ASME STS-1,2006 Input values
Reference
3 sec gust basic wind speed, V Importance factor, I
34 m/s 1.15
76.011 mph
SP-1275
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
Minimum thickness
4.76 mm
0.1875 in
plate thickness 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 Mass/unit length of top 1/3 stack,
ma
Air density ρ
Table 4.4.7, ASME
1.898 Hz 621.2 kg/m
417.7 lb/ft
1.225 kg/cum
0.076 lbm/ft3
Moment of Inertia, Iz Damping calculaton Structural damping, βs Stack dia at top 1/3h, D_
0.002 3.500 m
Table 5.1, ASME
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
D*(qz)^0.5
3.66
h/D
11.43
22.793 psf
Eq 4.4, ASME
54.82
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_ α_ Mean hourly wind speed, Vz_ Aero dynamic damping, βa total damping, β
0.65 0.154 25.27 m/s 0.0045 0.007 βs+βa
Table I-1, ASME Table I-1, ASME
82.838 ft/sec
Gust effect calculation Zmin c Equi.str ht, z_ Intensity of turbulence, Iz_ l ε_ Intergral length scale of turbulence, Lz Background response, Q factor gq factor gv
4.572 m 0.2 24 m
3.400 3.400
15 ft 0.2 78.740 ft 0.173
Table I-1, ASME
500 ft 0.200 594.986 0.892
Table I-1, ASME
Table I-1, ASME
Table I-1, ASME
App I, ASME App I, ASME
gr N1 Rn Rh RB Rd Resonant Response factor, R Calculated Gust factor, Gf Assumed Gust factor, Gf
4.340 13.632 0.0265 0.06972 0.51541 0.21647 0.304 0.912 1.0
App I, ASME
ηh ηb ηd
13.832 1.210 4.052
GEOMETRY Shell Inernal External Sectional Section Elevation External thickness corrosion corrosion Full weight area Full inertia modulus (mm) Dia (mm) (mm) (mm) (mm) (kN/m) (cm2) J (cm4) 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 External (mm) Dia (mm) 0 3500 2000 3500 4300 3500 6000 3500 8000 3500 10000 3500 12000 3500 14000 3500 16000 3500 18000 3500 20000 3500 21300 3500 24000 3500 26000 3500
Velocity wind load Shear Moment pressure Force Wind along wind due to Shear due due to coefficie coefficient pressure, dir wind to wind wind wz_ nt, Kz (Cf) qz (kN/m2) wz_(kN/m) wz_(kN) wz_(kN) (kNm) 0.85 0.7 0.692 0.065 5.041 50.411 20.511 0.85 0.7 0.692 0.065 4.911 49.112 20.648 0.85 0.7 0.692 0.065 4.762 47.619 16.589 0.9 0.7 0.733 0.069 4.645 46.450 18.145 0.95 0.7 0.774 0.073 4.500 44.998 17.541 1 0.7 0.814 0.076 4.347 43.470 16.911 1.04 0.7 0.847 0.079 4.188 41.881 16.262 1.07 0.7 0.871 0.082 4.025 40.247 15.590 1.11 0.7 0.904 0.085 3.855 38.551 14.902 1.13 0.7 0.920 0.086 3.682 36.824 12.971 1.16 0.7 0.945 0.089 3.505 35.052 11.259 1.17 0.7 0.953 0.089 3.389 33.890 16.198 1.2 0.7 0.977 0.092 3.141 31.414 11.447 1.22 1.4 0.994 0.186 2.769 27.686 9.938
28000 30000 32000 34000 36000 38000 40000
3500 3500 3500 3500 3500 3500 3500
1.24 1.26 1.28 1.3 1.31 1.33 1.34
1.4 1.4 1.4 1.4 1.4 1.4 1.4
1.010 1.026 1.042 1.059 1.067 1.083 1.091
0.189 0.193 0.196 0.199 0.200 0.203 0.205
2.390 2.005 1.613 1.216 0.816 0.409 0
23.897 20.046 16.135 12.162 8.159 4.095 0.000
8.404 6.845 5.262 3.664 2.044 0.409 0
STRESS VERIFICATIONS Material properties Steel for shell fy Mean temperature of shell Fy, op E, op parameters 2.8Fy/E 7.2Fy/E 10Fy/E Le = 2h Factor of safety Maximum stiffener spacing Design stiffener offset
Elevation (mm) 0 2000 4300 6000 8000 10000 12000 14000 16000 18000 20000 21300 24000 26000 28000 30000 32000 34000 36000 38000 40000
Axial force (kN) 772.15 746.83 722.36 699.06 666.17 631.28 596.39 561.50 530.05 498.59 467.14 440.51 400.23 360.45 343.17 326.39 185.12 169.34 154.06 139.28 0.00
Shear force (kN) 167 165 163 161 155 148 140 132 123 114 105 97 86 76 68 58 45 35 25 15 0
Bending moment (kNm) 4045 3708 3325 3046 2728 2424 2135 1862 1605 1366 1146 1014 762 594 442 309 204 117 53 11 0
S275JR 275 150 200 203000
N/mm2 degC N/mm2 N/mm2
0.0028 0.0071 0.0099 80000 mm 1.5 7000 mm 3000 mm
22.96588 ft
Complied?
