Exercícios resolvidos ASME, Exercícios de Vasos e Caldeiras de Alta Pressão

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ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 1 5-Mar-2014 Layout Input values: 1.234 or 1.234 Calculated values: 1.234 or 1.234 Critical values: 1.234 or 1.234 Estimated values: 1.234 or 1.234 Table of contents Table of contents ................................................................ 1 Example E4.18.5 - Fixed Tubesheet Exchanger, Configuration b, Tubesheet Integral with Shell, Extended as a Flange and Gasketed on the Channel Side ................ 2 E4.18.5.D1 - LV Calculation ...................................................... 5 E4.18.5.D2 - LV Calculation ..................................................... 11 E4.18.5.D3 - LV Calculation ..................................................... 17 E4.18.5.O4 - LV Calculation ..................................................... 22 E4.18.5.O1 - LV Calculation ..................................................... 27 E4.18.5.O2 - LV Calculation ..................................................... 32 E4.18.5.O3 - LV Calculation ..................................................... 37 E4.18.5.D1-plastic - LV Calculation ............................................. 42 Comparison Table ................................................................ 47 Comparison Table ................................................................ 48 Comparison Table ................................................................ 49 Appendix : Material documentation ............................................... 49 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 2 5-Mar-2014 Example E4.18.5 - Fixed Tubesheet Exchanger, Configuration b, Tubesheet Integral with Shell, Extended as a Flange and Gasketed on the Channel Side A fixed tubesheet hegt exchanger is to be designed with the tubesheet construction in accordance with configuration b as shown in VIII-1, Figure UHX-13.1, Configuration b. • For the Design Condition, the shell side design pressure is 150 psig at 700°F, and the tube side design pressure is 400 psig at 700°F. • There is one operating condition. For Operating Condition 1, the shell side design pressure is 150 psig at 700°F, the tube side design pressure is 400 psig at 700°F, the shell mean metal temperature is 550°F, and the tube mean metal temperature is 510°F. For this example, the operating pressures and operating metal temperatures are assumed to be the same as the design values. • The tube material is SA-214 welded (K01807). The tubes are 1 in. outside diameter, 0.083 in. thick and are to be expanded to 95% of the tubesheet thickness. • The tubesheet material is SA-516, Grade 70 (K02700). The tubesheet outside diameter is 40.5 in. There are 649 tube holes on a 1.25 in. triangular pattern. There is no pass partition lane, and the outermost tube radius from the tubesheet center is 16.625 in. The distance between the outer tubesheet faces is 168 in. There is no corrosion allowance on the tubesheet. • The shell material is SA-516, Grade 70 (K02700). The shell inside diameter is 34.75 in. and the thickness is 0.1875 in. There is no corrosion allowance on the shell. The shell contains an expansion joint that has an inside diameter of 38.5 in. and an axial rigidity of 11.388 Ib/in. The efficiency of the shell circumferential welded joint (Category B) is 1.0. • The diameter of the channel flange gasket load reaction is 36.8125 in., the bolt circle diameter is 38.875 in., the design bolt load is 512,937 Ib, and the operating condition bolt load is 512,473 Ib. ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 5 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 1 (1-7) Tube side pressure only (Ps=0) without differential thermal Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 1 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 10430 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² Tube pitch (center distance) p 1.25 in — Expanded length of tube in tubesheet ltx 2.909 in E4.18.5.D1 - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 6 5-Mar-2014 Total untubed area UL1*LL1+UL2*LL2.. Fig.UHX11.2 AL 0 in² Depth of tube side pass partition groove hg 0 in Expanded length ratio ltx/h ρ 0.95 Tube length between inner tubesheet faces L 161.9 in Unsupported tube span for buckling l 59 in Type of tube support (0.6=tubesheet-tubesheet, 0.8=tubesheet - support plate, 1=plate-plate ) k 1 Equivalent free buckling length k* l lt 59 in Bellows inside diameter at its convolution height Dj 38.5 in Bellows axial rigidity(e.g. 1E+38 without bellows) Kj 11388 lbf/in Shell weld efficiency factor for axial stress Esw 1 - Material properties for mean operation temperature Mean temperature along the shell length Tsm 287.8 °C Mean temperature along the tube length Ttm 265.6 °C Mean coefficient of thermal exp. of shell at Tsm α sm 13.14 1E-6/°C Mean coefficient of thermal exp. of tubes at Ttm α tm 13.14 1E-6/°C UHX-13.6: Specification of values only for variable shell thickness of type abc for the shell region close to the tubesheet Shell material Increased shell thickness with allowances t1s in Thickness allowance c1s in