DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACKDesigned by : Eng. Abdel Halim Galala, Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter Page : 1 of 24 REV. : 0 Date : 4.4.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 ELEVATED FLARE STACK SELF SUPPORTED & MULTIPLE DIAMETER Design General Mgr. BY Eng. Abd El Halim Galala Design General Manager Assistance 1st issue Dated : 6.6.1985 DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK According to ASME Code, Sec. VIII, Div. 1, Edition 95, Addenda 96. Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant) Page : 2 of 24 REV. : 0 Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. : Stack Type : Self supported & Multiple Diameter Date : 4.4.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Contents Page A. Wind Loads as Computed in Accordance with ANSI A58.1. B. Allowable Shell Buckling (Compression) Stress. C. Shell Plate Thickness, Design Procedure. 1. Total Uncrodded Stack Weight. 2. Computation of the Projected Area. 3. Computation of the Wind Loads. 4. Computation of the Wind Moments. 5. Required Shell Plate Thickness. 6. Anchor Bolt Chair. 7. Width of Base Ring. 8. Base Plate Thickness. 9. Top Plate Thickness. 3 5 7 7 8 9 11 12 13 14 15 15 D. Vibration Analysis. 1. Cantilever Vibration. - Analyzing Technique. - Static Deflection. - Dynamic Deflection. 2. Ovaling Vibration. - Design of Ovaling Ring : - Critical Wind Velocity. - Required Ring Section Modulus. E. References. 16 16 17 18 19 20 22 22 22 24 normal to all exposed windward surfaces of the structure. The required projected area A will then be equal to : A = De Ls where Ls = length of the shell section in the zone of the uniform wind velocity. Abdel Halim Galala. To calculate design wind forces from wind pressures. 1.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 The procrdure for calculation of the minimum design wind load normal to the surface is as follows : 1. Edition 95. : Stack Type : Self supported & Multiple Diameter A. . Design General Manager (Assistant) Page : 3 of 24 REV. An approach to computing A which is often used and is recommended here is to increase the vessel diameter D to the so called effective vessel diameter to approximate the combined design wind load : De = (Vessel OD + Twice insulation Thickness) x Kd The coefficient Kd is given in Table 2.4. for various height zones above the ground are given in Table 1. 3. shape factor B shall be used.1-1955. WIND LOADS AS COMPUTED IN ACCORDANCE WITH ANSI A58.The shape factor for round objects is equal to 0. Sec. p. see Table-1. If the windward surface area projected on the vertical plane normal to the direction of the wind is A ft2.3612 75 100 32 to 46 10 to 14 20. then the resultant of the wind pressure load over the area pw is assumed to act at the area centroid and is given by : pw = A B pz. lb The wind pressure forces are applied simultaneously. 2. p Kg/m2 Ft M PSF 30 9 15. The geographical area of the job site (Gulf of Suez & Mostorod) is located on the wind pressure map. Div.7224 150 1 Kg/M2 = 0.602 125 over 65 over 20 30.4816 49 to 62 15 to 19 25. Addenda 96. Designed by : Eng. The wind design pressure pz.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK According to ASME Code. corresponding to tha basic wind pressure p. Table 1.6 and is applied to the design pressure pz. A. Date : 4. and D is the vessel nominal diameter. VIII.2048159 lb/Ft2 Computation of the Projected Area. The minimum net pressure B*pz in the above formula for cylindrical vertical vessels is not less than : for L/D <= 10 13 PSF and for L/D >= 10 18 PSF Where L is the overall tangent-to-tangent length of the vessel. Height zone Basic wind above grade pressure. 4. : 0 Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. Design Wind Pressure of the Job Site. The basic wind pressure p is selected. Ls 7850 3. No.8 MM *Ls5-6 10 Ft 3048 MM Ls6-7 10 Ft 3048 MM Total vessel height Figure (1) 114.4.64 MM *Ls3-4 17 Ft 5181. Designed by : Eng.