.953 3.77 9.728 5.14 13.8 OK 24000 3000 0.977 3.87 9.728 5.27 14.1 OK 26000 3000 0.994 3.93 9.728 5.36 14.4 OK 28000 3000 1.010 4.00 9.728 5.45 14.6 OK 30000 3000 1.026 4.06 9.728 5.54 14.8 OK 32000 3000 1.042 4.13 9.728 5.63 15.1 OK 34000 3000 1.059 4.19 9.728 5.71 15.3 OK 36000 3000 1.067 4.23 9.728 5.76 15.4 OK 38000 3000 1.083 4.29 9.728 5.85 15.7 OK 40000 3000 1.091 4.32 9.728 5.89 15.8 OK
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 zmin
Table I-1, ASME
Table I-1, ASME Table I-1, ASME
Corroded thickness (mm) Sectiona l area (cm2) Full inertia J (cm4) Section modulus W (cm3) Radius of gyration (cm) Ladder presence Walkway presence Shell weight (kN) Ladder wt (kN) 9.0 987.06 1.50E+07 85924 123.43 0 0 303.05 4.68 9.0 987.06 1.50E+07 85924 123.43 0 0 282.41 4.68 7.0 768.15 1.17E+07 66945 123.50 0 0 262.61 4.68 7.0 768.15 1.17E+07 66945 123.50 0 0 247.98 4.68 7.0 768.15 1.17E+07 66945 123.50 0 0 230.77 4.68 7.0 768.15 1.17E+07 66945 123.50 0 0 213.55 4.68 7.0 768.15 1.17E+07 66945 123.50 0 0 196.34 4.68 7.0 768.15 1.17E+07 66945 123.50 0 0 179.13 4.68 5.0 548.99 8.38E+06 47900 123.57 0 0 165.35 4.68 5.0 548.99 8.38E+06 47900 123.57 0 0 151.57 4.68 5.0 548.99 8.38E+06 47900 123.57 0 0 137.79 4.68 5.0 548.99 8.38E+06 47900 123.57 1 0 128.83 4.68 5.0 548.99 8.38E+06 47900 123.57 1 0 110.23 4.00 5.0 548.99 8.38E+06 47900 123.57 1 0 96.45 3.50 5.0 548.99 8.38E+06 47900 123.57 1 0 82.67 3.00 5.0 548.99 8.38E+06 47900 123.57 1 1 68.89 2.50 5.0 548.99 8.38E+06 47900 123.57 1 0 55.12 2.00 5.0 548.99 8.38E+06 47900 123.57 1 0 41.34 1.50 5.0 548.99 8.38E+06 47900 123.57 1 0 27.56 1.00 5.0 548.99 8.38E+06 47900 123.57 1 1 13.78 0.50 5.0 548.99 8.38E+06 47900 123.57 1 0 0 0.00
Additional loads (wind load on ladders + horizontal thrust loads) Moment due to wind wz_ (kNm) Fluctuati ng 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) 1455 0.00 67.45 1649 117.860 3104.00 4.68 169 44.2 1340 0.16 67.13 1527 116.240 2867.00 4.68 158 44.2 1211 0.35 66.33 1387 113.953 2598.00 4.68 145 44.2 1119 0.48 65.52 1284 111.966 2403.00 4.68 136 44.2 1014 0.64 64.23 1165 109.230 2179.00 4.68 125 41.4 912 0.80 62.63 1048 106.098 1960.00 4.68 114 37.1 814 0.96 60.70 934 102.583 1748.00 4.68 103 32.8 719 1.12 58.45 824 98.701 1543.00 4.68 92 28.5 628 1.28 55.89 717 94.438 1345.00 4.68 81 24.2 542 1.44 53.00 616 89.822 1158.00 4.68 69 19.9 460 1.60 49.79 520 84.840 980.00 4.68 58 15.6 409 1.71 47.57 461 81.456 870.00 4.68 51 11.3 308 1.93 42.37 347 73.782 655.00 4.00 37 8.5 238 2.09 38.19 271 65.881 509.00 3.50 29 7
176 2.25 33.70 203 57.598 379.00 3.00 21 7 122 2.41 28.89 144 48.933 266.00 2.50 15 7 79 2.57 23.75 94 39.886 173.00 2.00 10 3.5 44 2.73 18.29 54 30.457 98.00 1.50 5 3.5 20 2.89 12.52 24 20.677 44.00 1.00 2 3.5 5 3.05 6.42 6 10.514 11.00 0.50 0 3.5 0 3.21 0 0 0.000 0.00 0.00 0 0 Table 4.4.7, ASME