Corrosion allowance c2s in Length of thickness t1s (tubesheet1, l1=0: none) l1 0 in Length of thickness t1s (tubesheet2, l'1=0: none) l'1 0 in Required length of incr. thickness 1.8* √ (Ds*t1s) lmin in Yield strength of shell at Ts = 371.1 °C Sy1s psi Strength of shell at Ts K1s psi Safety factor of shell at Ts Ss1 Allowable stress for shell at Ts S1s psi Tensile strength at room temperature 20°C Sz1s psi Limit temperature for time dependent properties TG1s °C Allowable primary and secondary stress at Ts Sps1s psi E-Modulus of shell at Ts E1s psi Mean coefficient of thermal exp. at Tsm α sm1 1E-6/°C UHX-13.8: Specification of values only for radial diff. therm. exp. type abc (Thermal expansion = 0 for ambient temperature=20°C=68°F) Tubesheet metal temperature at the rim T' 20 °C Channel metal temperature at the tubesheet T'c 20 °C Shell metal temperature at the tubesheet T's 20 °C Mean coefficient of thermal expansion of Tubesheet at T' α ' 11.5 1E-6/°C Channel at T'c α 'c 1E-6/°C Shell unreinforced (for l1+l'1=0) at T's α 's 11.5 1E-6/°C Shell reinforced acc. UHX-13.6 at T's α 's 1E-6/°C Flange (Type bcd): Mean contact diameter tubesheet-flange (type c) G1 in Bolt circle diameter C 38.88 in Number of bolts n 68 - Bolt root diameter dB 0.62 in Total bolt area Ab 20.53 in² Bolt material G41400-SA-193-B7-Class:-Size:<=64 Strength for operation Ks 25000 psi Strength for test Ksp 25000 psi Safety for operation Ss 1 - Safety for test Ssp 1 - Stress increasement factor for testing (see App.S) Fs 1 - ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 7 5-Mar-2014 Shell Channel — Gasket Type d Type b,c,d Contact outside diameter Ga in 37.31 in Contact inside diameter Gi in 36.31 in Basic seating width b0 in 0.255 in Gasket factor (Table 2-5.1) m 3.75 Gasket seating pressure Y psi 7600 psi Diameter of gasket force G in 36.81 in Poisson's ratio ν 0.3 0.3 Results acc. UHX-9 Shell Channel Effective seating width b in 0.2505 in Gasket operating force W 0 N 512365 lbf Total req. bolt root area Am 0 mm² 20.49 in² Am < actual bolt area = 20.53 in² Tubesheet flange thickness hr 0 in 1.234 in Maximum bolt force for all calculation cases Wmax 512937 lbf Results acc. UHX-13 Apply actual version UHX-13.5 (Y) or UHX-20.2:2008 (N) Y (Y/N) Gasket seat. force chan.=0.5(Am+Ab)*Ksp/Ssp,App.2-5 W 512806 lbf Stiffness ratio Bellows/Shell (=1 without bellows) J 0.003504 Channel shell thickness without allowances tc in Shell thickness without allowances ts 0.1875 in Shell inside diameter corroded (type abc) Ds 34.75 in Step 1 acc. UHX 11.5+13.5 Tube material mod. of elast. at tubesheet temp. T EtT 2.547E+7 psi Tube material allowable stress basis at T KtT 12000 psi Tube material allowable stress safety at T SfT 1 - Basic ligament efficiency for shear µ 0.2 Effective tube hole diameter d* 0.8946 in Effective pitch p* 1.25 in Effective ligament efficiency for shear µ * 0.2843 Effective depth of pass partition groove hg' 0 in Equivalent radius of outer tube limit circle a0 17.13 in Radial channel dimension (type a: Dc/2, else:Gc/2) ac 18.41 in Radial shell dimension (type d: Gs/2, else: Ds/2) as 17.38 in Ratio = ac/a0 ρ C 1.075 Ratio = as/a0 ρ S 1.015 Parameter = 1-Nt*(0.5*daROHR/a0)² xs 0.4467 Parameter = 1-Nt*(0.5*diROHR/a0)² xt 0.6152 Step 2 Shell axial rigidity Ks or Ks* Ks 3238266 lbf/in Tube axial rigidity Kt 37624 lbf/in Stiffness ratio Ks/(Nt*Kt) Kst 0.1326 Stiffness ratio Kj/(Ks+Kj) J 0.003504 Type abc: Coefficients for shell pressure δ S 0.000054 in^3/lbf ßS= 0.7102 1/in , kS= 21842 lbf , λ S= 878461 psi — ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 10 5-Mar-2014 UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 11 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 2 (1-7) Shell side pressure only (Pt=0) without differential thermal Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 1 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 12353 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² Tube pitch (center distance) p 1.25 in — Expanded length of tube in tubesheet ltx 2.909 in Total untubed area UL1*LL1+UL2*LL2.. Fig.UHX11.2 AL 0 in² E4.18.5.D2 - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 12 5-Mar-2014 Depth of tube side pass partition groove hg 0 in Expanded length ratio ltx/h ρ 0.95 Tube length between inner tubesheet faces L 161.9 in Unsupported tube span for buckling l in Type of tube support (0.6=tubesheet-tubesheet, 0.8=tubesheet - support plate, 1=plate-plate ) k Equivalent free buckling length k* l lt 59 in Bellows inside diameter at its convolution height Dj 38.5 in Bellows axial rigidity(e.g. 1E+38 without bellows) Kj 11388 lbf/in Shell weld efficiency factor for axial stress Esw 1 - Material properties for mean operation temperature Mean temperature along the shell length Tsm 287.8 °C Mean temperature along the tube length Ttm 265.6 °C Mean coefficient of thermal exp. of shell at Tsm α sm 13.14 1E-6/°C Mean coefficient of thermal exp. of tubes at Ttm α tm 13.14 1E-6/°C UHX-13.6: Specification of values only for variable shell thickness of type abc for the shell region close to the tubesheet Shell material Increased shell thickness with allowances t1s in Thickness allowance c1s in Corrosion