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 * The method of determining wind loads on vessels of two or more diameters is the same as for a vessel of a uniform diameter. : 0 Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. Table 2. the transition section should be considered as separate section.2 1.4 1. : Stack Type : Self supported & Multiple Diameter Date : 4. C = Corrosion allowance Flare stack segment lengths. E = Modulus of elasticity of plate material @ operating temp.6 MM *Ls4-5 11 Ft 3352.8 Ft 34991 MM . cylindrical sections can be assumed to extend to the midhight of the conical section. VIII. Design General Manager (Assistant) Page : 4 of 24 REV. Edition 95. St = Allowable Tensile Strength of Plate Material @ operating temp.175 Kg/M3 MM Ls1-2 50 Ft 15240 MM Ls2-3 16. Y = Yield point stress of plate material @ operating temp.18 For Stack material Where. Sec. Vessel OD including insulation INCH MM Less than 36 36 to 60 60 to 84 84 to 108 over 108 ASTM A285 Grade C 27600000 30000 15000 490 100 0. When the conical transition section is no more than 10% of the total height.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK According to ASME Code. Abdel Halim Galala.3 1. r = Steel Density V30 = 'Wind velocity at 30 ft height.125 PSI PSI PSI lb/ft3 MPH INCH Coefficient Kd 1. Otherwise. 1.5 1.8 Ft 5120. Div. Addenda 96. : Stack Type : Self supported & Multiple Diameter B. Stack OD1-2 Stack OD2-3 Stack OD3-4 Stack OD4-5 Stack OD5-6 Stack OD6-7 By assuming corroded thicknesses as follows: ta 1-2 ta2-3 ta 3-4 ta 4-5 ta 5-6 ta 6-7 Internal vessel dia.56 ta E)/d(1+0.007774 .2 914. Allowable compression stresses at each level are determined from the following formula : .8 5.44882 INCH 0.224409 INCH 0.015631 0.56 492. some thicknesses at each section are assumed.3937 INCH 19.00425 Sc = (0.01575 INCH 27.7 12.6 483 695. ta1-2 / d1-2 ta2-3 / d2-3 ta3-4 / d3-4 ta4-5 / d4-5 ta5-6 / d5-6 ta6-7 / d6-7 20 20 20 28 36 36 INCH INCH INCH INCH INCH INCH Page : 5 of 24 REV.004 E/Y) .006312 0. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.00425 where ta = assumed corroded plate thickness at each level under consideration.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.For higher ta/d ratios. at each level.166142 INCH 0.22 7.7 7 499.66772 INCH 19.4 MM MM MM MM MM MM 0.5 7.4 > > > > > > 0. Abdel Halim Galala.00425 0.30315 INCH 4. : 0 Date : 4. No.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 508 508 508 711.492126 INCH 0.For ta/d < 0.00425 0. in. d 1-2 = OD1-2 .00425 0.4 914.008447 0.275591 INCH 19. ALLOWABLE SHELL BUCKLING (COMPRESSION) STRESS.38583 INCH 35.55118 INCH 35. in. the allowable compression stress used is that calculated for t/d = 0.011213 0. Intially.4. d = internal stack diameter at level under consideration.02588 0.6 903 900.2 ta1-2 d2-3 d 3-4 d 4-5 d 5-6 d 6-7 Since the calculated ratio.00425 MM MM MM MM MM MM MM MM MM MM MM MM 0.00425 0.307087 INCH 0.00425 0. 00425 0. : 0 Date : 4.00425 0. (Calculated value. No.9 14035.00425) ta2-3 / d2-3 ta3-4 / d3-4 ta4-5 / d4-5 ta5-6 / d5-6 ta6-7 / d6-7 Therefore. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 The ratio ta/d to be used in calculations shall be computed as follows : Use ta1-2 / d1-2 = Min.56 E) / (1+ 0.00425 14035.9 14035.00425 0.004 E/Y) = (ta/d) (0. 0.00425 0.56 ta E) / d(1+ 0.004 E/Y) Final allowable buckling (compression) stress.9 14035.4.00425 0.9 14035. Abdel Halim Galala. Sc1-2 Sc2-3 Sc3-4 Sc4-5 Sc5-6 Sc6-7 0.9 PSI PSI PSI PSI PSI PSI .9 14035. : Stack Type : Self supported & Multiple Diameter Page : 6 of 24 REV.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. the allowable buckling (compression) stress Sc shall be : Sc = (0. 