t/D 0.0026 0.0026 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014
STIFFENER VERIFICATIONS Stiffener considered L 150*10 Moment of Inertia 258 Area 29.3 Section modulus 64.02 Elastic modulus, E 203000
29.00653 ksi 29441624 psi
(t/D <=10Fy/E)
OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK
cm4 cm2 cm3 N/mm2
σ1 N/A (N/mm2) 7.82 7.57 9.40 9.10 8.67 8.22 7.76 7.31 9.65 9.08 8.51 8.02 7.29 6.57 6.25 5.95 3.37 3.08 2.81 2.54 0.00
Table 4.4.7, ASME
σ2 M/W (N/mm2) 47.08 43.15 49.67 45.50 40.75 36.21 31.89 27.81 33.51 28.52 23.92 21.17 15.91 12.40 9.23 6.45 4.26 2.44 1.11 0.23 0.00
σ3 fc (N/mm2) 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
Wind Stiffener pressure Elevation spacing, coeff, q ls (mm) (kN/m2) (mm) 0 3000 0.692 2000 3000 0.692 4300 3000 0.692 6000 3000 0.733 8000 3000 0.774 10000 3000 0.814 12000 3000 0.847 14000 3000 0.871 16000 3000 0.904 18000 3000 0.920 20000 3000 0.945 21300 3000 0.953 24000 3000 0.977 26000 3000 0.994 28000 3000 1.010 30000 3000 1.026 32000 3000 1.042 34000 3000 1.059 36000 3000 1.067 38000 3000 1.083 40000 3000 1.091
Min. Stiffener inertia (cm4) 2.74 2.74 2.74 2.90 3.06 3.23 3.35 3.45 3.58 3.64 3.74 3.77 3.87 3.93 4.00 4.06 4.13 4.19 4.23 4.29 4.32
Allowable compress. stress in stiffeners Sccs N/mm2 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728 9.728
Min. sectional area of stiffener cm2 3.74 3.74 3.74 3.96 4.18 4.40 4.57 4.70 4.88 4.97 5.10 5.14 5.27 5.36 5.45 5.54 5.63 5.71 5.76 5.85 5.89
Min. sectional modulus of stiffener Stiffener Ss cm3 verification 10.0 OK 10.0 OK 10.0 OK 10.6 OK 11.2 OK 11.8 OK 12.2 OK 12.6 OK 13.1 OK 13.3 OK 13.7 OK 13.8 OK 14.1 OK 14.4 OK 14.6 OK 14.8 OK 15.1 OK 15.3 OK 15.4 OK 15.7 OK 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
Table I-4, ASME
Table I-5, ASME Table I-5, ASME Table I-1, ASME Table I-1, ASME
Table I-1, ASME Table I-1, ASME
Table I-1, ASME Table I-1, ASME
0.6h or zmin
k1
0
k2
1
k3
1
kzt
1.0
Corroded Sectiona Full Section Radius of thickness l area inertia J modulus gyration Ladder Walkway (mm) (cm2) (cm4) W (cm3) (cm) presence presence 9.0 987.06 1.50E+07 85924 123.43 0 0 9.0 987.06 1.50E+07 85924 123.43 0 0 7.0 768.15 1.17E+07 66945 123.50 0 0 7.0 768.15 1.17E+07 66945 123.50 0 0 7.0 768.15 1.17E+07 66945 123.50 0 0 7.0 768.15 1.17E+07 66945 123.50 0 0 7.0 768.15 1.17E+07 66945 123.50 0 0 7.0 768.15 1.17E+07 66945 123.50 0 0 5.0 548.99 8.38E+06 47900 123.57 0 0 5.0 548.99 8.38E+06 47900 123.57 0 0 5.0 548.99 8.38E+06 47900 123.57 0 0 5.0 548.99 8.38E+06 47900 123.57 1 0 5.0 548.99 8.38E+06 47900 123.57 1 0 5.0 548.99 8.38E+06 47900 123.57 1 0 5.0 548.99 8.38E+06 47900 123.57 1 0 5.0 548.99 8.38E+06 47900 123.57 1 1 5.0 548.99 8.38E+06 47900 123.57 1 0 5.0 548.99 8.38E+06 47900 123.57 1 0 5.0 548.99 8.38E+06 47900 123.57 1 0 5.0 548.99 8.38E+06 47900 123.57 1 1 5.0 548.99 8.38E+06 47900 123.57 1 0
Moment Fluctuati due to ng Wind wind wz_ load Wd (kNm) (kN) 1455 0.00 1340 0.16 1211 0.35 1119 0.48 1014 0.64 912 0.80 814 0.96 719 1.12 628 1.28 542 1.44 460 1.60 409 1.71 308 1.93 238 2.09
Shear due to wind wd(kN) 67.45 67.13 66.33 65.52 64.23 62.63 60.70 58.45 55.89 53.00 49.79 47.57 42.37 38.19
Moment due to wind wd (kNm) 1649 1527 1387 1284 1165 1048 934 824 717 616 520 461 347 271