allowance c2s in Length of thickness t1s (tubesheet1, l1=0: none) l1 0 in Length of thickness t1s (tubesheet2, l'1=0: none) l'1 0 in Required length of incr. thickness 1.8* √ (Ds*t1s) lmin in Yield strength of shell at Ts = 371.1 °C Sy1s psi Strength of shell at Ts K1s psi Safety factor of shell at Ts Ss1 Allowable stress for shell at Ts S1s psi Tensile strength at room temperature 20°C Sz1s psi Limit temperature for time dependent properties TG1s °C Allowable primary and secondary stress at Ts Sps1s psi E-Modulus of shell at Ts E1s psi Mean coefficient of thermal exp. at Tsm α sm1 1E-6/°C UHX-13.8: Specification of values only for radial diff. therm. exp. type abc (Thermal expansion = 0 for ambient temperature=20°C=68°F) Tubesheet metal temperature at the rim T' 20 °C Channel metal temperature at the tubesheet T'c 20 °C Shell metal temperature at the tubesheet T's 20 °C Mean coefficient of thermal expansion of Tubesheet at T' α ' 11.5 1E-6/°C Channel at T'c α 'c 1E-6/°C Shell unreinforced (for l1+l'1=0) at T's α 's 11.5 1E-6/°C Shell reinforced acc. UHX-13.6 at T's α 's 1E-6/°C Flange (Type bcd): Mean contact diameter tubesheet-flange (type c) G1 in Bolt circle diameter C 38.88 in Number of bolts n 68 - Bolt root diameter dB 0.62 in Total bolt area Ab 20.53 in² Bolt material G41400-SA-193-B7-Class:-Size:<=64 Strength for operation Ks 25000 psi Strength for test Ksp 25000 psi Safety for operation Ss 1 - Safety for test Ssp 1 - Stress increasement factor for testing (see App.S) Fs 1 - ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 15 5-Mar-2014 Step 10: Axial membrane stress σ Sm in the shell Region of smaller wall thickness ts= 0.1875 in : (calculation case) σ Sm ≤ 1 * 17952 psi = Esw* σ zulS (1-3) σ Sm = -761.4 psi ≤ 2* 17952 psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) -761.4 psi < Min( 8493 psi , 16996 psi ) ASME external pressure chart CS-2 , A = 0.001335 — Region of increased thickness t1s= in : (calculation case) σ Sm ≤ 1 * psi = Esw* σ zulS (1-3) σ Sm = psi ≤ 2* psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) psi < Min( psi , psi ) ASME external pressure chart , A = Strength condition 13.5.10 satisfied Step 11: Absolute value of stresses σ S in the shell and σ C in the channel σ S = σ Sm + σ Sb = 19973 psi ≤ 1.5 * σ zulS, SPSs or SPSs1 σ S = -761.4 + 19211 psi ≤ 26929 psi σ C = σ Cm + σ Cb = 0 psi ≤ 1.5 * σ zulC or SPSc σ C = 0 psi + 0 psi ≤ 0 psi Minimum shell length with uniform thickness lSm 4.595 in Minimum channel thickness with uniform thickness lCm in Strength condition UHX-13.5.11 is satisfied Step 12 option 3 : If the strength condition in step 11 is violated, the tubesheet, shell or channel thickness can be increased acc. to option 1+2. Option 3 permits also the reduction of the modulus of elasticity of the shell or channel. Modulus of elasticity elastic Option 3 Shell 2.547E+7 psi 2.547E+7 psi Channel psi psi Acc. to option 3 the modulus of elasticity of the shell ES is replaced by ES* factS, under the conditions: σ S= 19973 psi ≤ 54515 psi =SPSS, with the allowable primary and secondary stress SPSS, if the allowable stress σ allS is outside of the creep range! Analogously for the channel: σ C= 0 psi ≤ 0 psi =SPSC, Geometric conditions: valid Strength condition for linked modules (Connection activated: No ): 13.4(d) If: Tube sheet thickness= 3.063 in < 1 in = tube outsied diameter, the tubesheet deformation must be considered. ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 16 5-Mar-2014 UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 17 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 3 (1-7) Tube and shell side pressure acting without differential thermal Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 1 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 12353 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² Tube pitch (center distance) p 1.25 in — Expanded length of tube in tubesheet ltx 2.909 in E4.18.5.D3 - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 20 5-Mar-2014 Step 3 Effective modulus of el. tubesheet (Fig.UHX-11.3) E* 6640236 psi Ratio of elasticity tubesheet E*/E 0.2607 effective Poisson's ratio tubesheet ν * 0.3653 Parameter for table UHX-13.1 Xa 3.971 Zd= 0.02446 , Zv= 0.06398 , Zm= 0.3705 , Za= 6.611 , Zw= 0.06398 Step 4 Diameter ratio = A/D0 K 1.182 F = 0.492 , Φ = 0.6718 , Q1 -0.02273 Qz1 = 2.859 , Qz2 = 6.905 , U 13.81 UHX-13.5.5 Step 5, coefficients γ (*)= 0 in , ω S = 2.685 in² , ω S* -1712 mm² ω C = 0 in² , ω C* = 9.677 in² , γ b -0.06025 Results acc. UHX-13.8 Radial differential thermal expansion Tr = 20 °C , Ts* = 68 °F , Tc* 68 °F Ps*= 0 psi , Pc* = 0 psi , P ω 0 psi Step 6 Ps' = -46334 psi , Pt' = 861032 psi , P γ 0 psi PW = 231.6 psi , Prim= 201 psi , Pe -420.9 psi UHX-13.5.7 Step 7 Q2 = -32722 N , Q3 = 0.09646 , Fm 0.09699 Strength condition for the tubesheet bending stress, case 3 : Sig = 26936 psi < 1.5 * SigB = 1.5* 17952 psi case 1-3 < SPS= 54515 psi case 4-7 Step 8 Strength condition for the tubesheet shear stress: Tau = 5884 psi < 0.8* SigB = 14362 psi UHX-13.5.7 Schritt 7: Bending stress Sig > 1.5*SigZul, tubesheet too thin Step 9, acc. to actual addenda or edition of UHX-13.5.9 ( Y ) Ftmin = -1.078 