943 lb 2173.14) [OD3-42-(d3-4 . Total Uncrodded Stack Weights.14) [OD2-3 -(d2-3 . No.2C) ] Ls4-5 Wt5-6 = r (3.824 lb 1400.2C)2] Ls6-7 Total Weight 2 2 2 2 2 3067..718 lb 1331.826 lb 1531.14) [OD5-62-(d5-6 .14) [OD6-72-(d6-7 . internals.2C)2] Ls3-4 Wt4-5 = r (3. we get : Wt1-2 Wt2-3 Wt3-4 Wt4-5 Wt5-6 Wt6-7 (Total Weight + 15%).DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. Abdel Halim Galala. etc.173 lb 12653.14) [OD4-5 -(d4-5 .4.2C)2] Ls2-3 Wt3-4 = r (3. : 0 Date : 4.14) [OD1-2 -(d1-2 .06 lb Kg .2C) ] Ls1-2 Wt2-3 = r (3. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 C. ladders. SHELL PLATE THICKNESS. 1.2C)2] Ls5-6 Wt6-7 = r (3.634 lb 1524.498 lb 11002. Wt 3527.898 lb 1610. : Stack Type : Self supported & Multiple Diameter Page : 7 of 24 REV. platforms.096 lb 1730. [Uncorroded mean adding corrosion allowance ] Wt1-2 = r (3.685 lb 2499. Weights at each level are calculated by adding corrosion allowance to the thicknesses assumed above. DESIGN PROCEDURE.66 lb Kg By adding 15% of the calculated weight to compensate weight of piping.04 lb 1504.379 lb 1753. Sec. No. = 36"] Effective Diameter.5 1. VIII. Dwg. : 0 Date : 4.5 3. Addenda 96.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 2. In our case.5 4. < [dia. < [dia.Ls1-2 A2-3 A3-4 A4-5 A5-6 A6-7 125 42 42.4 1.5 2.4 914. + (platform + ladder)] The coefficient Kd is given in Table 2.2 [dia.4. De = Kd [Stack OD + Fuel Gas Pipe OD + Steam Pipe OD] N. De1-2 = Kd1-2 * OD1-2 De2-3 De3-4 De4-5 De5-6 De6-7 Projected Area.5 2.B. 1.5 1.5 1. = 36"] [dia. Stack OD INCH MM 20 508 20 20 28 36 36 Ft Ft Ft Ft Ft Ft 508 508 711.2 914.5 1. A An approach to computing A which is often used and is recommended here is to increase the vessel diameter D to the so-called effective stack diameter De to approximate the combined design wind load : De = Kd [(Vessel OD + 2 insulation thk. < [dia. Div. De = Kd * Stack OD. Abdel Halim Galala.5 42 42 Ft2 Ft Ft Ft Ft 2 2 M2 M2 M2 M2 M2 M2 Ft2 2 2 .) + (pipe OD + 2 insulation thk.2 4. A = De * Height Ls A1-2 = De1-2 . : Stack Type : Self supported & Multiple Diameter Page : 8 of 24 REV. Design General Manager (Assistant) Project : Design & procurement of Flare Stack According to ASME Code.4 MM MM MM MM MM Coefficient Kd [fromTable 2] Kd1-2 Kd2-3 Kd3-4 Kd4-5 Kd5-6 Kd6-7 [dia. Computation of the Projected Area.5 38.4 2. The required projected area A will then equal to : A = De * Ls where Ls = Length of the shell section in the zone of the uniform wind velocity. < 36"] 36"] 36"] 36"] 1. Edition 95.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. the size of fuel gas and steam pipes can be neglected. net wind pressure. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.962834 Ft 58.4. B Pz = Min. for round objects B = 0. : 0 Date : 4.8 Ft 34991 MM MM 1. BPz not less than 18 PSF where. depends upon the geographical area of the job site (see Table 1). BPz not less than 13 PSF . The resultant of the wind pressure load Pw over the area A is given by : Pw = A * B * Pz where Pw = Wind pressure load over the projected area A. Abdel Halim Galala.For L/D >= 10. L is the overall tangent-to-tangent length of the vessel. lb.6 Pz = Design wind pressure.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. Computation of Wind Loads.For L/D <= 10. ft2. Davg. psf. No. Therefore. For cylindrical vertical vessels : . psf. the net wind pressure BPz shall not be less than .2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 3.6 0. B = Shape Factor. is the vessel average diameter. =B451= (L1-2 D1-2 + L2-3 D2-3 + L3-4 D3-4 + L4-5 D4-5 + L5-6 D5-6 + L6-7 D6-7) / L 114. : Stack Type : Self supported & Multiple Diameter Page : 9 of 24 REV.48686 > 18 PSF 10 L/Davg. A = Windward surface area projected on the vertical plane normal to the direction of the wind. 2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Determining Design Wind Pressure B Pz for each Segment [based upon Table 1]. P grade PSF M Design wind pessure.28895 PSF 9.3611925 15.18) B Pz2-3 B Pz3-4 B Pz4-5 B Pz5-6 B Pz6-7 Wind Load shall be as follows : Pw = A * B Pz Pw1-2 = A1-2 B Pz1-2 Pw2-3 Pw3-4 Pw4-5 Pw5-6 Pw6-7 2304. Height zone above grade M Segment Basic height. : 0 Date : 4.4488 20. H wind above pressure. Pz PSF Design Wind Pressure.216716 PSF 9.