τ
T/A (N/mm2) σ1 + σ2 (N/mm2) Vonmises (N/mm2) Parameter Ks Parameter Y Allow. Compressi ve stress Scl (N/mm2) Verify N/A < Scl Allowable bending stress Sbl (N/mm2) Verify N/A +M/W< Sbl 1.69 54.90 54.90 1.053 1.00 87.00 OK 87.00 OK 1.67 50.72 50.72 1.053 1.00 87.00 OK 87.00 OK 2.12 59.07 59.07 1.225 1.00 67.67 OK 67.67 OK 2.09 54.60 54.60 1.225 1.00 67.67 OK 67.67 OK 2.02 49.42 49.42 1.225 1.00 67.67 OK 67.67 OK 1.93 44.43 44.43 1.225 1.00 67.67 OK 67.67 OK 1.82 39.66 39.66 1.225 1.00 67.67 OK 67.67 OK 1.72 35.12 35.12 1.225 1.00 67.67 OK 67.67 OK 2.25 43.16 43.16 1.410 1.00 48.33 OK 48.33 OK 2.08 37.60 37.60 1.410 1.00 48.33 OK 48.33 OK 1.91 32.43 32.44 1.410 1.00 48.33 OK 48.33 OK 1.77 29.19 29.19 1.410 1.00 48.33 OK 48.33 OK 1.57 23.20 23.20 1.410 1.00 48.33 OK 48.33 OK 1.39 18.97 18.97 1.410 1.00 48.33 OK 48.33 OK 1.23 15.48 15.48 1.410 1.00 48.33 OK 48.33 OK 1.06 12.40 12.40 1.410 1.00 48.33 OK 48.33 OK 0.83 7.63 7.63 1.410 1.00 48.33 OK 48.33 OK 0.65 5.53 5.53 1.410 1.00 48.33 OK 48.33 OK 0.46 3.91 3.91 1.410 1.00 48.33 OK 48.33 OK 0.26 2.77 2.77 1.410 1.00 48.33 OK 48.33 OK 0.00 0.00 0.00 1.410 1.00 48.33 OK 48.33 OKInsulatio n wt (kN) Additiona l dead load (kN) Live loads (kN) Total Dead load (kN) Total wt (kN) 0 0 562.15 772.15 0 0 536.83 746.83 0 4 512.36 722.36 0 11 489.06 699.06 0 13 456.17 666.17 0 13 421.28 631.28 0 13 386.39 596.39 0 13 351.50 561.50 0 13 320.05 530.05 0 13 288.59 498.59 0 13 257.14 467.14 0 17 230.51 440.51 0 12 10 190.23 400.23 0 0 160.45 360.45 0 0 143.17 343.17 0 25 100 126.39 326.39 0 0 85.12 185.12 0 0 69.34 169.34 0 0 54.06 154.06 0 25 100 39.28 139.28 0 0 0 0.00
Additional loads (wind load on ladders + horizontal thrust loads) Moment due to thrust loads (kNm) Total shear (kN) Total Moment (kNm) 772 166.74 4045 683 165.12 3708 582 162.83 3325 507 160.84 3046 424 155.31 2728 350 147.87 2424 284 140.06 2135 227 131.88 1862 179 123.31 1605 139 114.40 1366 108 105.12 1146 93 97.43 1014 70 86.28 762 56 76.38 594
42 67.60 442 28 58.43 309 21 45.39 204 14 35.46 117 7 25.18 53 0 14.51 11 0 0.00 0 Parameter K (for Scc) Allowable circumfere ntial stress Scc (N/mm2) Verify fc < Scc Combined Scl and Scc Verify combined Scl and Scc <1 1.0 26.76 OK 0.63 OK 1.0 26.76 OK 0.58 OK 1.0 18.36 OK 0.87 OK 1.0 18.36 OK 0.81 OK 1.0 18.36 OK 0.73 OK 1.0 18.36 OK 0.66 OK 1.0 18.36 OK 0.59 OK 1.0 18.36 OK 0.52 OK 1.0 11.08 OK 0.89 OK 1.0 11.08 OK 0.78 OK 1.0 11.08 OK 0.67 OK 1.0 11.08 OK 0.60 OK 1.0 11.08 OK 0.48 OK 1.0 11.08 OK 0.39 OK 1.0 11.08 OK 0.32 OK 1.0 11.08 OK 0.26 OK 1.0 11.08 OK 0.16 OK 1.0 11.08 OK 0.11 OK 1.0 11.08 OK 0.08 OK 1.0 11.08 OK 0.06 OK 1.0 11.08 OK 0.00 OK