Ftmax = 3.807 xmin = 0 xmax = 3.971 SigT,1 = -3756 psi SigT,2 = 8451 psi σ tmax = 8451 psi ≤ SigT = 12353 psi for calculation case 1-3 ≤ 2*SigT= 24706 psi for calculation case 4-7 Tube weld force Wt = 2021 lbf ≤ Wt,all = 0 N (only when weld thickness < tube thickness: enter Wt,all>0 acc. UW-20) rt = 0.3255 in , Ft = 181.2 , Ct = 164.2 , Fs = 1.346 σ tmin = -3756 psi ≤ Stb = 5684 psi (only σ tmin < 0 buckl.) Buckling stability acc. UHX-13.5.9 satisfied Step 10: Axial membrane stress σ Sm in the shell Region of smaller wall thickness ts= 0.1875 in : (calculation case) σ Sm ≤ 1 * 17952 psi = Esw* σ zulS (1-3) σ Sm = -738.6 psi ≤ 2* 17952 psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) -738.6 psi < Min( 8493 psi , 16996 psi ) ASME external pressure chart CS-2 , A = 0.001335 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 21 5-Mar-2014 — Region of increased thickness t1s= in : (calculation case) σ Sm ≤ 1 * psi = Esw* σ zulS (1-3) σ Sm = psi ≤ 2* psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) psi < Min( psi , psi ) ASME external pressure chart , A = Strength condition 13.5.10 satisfied Step 11: Absolute value of stresses σ S in the shell and σ C in the channel σ S = σ Sm + σ Sb = 24117 psi ≤ 1.5 * σ zulS, SPSs or SPSs1 σ S = -738.6 + -23378 psi ≤ 26929 psi σ C = σ Cm + σ Cb = 0 psi ≤ 1.5 * σ zulC or SPSc σ C = 0 psi + 0 psi ≤ 0 psi Minimum shell length with uniform thickness lSm 4.595 in Minimum channel thickness with uniform thickness lCm in Strength condition UHX-13.5.11 is satisfied Step 12 option 3 : If the strength condition in step 11 is violated, the tubesheet, shell or channel thickness can be increased acc. to option 1+2. Option 3 permits also the reduction of the modulus of elasticity of the shell or channel. Modulus of elasticity elastic Option 3 Shell 2.547E+7 psi 2.547E+7 psi Channel psi psi Acc. to option 3 the modulus of elasticity of the shell ES is replaced by ES* factS, under the conditions: σ S= 24117 psi ≤ 54515 psi =SPSS, with the allowable primary and secondary stress SPSS, if the allowable stress σ allS is outside of the creep range! Analogously for the channel: σ C= 0 psi ≤ 0 psi =SPSC, Geometric conditions: valid Strength condition for linked modules (Connection activated: No ): 13.4(d) If: Tube sheet thickness= 3.063 in < 1 in = tube outsied diameter, the tubesheet deformation must be considered. UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 22 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 4 (1-7) Differential thermal expansion only (Ps=Pt=0) Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 1 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 12353 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² E4.18.5.O4 - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 25 5-Mar-2014 Step 2 Shell axial rigidity Ks or Ks* Ks 3238266 lbf/in Tube axial rigidity Kt 37624 lbf/in Stiffness ratio Ks/(Nt*Kt) Kst 0.1326 Stiffness ratio Kj/(Ks+Kj) J 0.003504 Type abc: Coefficients for shell pressure δ S 0.000054 in^3/lbf ßS= 0.7102 1/in , kS= 21842 lbf , λ S= 878461 psi — Step 3 Effective modulus of el. tubesheet (Fig.UHX-11.3) E* 6640236 psi Ratio of elasticity tubesheet E*/E 0.2607 effective Poisson's ratio tubesheet ν * 0.3653 Parameter for table UHX-13.1 Xa 3.971 Zd= 0.02446 , Zv= 0.06398 , Zm= 0.3705 , Za= 6.611 , Zw= 0.06398 Step 4 Diameter ratio = A/D0 K 1.182 F = 0.492 , Φ = 0.6718 , Q1 -0.02273 Qz1 = 2.859 , Qz2 = 6.905 , U 13.81 UHX-13.5.5 Step 5, coefficients γ (*)= -0.04727 in , ω S = 2.685 in² , ω S* -1712 mm² ω C = 0 in² , ω C* = 9.677 in² , γ b -0.06025 Results acc. UHX-13.8 Radial differential thermal expansion Tr = 20 °C , Ts* = 68 °F , Tc* 68 °F Ps*= 0 psi , Pc* = 0 psi , P ω 0 psi Step 6 Ps' = 0 psi , Pt' = 0 psi , P γ -1253 psi PW = 231.6 psi , Prim= 0 psi , Pe -0.4739 psi UHX-13.5.7 Step 7 Q2 = -17518 N , Q3 = 56.65 , Fm 28.43 Strength condition for the tubesheet bending stress, case 4 : Sig = 8891 psi < 1.5 * SigB = 1.5* 17952 psi case 1-3 < SPS= 54515 psi case 4-7 Step 8 Strength condition for the tubesheet shear stress: Tau = 6.625 psi < 0.8* SigB = 14362 psi Strength condition of step 7-8 are satisfied. Step 9, acc. to actual addenda or edition of UHX-13.5.9 ( Y ) Ftmin = -213.1 Ftmax = 453.5 xmin = 1.032 xmax = 3.971 SigT,1 = -599.7 psi SigT,2 = 1276 psi σ tmax = 1276 psi ≤ SigT = 12353 psi for calculation case 1-3 ≤ 2*SigT= 24706 psi for calculation case 4-7 Tube weld force Wt = 305.1 lbf ≤ Wt,all = 0 N (only when weld thickness < tube thickness: enter Wt,all>0 acc. UW-20) rt = 0.3255 in , Ft = 181.2 , Ct = 164.2 , Fs = 1.25 σ tmin = -599.7 psi ≤ Stb = 6123 psi (only σ tmin < 0 buckl.) Buckling stability acc. UHX-13.5.9 satisfied ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 26 5-Mar-2014 Step 10: Axial membrane stress σ Sm in the shell Region of smaller wall thickness ts= 0.1875 in : (calculation case) σ Sm ≤ 1 * 17952 psi = Esw* σ zulS (1-3) σ Sm = -21.22 psi ≤ 2* 17952 psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) -21.22 psi < Min( 8493 psi , 16996 psi ) ASME external pressure chart CS-2 , A = 0.001335 — Region of increased thickness t1s= in : (calculation case) σ Sm ≤ 1 * psi = Esw* σ zulS (1-3) σ Sm = psi ≤ 2* psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) psi < Min( psi , psi ) ASME external pressure chart , A = Strength condition 13.5.10 satisfied Step 11: Absolute value of stresses σ S in the shell and σ C in the channel σ S = σ Sm + σ Sb = 10650 psi ≤ 1.5 * σ zulS, SPSs or SPSs1 σ S = -21.22 + -10628 psi ≤ 54515 psi σ C = σ Cm + σ Cb = 0 psi ≤ 1.5 * σ zulC or SPSc σ C = 0 psi + 0 psi ≤ 0 psi Minimum shell length with uniform thickness lSm 4.595 in Minimum channel thickness with uniform thickness lCm in Strength condition UHX-13.5.11 is satisfied Step 12 option 3 : If the strength condition in step 11 is violated, the tubesheet, shell or channel thickness can be increased acc. to option 1+2. Option 3 permits also the reduction of the modulus of elasticity of the shell or channel. Modulus of elasticity elastic Option 3 Shell 2.547E+7 psi 2.547E+7 psi Channel psi psi Acc. to option 3 the modulus of elasticity of the shell ES is replaced by ES* factS, under the conditions: σ S= 10650 psi ≤ 54515 psi =SPSS, with the allowable primary and secondary stress SPSS, if the allowable stress σ allS is outside of the creep range! Analogously for the channel: σ C= 0 psi ≤ 0 psi =SPSC, Geometric conditions: valid 13.4(d) If: Tube sheet thickness= 3.063 in < 1 in = tube outsied diameter, the tubesheet deformation must be considered. UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 27 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 5 (1-7) Tube side pressure only (Ps=0) with differential thermal expansion Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 1 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 12353 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² E4.18.5.O1 - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 30 5-Mar-2014 Step 3 Effective modulus of el. tubesheet (Fig.UHX-11.3) E* 6640236 psi Ratio of elasticity tubesheet E*/E 0.2607 effective Poisson's ratio tubesheet ν * 0.3653 Parameter for table UHX-13.1 Xa 3.971 Zd= 0.02446 , Zv= 0.06398 , Zm= 0.3705 , Za= 6.611 , Zw= 0.06398 Step 4 Diameter ratio = A/D0 K 1.182 F = 0.492 , Φ = 0.6718 , Q1 -0.02273 Qz1 = 2.859 , Qz2 = 6.905 , U 13.81 UHX-13.5.5 Step 5, coefficients γ (*)= -0.04727 in , ω S = 2.685 in² , ω S* -1712 mm² ω C = 0 in² , ω C* = 9.677 in² , γ b -0.06025 Results acc. UHX-13.8 Radial differential thermal expansion Tr = 20 °C , Ts* = 68 °F , Tc* 68 °F Ps*= 0 psi , Pc* = 0 psi , P ω 0 psi Step 6 Ps' = 0 psi , Pt' = 861032 psi , P γ -1253 psi PW = 231.6 psi , Prim= 182.3 psi , Pe -400 psi UHX-13.5.7 Step 7 Q2 = -31304 N , Q3 = 0.09726 , Fm 0.0973 Strength condition for the tubesheet bending stress, case 5 : Sig = 25681 psi < 1.5 * SigB = 1.5* 17952 psi case 1-3 < SPS= 54515 psi case 4-7 Step 8 Strength condition for the tubesheet shear stress: Tau = 5592 psi < 0.8* SigB = 14362 psi Strength condition of step 7-8 are satisfied. Step 9, acc. to actual addenda or edition of UHX-13.5.9 ( Y ) Ftmin = -1.081 Ftmax = 3.813 xmin = 0 xmax = 3.971 SigT,1 = -4027 psi SigT,2 = 7595 psi σ tmax = 7595 psi ≤ SigT = 12353 psi for calculation case 1-3 ≤ 2*SigT= 24706 psi for calculation case 4-7 Tube weld force Wt = 1816 lbf ≤ Wt,all = 0 N (only when weld thickness < tube thickness: enter Wt,all>0 acc. UW-20) rt = 0.3255 in , Ft = 181.2 , Ct = 164.2 , Fs = 1.343 σ tmin = -4027 psi ≤ Stb = 5697 psi (only σ tmin < 0 buckl.) Buckling stability acc. UHX-13.5.9 satisfied Step 10: Axial membrane stress σ Sm in the shell Region of smaller wall thickness ts= 0.1875 in : (calculation case) σ Sm ≤ 1 * 17952 psi = Esw* σ zulS (1-3) σ Sm = 0.138 psi ≤ 2* 17952 psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) 0.138 psi < Min( 8493 psi , 16996 psi ) ASME external pressure chart CS-2 , A = 0.001335 — ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 31 5-Mar-2014 Region of increased thickness t1s= in : (calculation case) σ Sm ≤ 1 * psi = Esw* σ zulS (1-3) σ Sm = psi ≤ 2* psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) psi < Min( psi , psi ) ASME external pressure chart , A = Strength condition 13.5.10 satisfied Step 11: Absolute value of stresses σ S in the shell and σ C in the channel σ S = σ Sm + σ Sb = 42620 psi ≤ 1.5 * σ zulS, SPSs or SPSs1 σ S = 0.138 + -42620 psi ≤ 54515 psi σ C = σ Cm + σ Cb = 0 psi ≤ 1.5 * σ zulC or SPSc σ C = 0 psi + 0 psi ≤ 0 psi Minimum shell length with uniform thickness lSm 4.595 in Minimum channel thickness with uniform thickness lCm in Strength condition UHX-13.5.11 is satisfied Step 12 option 3 : If the strength condition in step 11 is violated, the tubesheet, shell or channel thickness can be increased acc. to option 1+2. Option 3 permits also the reduction of the modulus of elasticity of the shell or channel. Modulus of elasticity elastic Option 3 Shell 2.547E+7 psi 2.547E+7 psi Channel psi psi Acc. to option 3 the modulus of elasticity of the shell ES is replaced by ES* factS, under the conditions: σ S= 42620 psi ≤ 54515 psi =SPSS, with the allowable primary and secondary stress SPSS, if the allowable stress σ allS is outside of the creep range! Analogously for the channel: σ C= 0 psi ≤ 0 psi =SPSC, Geometric conditions: valid Strength condition for linked modules (Connection activated: No ): 