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.601988 19.48159 14.4.361193 0 18.48159 15. NWP shall be as follows :B Pz1-2 B Pz2-3 B Pz3-4 B Pz4-5 B Pz5-6 B Pz6-7 Use the max.722385 25.722385 34. Table 3 From Table 1.43343 PSF 15.6019875 20. following wind pressure : B Pz1-2 = Max (NWP.6304 9.048 Net wind pressure.3611925 15.216716 PSF 9. : Stack Type : Self supported & Multiple Diameter Page : 10 of 24 REV.179 lb 756 765 693 756 756 lb lb lb lb lb Kg Kg Kg Kg Kg Kg . Pz1-2 20 19 Pz2-3 15 14 Pz3-4 Pz4-5 Pz5-6 Pz6-7 10 9 30. No. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. Abdel Halim Galala.216716 PSF 18.991 30.096 3.3611925 15.36119 PSF 12.43343 PSF 18 18 18 18 18 PSF PSF PSF PSF PSF 6.751 25. 1 M6 =Pw1-2 (0. No.78058 3060.50446 4518.1789 57604.5L2-3) M4 =Pw1-2 (0.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Figure (2) Moment = Wind Load x Arm 57604.1 161190. : Stack Type : Self supported & Multiple Diameter 4. : 0 Date : 4. In the following calculations we assumed that geographical location of the job site does not required a moment calculation for the earthquake.1789 102665 765 7757.5 L1-2+L2-3+L3-4)+Pw2-3(0.5L3-4) Load W.5L2-3+L3-4+L4-5+L5-6)+ Pw3-4(0. lb Table 4.09562 2304. Abdel Halim Galala.5 L1-2) M3 =Pw1-2 (0.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.1789 207079 756 10899.5 L1-2+L2-3+L3-4+L4-5+L5-6)+Pw2-3(0.5L2-3+L3-4)+ Pw3-4(0.5L3-4+L4-5+L5-6)+Pw 256040. Computation of Wind Moments.5L3-4+L 312562.1789 312563 .5L2-3+L3-4+L4-5)+ Pw3-4(0.5L3-4+L4-5)+Pw4-5(0.5 L1-2+L2-3+L3-4+L4-5+L5-6+L6-7)+Pw2-3(0.5 756 5257.5 L1-2+L2-3)+Pw2-3(0.5 L4-5) 207079. the total wind moment shall be calculated as follows : Page : 11 of 24 REV.5L2-3+L3-4+L4-5+L5-6+L6-7)+ Pw3-4(0.67823 3825.5 L1-2+L2-3+L3-4+L4-5)+Pw2-3(0. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. Weight Moment @ section M.6 M5 =Pw1-2 (0. lb-ft WT. Therefore.9 M7 =Pw1-2 (0.179 lb-ft lb-ft lb-ft lb-ft lb-ft lb-ft Wind Shear Q.4.0565 Figure (3) 6030.1789 161191 693 9368.1789 256041 756 12653. lb 3527.7 M2 = Pw1-2 (0.47 102665. lb 2304.8834 5274. 433071 INCH 0.A For construction.70337 MM 10.A) tr2-3 = (WT2-3 dr2-3 + 48 M3) / PI( ) dr2-32 Sc2-3 tr2-3 + C.B.7353 MM 16 MM N. No. The assumed thickness must be changed untill the calculated > the assumed thickness. use (tr4-5 + C. use (tr6-7 + C.166142 INCH 0.A) tr5-6 = (WT5-6 dr5-6 + 48 M6) / PI( ) dr5-62 Sc5-6 tr5-6 + C.492126 INCH 0.227475 INCH 0.4945 0.A 2 0. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.7 12. Since there is no appreciable change in calculated thicknesses. .291173 INCH 0.307087 INCH 0. : Stack Type : Self supported & Multiple Diameter 5. Abdel Halim Galala.2208 7.433071 INCH N.A For construction.22 7.224409 INCH 0. the weights based on the required thicknesses are almost the same as previouslyestimated.B.8784 MM 11 MM N.403855 INCH For construction.314961 INCH 0.A For construction.B.08291 MM 10.354331 INCH 0.B. The required shell plate thickness shall be computed as follows : 2 tr = (WT dr + 48 M) / 3. The assumed thickness must be changed untill the calculated > the assumed thickness.275591 INCH 0. 0.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 0.95287 MM 9 MM 7. 0.B.352475 INCH 0.7 7 4.0064 MM 12 MM 5.4.A For construction.B. 7.629921 INCH 0.6195 INCH INCH N.A) tr6-7 = (WT6-7 dr6-7 + 48 M7) / PI( ) dr6-7 Sc6-7 tr6-7 + C. N. use (tr2-3 + C.83136 MM 11.166173 INCH 0. 