Total V on cylinder (kN) 117.860 116.240 113.953 111.966 109.230 106.098 102.583 98.701 94.438 89.822 84.840 81.456 73.782 65.881
Total M on cylinder (kNm) 3104.00 2867.00 2598.00 2403.00 2179.00 1960.00 1748.00 1543.00 1345.00 1158.00 980.00 870.00 655.00 509.00
Shell weight (kN) 303.05 282.41 262.61 247.98 230.77 213.55 196.34 179.13 165.35 151.57 137.79 128.83 110.23 96.45 82.67 68.89 55.12 41.34 27.56 13.78 0
Ladder wt (kN) 4.68 4.68 4.68 4.68 4.68 4.68 4.68 4.68 4.68 4.68 4.68 4.68 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00
Additional loads (wind load on ladders + horizontal thrust Shear Moment due to due to wind on wind on Shear due ladders ladders to thrust (kN) (kNm) loads (kN) 4.68 169 44.2 4.68 158 44.2 4.68 145 44.2 4.68 136 44.2 4.68 125 41.4 4.68 114 37.1 4.68 103 32.8 4.68 92 28.5 4.68 81 24.2 4.68 69 19.9 4.68 58 15.6 4.68 51 11.3 4.00 37 8.5 3.50 29 7
176 122 79 44 20 5 0
2.25 2.41 2.57 2.73 2.89 3.05 3.21
33.70 28.89 23.75 18.29 12.52 6.42 0
203 144 94 54 24 6 0
57.598 48.933 39.886 30.457 20.677 10.514 0.000
379.00 266.00 173.00 98.00 44.00 11.00 0.00
3.00 2.50 2.00 1.50 1.00 0.50 0.00
21 15 10 5 2 0 0
7 7 3.5 3.5 3.5 3.5 0
Table 4.4.7, ASME
τ T/A (N/mm2) 1.69 1.67 2.12 2.09 2.02 1.93 1.82 1.72 2.25 2.08 1.91 1.77 1.57 1.39 1.23 1.06 0.83 0.65 0.46 0.26 0.00
Allow. Compressi ve stress σ1 + σ2 Vonmises Parameter Parameter Scl Verify (N/mm2) (N/mm2) Ks Y (N/mm2) N/A < Scl 54.90 54.90 1.053 1.00 87.00 OK 50.72 50.72 1.053 1.00 87.00 OK 59.07 59.07 1.225 1.00 67.67 OK 54.60 54.60 1.225 1.00 67.67 OK 49.42 49.42 1.225 1.00 67.67 OK 44.43 44.43 1.225 1.00 67.67 OK 39.66 39.66 1.225 1.00 67.67 OK 35.12 35.12 1.225 1.00 67.67 OK 43.16 43.16 1.410 1.00 48.33 OK 37.60 37.60 1.410 1.00 48.33 OK 32.43 32.44 1.410 1.00 48.33 OK 29.19 29.19 1.410 1.00 48.33 OK 23.20 23.20 1.410 1.00 48.33 OK 18.97 18.97 1.410 1.00 48.33 OK 15.48 15.48 1.410 1.00 48.33 OK 12.40 12.40 1.410 1.00 48.33 OK 7.63 7.63 1.410 1.00 48.33 OK 5.53 5.53 1.410 1.00 48.33 OK 3.91 3.91 1.410 1.00 48.33 OK 2.77 2.77 1.410 1.00 48.33 OK 0.00 0.00 1.410 1.00 48.33 OK
Allowable bending stress Sbl Verify N/A (N/mm2) +M/W< Sbl 87.00 OK 87.00 OK 67.67 OK 67.67 OK 67.67 OK 67.67 OK 67.67 OK 67.67 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK 48.33 OK
Additiona Insulatio l dead n wt (kN) load (kN) 0 0 0 0 0 4 0 11 0 13 0 13 0 13 0 13 0 13 0 13 0 13 0 17 0 12 0 0 0 0 0 25 0 0 0 0 0 0 0 25 0 0
Live loads (kN)
10
100
100
ds (wind load on ladders + horizontal thrust loads) Moment due to thrust Total Total loads shear Moment (kNm) (kN) (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
Total Dead load (kN) 562.15 536.83 512.36 489.06 456.17 421.28 386.39 351.50 320.05 288.59 257.14 230.51 190.23 160.45 143.17 126.39 85.12 69.34 54.06 39.28 0
Total wt (kN) 772.15 746.83 722.36 699.06 666.17 631.28 596.39 561.50 530.05 498.59 467.14 440.51 400.23 360.45 343.17 326.39 185.12 169.34 154.06 139.28 0.00
42 28 21 14 7 0 0
67.60 58.43 45.39 35.46 25.18 14.51 0.00
442 309 204 117 53 11 0
Allowable circumfere ntial stress Verify Parameter Scc Verify fc Combined combined Scl K (for Scc) (N/mm2) < Scc Scl and Scc 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