13.4(d) If: Tube sheet thickness= 3.063 in < 1 in = tube outsied diameter, the tubesheet deformation must be considered. UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 32 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 6 (1-7) Shell side pressure only (Pt=0) with differential thermal expansion Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 1 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 12353 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² Tube pitch (center distance) p 1.25 in — E4.18.5.O2 - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 35 5-Mar-2014 Step 3 Effective modulus of el. tubesheet (Fig.UHX-11.3) E* 6640236 psi Ratio of elasticity tubesheet E*/E 0.2607 effective Poisson's ratio tubesheet ν * 0.3653 Parameter for table UHX-13.1 Xa 3.971 Zd= 0.02446 , Zv= 0.06398 , Zm= 0.3705 , Za= 6.611 , Zw= 0.06398 Step 4 Diameter ratio = A/D0 K 1.182 F = 0.492 , Φ = 0.6718 , Q1 -0.02273 Qz1 = 2.859 , Qz2 = 6.905 , U 13.81 UHX-13.5.5 Step 5, coefficients γ (*)= -0.04727 in , ω S = 2.685 in² , ω S* -1712 mm² ω C = 0 in² , ω C* = 9.677 in² , γ b -0.06025 Results acc. UHX-13.8 Radial differential thermal expansion Tr = 20 °C , Ts* = 68 °F , Tc* 68 °F Ps*= 0 psi , Pc* = 0 psi , P ω 0 psi Step 6 Ps' = -46334 psi , Pt' = 0 psi , P γ -1253 psi PW = 231.6 psi , Prim= 18.74 psi , Pe -21.97 psi UHX-13.5.7 Step 7 Q2 = -18936 N , Q3 = 1.299 , Fm 0.6701 Strength condition for the tubesheet bending stress, case 6 : Sig = 9714 psi < 1.5 * SigB = 1.5* 17952 psi case 1-3 < SPS= 54515 psi case 4-7 Step 8 Strength condition for the tubesheet shear stress: Tau = 307.1 psi < 0.8* SigB = 14362 psi Strength condition of step 7-8 are satisfied. Step 9, acc. to actual addenda or edition of UHX-13.5.9 ( Y ) Ftmin = -5.51 Ftmax = 13.37 xmin = 0.3971 xmax = 3.971 SigT,1 = -320.8 psi SigT,2 = 2141 psi σ tmax = 2141 psi ≤ SigT = 12353 psi for calculation case 1-3 ≤ 2*SigT= 24706 psi for calculation case 4-7 Tube weld force Wt = 512 lbf ≤ Wt,all = 0 N (only when weld thickness < tube thickness: enter Wt,all>0 acc. UW-20) rt = 0.3255 in , Ft = 181.2 , Ct = 164.2 , Fs = 1.25 σ tmin = -320.8 psi ≤ Stb = 6123 psi (only σ tmin < 0 buckl.) Buckling stability acc. UHX-13.5.9 satisfied Step 10: Axial membrane stress σ Sm in the shell Region of smaller wall thickness ts= 0.1875 in : (calculation case) σ Sm ≤ 1 * 17952 psi = Esw* σ zulS (1-3) σ Sm = -786 psi ≤ 2* 17952 psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) -786 psi < Min( 8493 psi , 16996 psi ) ASME external pressure chart CS-2 , A = 0.001335 — ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 36 5-Mar-2014 Region of increased thickness t1s= in : (calculation case) σ Sm ≤ 1 * psi = Esw* σ zulS (1-3) σ Sm = psi ≤ 2* psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) psi < Min( psi , psi ) ASME external pressure chart , A = Strength condition 13.5.10 satisfied Step 11: Absolute value of stresses σ S in the shell and σ C in the channel σ S = σ Sm + σ Sb = 9364 psi ≤ 1.5 * σ zulS, SPSs or SPSs1 σ S = -786 + 8578 psi ≤ 54515 psi σ C = σ Cm + σ Cb = 0 psi ≤ 1.5 * σ zulC or SPSc σ C = 0 psi + 0 psi ≤ 0 psi Minimum shell length with uniform thickness lSm 4.595 in Minimum channel thickness with uniform thickness lCm in Strength condition UHX-13.5.11 is satisfied Step 12 option 3 : If the strength condition in step 11 is violated, the tubesheet, shell or channel thickness can be increased acc. to option 1+2. Option 3 permits also the reduction of the modulus of elasticity of the shell or channel. Modulus of elasticity elastic Option 3 Shell 2.547E+7 psi 2.547E+7 psi Channel psi psi Acc. to option 3 the modulus of elasticity of the shell ES is replaced by ES* factS, under the conditions: σ S= 9364 psi ≤ 54515 psi =SPSS, with the allowable primary and secondary stress SPSS, if the allowable stress σ allS is outside of the creep range! Analogously for the channel: σ C= 0 psi ≤ 0 psi =SPSC, Geometric conditions: valid Strength condition for linked modules (Connection activated: No ): 13.4(d) If: Tube sheet thickness= 3.063 in < 1 in = tube outsied diameter, the tubesheet deformation must be considered. UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 37 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 7 (1-7) Tube and shell side pressure acting with differential thermal Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 1 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 12353 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² Tube pitch (center distance) p 1.25 in — Expanded length of tube in tubesheet ltx 2.909 in E4.18.5.O3 - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 40 5-Mar-2014 Step 3 Effective modulus of el. tubesheet (Fig.UHX-11.3) E* 6640236 psi Ratio of elasticity tubesheet E*/E 0.2607 effective Poisson's ratio tubesheet ν * 0.3653 Parameter for table UHX-13.1 Xa 3.971 Zd= 0.02446 , Zv= 0.06398 , Zm= 0.3705 , Za= 6.611 , Zw= 0.06398 Step 4 Diameter ratio = A/D0 K 1.182 F = 0.492 , Φ = 0.6718 , Q1 -0.02273 Qz1 = 2.859 , Qz2 = 6.905 , U 13.81 UHX-13.5.5 Step 5, coefficients γ (*)= -0.04727 in , ω S = 2.685 in² , ω S* -1712 mm² ω C = 0 in² , ω C* = 9.677 in² , γ b -0.06025 Results acc. UHX-13.8 Radial differential