12. The assumed thickness must be changed untill the calculated > the assumed thickness.472441 INCH 0.428282 INCH 0.433321 INCH 0. Required Shell Plate Thickness.3958 8 MM MM MM MM MM MM MM MM ta2-3 ta 3-4 ta 4-5 ta 5-6 ta 6-7 tr1-2 = (WT1-2 dr1-2 + 48 M2) / PI( ) dr1-22 Sc1-2 tr1-2 + C.8 5.A) 0.B. The assumed thickness must be changed untill the calculated > the assumed thickness. The assumed thickness must be changed untill the calculated > the assumed thickness. use (tr3-4 + C.77787 MM 8.14 dr Sc where W T = Total weight @ Section under consideration By assuming corroded thicknesses as follows: ta 1-2 Page : 12 of 24 REV. use (tr1-2 + C. : 0 Date : 4.A For construction.5 7.308321 INCH 0.303282 INCH 0.5603 MM 15. use (tr5-6 + C.2579 MM 11 MM N.278855 INCH 7. The assumed thickness must be changed untill the calculated > the assumed thickness.30315 INCH 4. N.A) tr3-4 = (WT3-4 dr3-4 + 48 M4) / PI( ) dr3-42 Sc3-4 tr3-4 + C.A) tr4-5 = (WT4-5 dr4-5 + 48 M5) / PI( ) dr4-52 Sc4-5 tr4-5 + C. R .5 Use 16 holding down bolts with a dia.Total length.83 lb Thus. . the anchor bolt area required at the root of the thread shall be: AB = W B / SB Diameter of the anchor bolt at the root of thread.75 INCH INCH INCH INCH INCH INCH 33. : 0 Date : 4.45 150 90 350 1085 MM MM MM MM MM MM Figure (4) Figure (5) . No. L .4.14)0.93701 INCH 15000 PSI 1116 MM The total tension in each anchor bolt is determined from the relationship: W B = (48 M / N DBC) . l . D = (4 AB/3.Wt / N 20550. d Each bolt shall be provided with two hex heavy nuts and washer. : Stack Type : Self supported & Multiple Diameter Page : 13 of 24 REV.320761 INCH 1.Length of threaded portion.Length.370055 INCH 2 883. N Bolt Circle Dia.Bolt projection . of .2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 6. DBC Max.5473 MM 44. Ancor Bolt Chair. M Kg 2 1. of anchor bolts. Abdel Halim Galala. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.905 MM 1. Allowable stress of Anchor Bolt Material. SB ASTM A36 16 BOLTS 43.Radius. Anchor bolt material Assume No.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. .) (Max. If the calculated Pb exceeds the above limit.For 2000 lb concrete 750 500 PSI PSI (Max.10236 INCH 282 MM 341.B.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.4 MM Assume C. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. No. Abdel Halim Galala.9775 PSI SAFE 36 INCH < 500 where Db = OD at bottom of stack 914. C.For 3000 lb concrete .4. and note that the value of Pb is limited to : . : Stack Type : Self supported & Multiple Diameter Page : 14 of 24 REV.) N. C Bearing pressure on concrete foundation is calculated from the following formula : Pb = (48 M / PI Db2 C) + (Wt / 3. Assume width of base ring.14 Db C) 11. : 0 Date : 4.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 7. Width of Base Ring. the value of C is modified so that Pb falls within the allowable limit. 2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 8. Abdel Halim Galala. TT TT = SQRT[ 3 * W B * 6 / (4 * 20000 * e)] where W B = Total tension in each bolt Use TT 0.535433 INCH 37.83 PSI 1. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.365 MM . Top Plate Thickness.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.841141 INCH 20550. : 0 Date : 4. No.480195 INCH 6.771654 INCH Figure (6) 9. Tb Base plate thickness Tb is calculated from the following equation: Tb = e SQRT(3 Pb / 20000) where e = A + B A B Use Tb 1.4. Base Plate Thickness. : Stack Type : Self supported & Multiple Diameter Page : 15 of 24 REV.5969 MM 166 101 65 45 MM MM MM MM 1.181102 INCH 30 MM 21. 825 8.20 < W / L Dr2 <= 25 vibration analysis should be performed .347441 INCH 0.001312 ft 2.443917 < 20 vibration analysisis required . Lc = Total length of conical section(s) of stack. Abdel Halim Galala. : 0 Date : 4.W / L Dr <= 20 vibration analysis must be performed 9.4.504921 INCH 0. No.5 : 2 .189961 INCH 0. of top half of stack.001312 ft 0. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.002625 lb ft ft ft 610 610 MM MM 2. The following criteria is used to establish need for vibration analysis of stacks with Lc/L ratio not exceeding 0.229331 INCH 0.034866 OK 20 20 20 28 36 36 INCH INCH INCH INCH INCH INCH 508 508 508 711.825 5. Conical section height 28"/20" Conical section height 36"/28" We note that Lc / L < 0. Le = Total length of stack.981 114. : Stack Type : Self supported & Multiple Diameter Page : 16 of 24 REV.25 < W / L Dr2 vibration analysis need not be performed Where Wt = Total corroded stack weight (see next page).308071 INCH .2 914.8 2.825 MM MM MM MM MM MM MM MM MM MM MM MM 0. Stack OD1-2 Stack OD2-3 Stack OD3-4 Stack OD4-5 Stack OD5-6 Stack OD6-7 Corroded thickness tr1-2 Corroded thickness tr2-3 Corroded thickness tr3-4 Corroded thickness tr4-5 Corroded thickness tr5-6 Corroded thickness tr6-7 8071.825 7.4 4.308071 INCH 0.72862 4. Dr = Average internal dia.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 D. VIBRATION ANALYSIS.5 O.825 7. 1.825 12. Cantilever vibration.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.4 914.D. 879 lb 1129.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Corroded internal diameter in inches : Corroded ID1-2 Corroded ID2-3 Corroded ID3-4 Corroded ID4-5 Corroded ID5-6 Corroded ID6-7 Flare stack segment heights. without taking into account adding corrosion allowance to the thicknesses assumed above.8 3048 3048 MM MM MM MM MM 5120.776 lb 876. : 0 Date : 4.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.39 Kg 8071. : Stack Type : Self supported & Multiple Diameter Page : 17 of 24 REV.459 Kg 397.4.99016 INCH 27.64 MM Wt1-2 = r (PI/4) [do2-di2]1-2 L1-2 Wt2-3 = r (PI/4) [do2-di2]2-3 L2-3 Wt3-4 = r (PI/4) [do2-di2]3-4 L3-4 Wt4-5 = r (PI/4) [do -di ]4-5 L4-5 Wt5-6 = r (PI/4) [do2-di2]5-6 L5-6 Wt6-7 = r (PI/4) [do2-di2]6-7 L6-7 Total corroded stack Weight.9458 lb 1175. Wt Analyzing technique.511 lb 1788.423 Kg 512.8 ft 0.45 lb 912.176 Kg 3661.5 'where Le = effective length of stack Natural frequency of stack vibration. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.38386 INCH 18.981 lb 1. 19. Corroded mean neglecting corrosion allowance.8 17 11 10 10 Ft Ft Ft Ft Ft Ft 15240 5181.54134 INCH 35. Period of vibration is determined as follows : T = 1.194 Kg 811.402825 MPH . No.365 Kg 494.515107 second 114. Abdel Halim Galala.62008 INCH 19. Vc = 3 f Dr 2 2 2011. Weights at each level are calculated.660019 cps 5.418 lb 1089.30512 INCH 35. f = 1 / T Critical wind velocity. L1-2 L2-3 L3-4 L4-5 L5-6 L6-7 Total Corroded Stack Weights.38386 INCH 50 16.6 3352.776 Kg 533.648 (Le2) / Dr E0. 467 Vc)2 / 2 C1 = Lift coefficient (usually taken as1) pair = mass density of air I = Moment of inertia of top half of stack = 3.06666667 where. if K in the above equation exceeds 1/15.B.0678 INCH 9. the stack is free from cantilever vibration.86 MM 8. W can be used in place of Ws in order to reduce vibration.71321 MM 5 3 0. Design modifications are required.4. Pc = Total wind force at critical velocity = C1 pair (1. No. gust velocity. the ratio K should be less than 1/15.5022 MPH Since the critical wind velocity.00238 lb. wind velocity at the top of the stack is Vw = V30 (L / 30)0. Static deflection.320472 INCH . Vc falls within max. K = Pc Dr Le / W s = 0. corroded stack weight must be > 15 times the wind force at critical velocity or expressed as a formula. In that case. the stack must be checked further for K. Ds = Pc Dr (Le)4 (12)3 / 8 E I 0.143 V30 = Wind velocity at 30 ft height (basic wind velocity) Max.14 * r3 * t r = Average internal radius of top half of stack t = Average corroded plate thick.sec2/ft4 4 38004.8 CM 245. The computed dynamic loading is applied as a stagnant pressure to the stack.002632 < l / 15 0. gust velocity = 1. of top half of stack 0. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.303669 INCH 7.1556 MPH 100 MPH 157.074756 psf 1 0. For lined stacks.