thermal expansion Tr = 20 °C , Ts* = 68 °F , Tc* 68 °F Ps*= 0 psi , Pc* = 0 psi , P ω 0 psi Step 6 Ps' = -46334 psi , Pt' = 861032 psi , P γ -1253 psi PW = 231.6 psi , Prim= 201 psi , Pe -421.5 psi UHX-13.5.7 Step 7 Q2 = -32722 N , Q3 = 0.0963 , Fm 0.09692 Strength condition for the tubesheet bending stress, case 7 : Sig = 26955 psi < 1.5 * SigB = 1.5* 17952 psi case 1-3 < SPS= 54515 psi case 4-7 Step 8 Strength condition for the tubesheet shear stress: Tau = 5892 psi < 0.8* SigB = 14362 psi Strength condition of step 7-8 are satisfied. Step 9, acc. to actual addenda or edition of UHX-13.5.9 ( Y ) Ftmin = -1.077 Ftmax = 3.806 xmin = 0 xmax = 3.971 SigT,1 = -3758 psi SigT,2 = 8461 psi σ tmax = 8461 psi ≤ SigT = 12353 psi for calculation case 1-3 ≤ 2*SigT= 24706 psi for calculation case 4-7 Tube weld force Wt = 2023 lbf ≤ Wt,all = 0 N (only when weld thickness < tube thickness: enter Wt,all>0 acc. UW-20) rt = 0.3255 in , Ft = 181.2 , Ct = 164.2 , Fs = 1.347 σ tmin = -3758 psi ≤ Stb = 5681 psi (only σ tmin < 0 buckl.) Buckling stability acc. UHX-13.5.9 satisfied Step 10: Axial membrane stress σ Sm in the shell Region of smaller wall thickness ts= 0.1875 in : (calculation case) σ Sm ≤ 1 * 17952 psi = Esw* σ zulS (1-3) σ Sm = -764.7 psi ≤ 2* 17952 psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) -764.7 psi < Min( 8493 psi , 16996 psi ) ASME external pressure chart CS-2 , A = 0.001335 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 41 5-Mar-2014 — Region of increased thickness t1s= in : (calculation case) σ Sm ≤ 1 * psi = Esw* σ zulS (1-3) σ Sm = psi ≤ 2* psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) psi < Min( psi , psi ) ASME external pressure chart , A = Strength condition 13.5.10 satisfied Step 11: Absolute value of stresses σ S in the shell and σ C in the channel σ S = σ Sm + σ Sb = 24177 psi ≤ 1.5 * σ zulS, SPSs or SPSs1 σ S = -764.7 + -23413 psi ≤ 54515 psi σ C = σ Cm + σ Cb = 0 psi ≤ 1.5 * σ zulC or SPSc σ C = 0 psi + 0 psi ≤ 0 psi Minimum shell length with uniform thickness lSm 4.595 in Minimum channel thickness with uniform thickness lCm in Strength condition UHX-13.5.11 is satisfied Step 12 option 3 : If the strength condition in step 11 is violated, the tubesheet, shell or channel thickness can be increased acc. to option 1+2. Option 3 permits also the reduction of the modulus of elasticity of the shell or channel. Modulus of elasticity elastic Option 3 Shell 2.547E+7 psi 2.547E+7 psi Channel psi psi Acc. to option 3 the modulus of elasticity of the shell ES is replaced by ES* factS, under the conditions: σ S= 24177 psi ≤ 54515 psi =SPSS, with the allowable primary and secondary stress SPSS, if the allowable stress σ allS is outside of the creep range! Analogously for the channel: σ C= 0 psi ≤ 0 psi =SPSC, Geometric conditions: valid Strength condition for linked modules (Connection activated: No ): 13.4(d) If: Tube sheet thickness= 3.063 in < 1 in = tube outsied diameter, the tubesheet deformation must be considered. UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 42 5-Mar-2014 Fixed tubesheets according to ASME-UHX-13 Configuration of the tubesheet (a, b, c, d) Type b (a-d) Tubesheet integral with shell, gasketed with channel, flange Channel type (1=Cylinder, 2=Hemispherical) CType 1 (1,2) Internal operation pressure shell side Ps 150 psi Internal operation pressure tube side Pt 400 psi Internal test pressure shell side Psp psi Internal test pressure tube side Ptp psi Load case (1=operation, 2+3=test at 20°C, 4=other) 1 load case: operation Calculation case acc. UHX-13.4(a): (1), (2) ... (7) 1 (1-7) Tube side pressure only (Ps=0) without differential thermal Tubesheet material K02700-SA-516-70-Class:-Size: Shell material (Type abc) K02700-SA-516-70-Class:-Size: Tube material K01807-SA-214--Class:-Size: Channel material(Type a) Operation Tubesheet Shell Tubes Channel Temperature 371.1 °C 371.1 °C 371.1 °C °C Thickness 3.063 in 0.1875 in 0.083 in in Outs.diam. 40.5 in 35.13 in 1 in in Poiss.-rat. - 0.3 0.3 0.3 Allow..c1 0 in 0 in 0 in in Corr.all.c2 0 in 0 in 0 in in Properties for the selected load case temperature Op.strength 17952 psi 17952 psi 10430 psi psi Oper.safety 1 1 0.85 E-module**) 2.547E+7 psi 2.547E+7 psi 2.547E+7 psi psi Therm.dil. 13.66 1E-6/°C 13.66 1E-6/°C 13.66 1E-6/°C 1E-6/°C Yield str. 27257 psi 27257 psi 18655 psi psi Limit temp. 400 °C 400 °C 400 °C °C All.stress*) 17952 psi 17952 psi 12271 psi 0 psi Pr.