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Max. Assuming it to be a cantilever beam.0077 Dr E / Le Ws Therefore.14 MM 4 913. Abdel Halim Galala.3 Vw 121. N.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. amplitude at the top is approximated by : Static Deflection.679528 INCH 0. : 0 Date : 4. : Stack Type : Self supported & Multiple Diameter Page : 18 of 24 REV. For dynamic deflection. The dynamic coefficient. Approximate value of magnification factors for different types of stacks as suggested by DeGhetto and Long are listed in Table 3.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. Hydrocarbon Processing 47. No. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.4. * "Shortcut method for calculating tower deflection".2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Dynamic deflection.B. which is a ratio of dynamic amplitude to static amplitude. Table 5. This is a function of the lining. p 230. It is assumed to be within the allowable limits when allowing about 7-inch deflection per 100 feet* of height of stack.036 INCH . The amount of static deflection must be multiplied by the magnification factor to determine dynamic deflection. stiffness of the soil and several other factors. and thus the amplitude of vibration is magnified greatly. No. 11. Nov.110085 INCH NotT Good > 8. Magnification factors Types of stacks Spread footings on soft soil (Bearing < 1500 psi) Spread footings Piled foundations on medium soil spread and (1500 psi < footings Bearing > on stiff soil 3000 psi) and rocks Lined stacks Unlined stacks Using a magnification factor of Dynamic deflection = Static Deflection * Magnification factor = Ds * Magnification factor 30 5 30 30 60 50 90 Allowed deflection 9. At a critical wind velocity.036 N. : Stack Type : Self supported & Multiple Diameter Page : 19 of 24 REV. Allowed deflection of stack under consideration = 7 x L / 100 8. the structure vibrates at resonant frequency. Abdel Halim Galala. : 0 Date : 4. 1968. is called the magnification factor. 58 tr4-5 E0. no ovaling rings are required.60222 cps Since fr > 2 fv .814 cps 8.14672 cps Since fr > 2 fv .35 492.961778 2. : Stack Type : Self supported & Multiple Diameter Page : 20 of 24 REV.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 2. Natural frequency of the free ring is given by : 0. Abdel Halim Galala.635007 1.53771 cps fv4-5 = 0. N.073362 cps cps = cycle per second 2 fv1-2 16.171748 cps 2 fv2-3 16.341163 cps 2 fv3-4 16.68233 cps Since fr > 2 fv .275427 2.36194 cps 8.5 2 fr = (7.5) / 60 D23-4 fv3-4 = 0.948655 Ft Ft Ft Ft Ft Ft 498.58 tr E ) / 60 D Vortex shedding frequency is given by : fv = 0.2 V / D2-3 0.35 482.2 V / D Where V = wind velocity for vortex shedding is 45 MPH or 66 fps as recommended by Dickey and Woodruff for most economical and safe stack design as far as vibration is concerned.75 898.5) / 60 D21-2 fv1-2 = 0. and the stack is free from ovaling vibration.B.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. no ovaling rings are required.55 902. .58 tr3-4 E0. At Section 4-5 : fr4-5 = (7.5) / 60 D24-5 44. t calculated upon corroded thk. & V = 66 fps.58 tr2-3 E ) / 60 D fv2-3 = 0. 45 66 MPH fps Both these frequencies should be calculated at each level using the corresponding thicknesses and diameters.2 V / D1-2 47. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.615322 1.4.5 2 2-3 78.16253 cps 8.2 V / D4-5 5. D D1-2 D2-3 D3-4 D4-5 D5-6 D6-7 1. no ovaling rings are required.3435 cps Since fr > 2 fv .2 V / D3-4 133. and the stack is free from ovaling vibration.58 tr1-2 E0. No.80111 cps 2 fv4-5 11. Ovaling vibration.582513 2. At Section 2-3 : fr2-3 = (7. : 0 Date : 4. no ovaling rings are required. and the stack is free from ovaling vibration. and the stack is free from ovaling vibration.35 693. At Section 3-4 : fr3-4 = (7. Corroded internal diameters in feet.75 MM MM MM MM MM MM At Section 1-2 : fr1-2 = (7. 3512 cps 4.51664 cps 4. Abdel Halim Galala. At Section 6-7 : fr6-7 = (7. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.58 tr5-6 E0. no ovaling rings are required.456782 cps 2 fv5-6 8.58 tr6-7 E ) / 60 D fv6-7 = 0.2 V / D6-7 0. no ovaling rings are required.4. and the stack is free from ovaling vibration.913564 cps Since fr > 2 fv .953235 cps Since fr > 2 fv .DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. : Stack Type : Self supported & Multiple Diameter Page : 21 of 24 REV. No.2 V / D5-6 17.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 At Section 5-6 : fr5-6 = (7.476618 cps 2 fv6-7 8. : 0 Date : 4.5 2 6-7 23. .5) / 60 D25-6 fv5-6 = 0. and the stack is free from ovaling vibration. different size and spacing should be used for economy. Now. If.5 St = Allowable tensile strength of stiffener material 15000 Sm1-2 = [ (7)10-7 (Vo1-2)2 D1-22 Hr1-2) ] / St Sm2-3 = [ (7)10 (Vo2-3) D2-3 Hr2-3) ] / St Sm3-4 = [ (7)10-7 (Vo3-4)2 D3-42 Hr3-4) ] / St Sm4-5 = [ (7)10-7 (Vo4-5)2 D4-52 Hr4-5) ] / St Sm5-6 = [ (7)10-7 (Vo5-6)2 D5-62 Hr5-6) ] / St Sm6-7 = [ (7)10-7 (Vo6-7)2 D6-72 Hr6-7) ] / St -7 2 2 FPM Ft PSI 3 0. No.563 FPM 10401.Critical wind velocity at the section under consideration is : Vo = ( 60 fr D ) / 2 S where fr = Natural frequency S = Strouhal number. : 0 Date : 4.34 FPM 7708. ovaling rings are required to stiffen that section. at any section. : Stack Type : Self supported & Multiple Diameter Page : 22 of 24 REV.417255 INCH 3 0. is 0. fr < 2fv. Vo1-2 = ( 60 fr1-2 D1-2 ) / 2 S Vo2-3 = ( 60 fr2-3 D2-3 ) / 2 S Vo3-4 = ( 60 fr3-4 D3-4 ) / 2 S Vo4-5 = ( 60 fr4-5 D4-5 ) / 2 S Vo5-6 = ( 60 fr5-6 D5-6 ) / 2 S Vo6-7 = ( 60 fr6-7 D6-7 ) / 2 S 11566. D = Intenal vessel dia. the section modulus of stiffeners at section under consideration can be found from the formula as used by Moody : Sm = [ (7)10-7 (Vo)2 D2 (Hr) ] / St INCH3 Where.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng.36 FPM 15201.121627 INCH 3 0. FPM cps 0. . Section modulus of the rings.002306 INCH 3 0.4.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Design of Ovaling Rings.66 FPM 18986. whenever required. Abdel Halim Galala.2 over a wide range of Reynolds numbers. can be determined as follows : .96 FPM 31764.37 FPM Required Section Modulus of the Ring.307085 INCH 3 0. (corroded) at level under consideration. If stiffeners are required for more than one section. Vo = Critical wind velocity at section of consideration Hr = Spacing throughout the length of the section under consideration Ls 0.219485 INCH Stiffeners having section modulus equal to or greater than Sm should be provided at spacing Hr throughout the length of the section under consideration.2 Ft Critical wind velocity at Section. if possible. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.368735 INCH 3 1. : Stack Type : Self supported & Multiple Diameter Page : 23 of 24 REV.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 Notes . No.4. Abdel Halim Galala.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK Designed by : Eng. Design General Manager (Assistant) Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg. : 0 Date : 4. No. دא ª . Pressure Vessel Design Handbook-2nd Edition. ASCI 7-1988. by Henry H. 1. Edition 95.DESIGN CALCULATIONS OF ELEVATED CYLINDRICAL FLARE STACK According to ASME Code. Designed by : Eng. 4. Sec. ANSI A58. 1.1-1955. 2. Div. Abdel Halim Galala.4. Addenda 96. Flare stack paper research. Design General Manager (Assistant) Page : 24 of 24 REV. : Stack Type : Self supported & Multiple Diameter Date : 4. REFERENCES. Bednar. 3. VIII. : 0 Project : Design & procurement of Flare Stack Job Name : Propylene Recovery Unit Dwg.2000 Location : Gulf of Seuz Client : ABB/OPC Item : X-06-02 E.
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