+sec.st*) 54515 psi 54515 psi 0 psi Properties for testing at 20°C Strength*) 33939 psi 33939 psi 23496 psi 0 psi Safety 1 1 1 Yield str. 37710 psi 37710 psi 26107 psi psi Tensile str. 70343 psi 70343 psi 47137 psi psi additional specifications for the geometry and loading Tubesheet Tube-tubesheet joint (1=expanded, 2=welded) 1 (1, 2) Tube pattern (1=Triangle, 2=Square) 1 (1, 2) Number of tubes Nt 649 Radius to outermost tube hole center, Fig.UHX-11.1a r0T 16.63 in Perimeter of the outermost tubes, Fig. UHX-12.2 Cp in Total area enclosed by Cp, Fig. UHX-12.2 Ap in² Tube pitch (center distance) p 1.25 in — Expanded length of tube in tubesheet ltx 2.909 in E4.18.5.D1-plastic - LV Calculation ASME UHX-13 Fixed Tubesheets ASME BPVC Edition 2013 ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 45 5-Mar-2014 Step 3 Effective modulus of el. tubesheet (Fig.UHX-11.3) E* 6640232 psi Ratio of elasticity tubesheet E*/E 0.2607 effective Poisson's ratio tubesheet ν * 0.3653 Parameter for table UHX-13.1 Xa 3.971 Zd= 0.02446 , Zv= 0.06398 , Zm= 0.3705 , Za= 6.611 , Zw= 0.06398 Step 4 Diameter ratio = A/D0 K 1.182 F = 0.492 , Φ = 0.6718 , Q1 -0.02273 Qz1 = 2.859 , Qz2 = 6.905 , U 13.81 UHX-13.5.5 Step 5, coefficients γ (*)= 0 in , ω S = 2.685 in² , ω S* -1712 mm² ω C = 0 in² , ω C* = 9.677 in² , γ b -0.06025 Results acc. UHX-13.8 Radial differential thermal expansion Tr = 20 °C , Ts* = 68 °F , Tc* 68 °F Ps*= 0 psi , Pc* = 0 psi , P ω 0 psi Step 6 Ps' = 0 psi , Pt' = 861032 psi , P γ 0 psi PW = 231.6 psi , Prim= 182.3 psi , Pe -399.4 psi UHX-13.5.7 Step 7 Q2 = -31304 N , Q3 = 0.09743 , Fm 0.09737 Strength condition for the tubesheet bending stress, case 1 : Sig = 25662 psi < 1.5 * SigB = 1.5* 17952 psi case 1-3 < SPS= 54515 psi case 4-7 Step 8 Strength condition for the tubesheet shear stress: Tau = 5584 psi < 0.8* SigB = 14362 psi Strength condition of step 7-8 are satisfied. Step 9, acc. to actual addenda or edition of UHX-13.5.9 ( Y ) Ftmin = -1.081 Ftmax = 3.815 xmin = 0 xmax = 3.971 SigT,1 = -4025 psi SigT,2 = 7585 psi σ tmax = 7585 psi ≤ SigT = 12271 psi for calculation case 1-3 ≤ 2*SigT= 24541 psi for calculation case 4-7 Tube weld force Wt = 1814 lbf ≤ Wt,all = 0 N (only when weld thickness < tube thickness: enter Wt,all>0 acc. UW-20) rt = 0.3255 in , Ft = 181.2 , Ct = 164.2 , Fs = 1.343 σ tmin = -4025 psi ≤ Stb = 5700 psi (only σ tmin < 0 buckl.) Buckling stability acc. UHX-13.5.9 satisfied Step 10: Axial membrane stress σ Sm in the shell Region of smaller wall thickness ts= 0.1875 in : (calculation case) σ Sm ≤ 1 * 17952 psi = Esw* σ zulS (1-3) σ Sm = 26.16 psi ≤ 2* 17952 psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) 26.16 psi < Min( 8493 psi , 16996 psi ) ASME external pressure chart CS-2 , A = 0.001335 — ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 46 5-Mar-2014 Region of increased thickness t1s= in : (calculation case) σ Sm ≤ 1 * psi = Esw* σ zulS (1-3) σ Sm = psi ≤ 2* psi = 2* σ zulS (4-7) For σ Sm < 0: σ Sm < Min( B, A*E/2 ) acc. UG-23(b) psi < Min( psi , psi ) ASME external pressure chart , A = Strength condition 13.5.10 satisfied Step 11: Absolute value of stresses σ S in the shell and σ C in the channel σ S = σ Sm + σ Sb = 42611 psi ≤ 1.5 * σ zulS, SPSs or SPSs1 σ S = 26.16 + -42585 psi ≤ 26929 psi σ C = σ Cm + σ Cb = 0 psi ≤ 1.5 * σ zulC or SPSc σ C = 0 psi + 0 psi ≤ 0 psi Minimum shell length with uniform thickness lSm 4.595 in Minimum channel thickness with uniform thickness lCm in Strength condition UHX-13.5.11 is violated! Step 12 option 3 : If the strength condition in step 11 is violated, the tubesheet, shell or channel thickness can be increased acc. to option 1+2. Option 3 permits also the reduction of the modulus of elasticity of the shell or channel. Modulus of elasticity elastic Option 3 Shell 2.547E+7 psi 2.547E+7 psi Channel psi psi Acc. to option 3 the modulus of elasticity of the shell ES is replaced by ES* factS, under the conditions: σ S= 42611 psi ≤ 54515 psi =SPSS, with the allowable primary and secondary stress SPSS, if the allowable stress σ allS is outside of the creep range! Analogously for the channel: σ C= 0 psi ≤ 0 psi =SPSC, Geometric conditions: valid Strength condition for linked modules (Connection activated: Yes ): Strength violated for calculation case: 1 13.4(d) If: Tube sheet thickness= 3.063 in < 1 in = tube outsied diameter, the tubesheet deformation must be considered. UHX-11.4(b): The calculation of fixed tubesheets shall be performed with corrosion (corrosion allowance c2>0) and without corrosion (c2=0). Acc. to UHX-13.4(e)(2) the shell must eventually be designed for column buckling (in the case of compression). ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 47 5-Mar-2014 Tables with comment every three lines Arrangement in 3 lines. Line 3 calculates the difference between line 1 and 2 in %. The maximum of each line is calculated in column 8 at the end. ------------------------------:-----------------------------------:------- : Conversion factors : Step 1-3 : Maximum : MPa2psi : N2lb : mm2in : hr : my* : Kst : J : Diff % 1 145 : 0.2248 : 0.03937 : 1.233 : 0.2843 : 0.1326 :0.003504 : 2 0 : 0 : 0 : 1.228 : 0.2861 : 0.1326 : 0.0035 : 3 0 : 0 : 0 : 0.4478 : 0.6187 :0.001885 : 0.125 : 0.6187 ---- Step 2 -------------------------------------------------------------- : betaS : kS : lambdaS : deltaS : 4 0.7102 : 21841 : 878238 :0.000054 : 0 : 0 : 0 : 5 0.7102 : 21866 : 879437 :0.000054 : 0 : 0 : 0 : 6 0.006745 : 0.1164 : 0.1363 : 0.114 : 0 : 0 : 0 : 0.1363 ---- Step 3 -------------------------------------------------------------- : ny* : E* : Xa : Zd : Zv : Zm : Za :MaxDiff% 7 0.3653 : 6638545 : 3.971 : 0.02446 : 0.06398 : 0.3705 : 6.611 : 8 0.364 : 6706322 : 3.963 : 0.02461 : 0.06426 : 0.3715 : 6.547 : 9 0.3794 : 1.011 : 0.1909 : 0.5934 : 0.4276 : 0.2606 : 0.9643 : 1.011 ---- Step 4 -------------------------------------------------------------- : K : F : phi : Q1 : 10 1.182 : 0.492 : 0.6718 :-0.02273 : 2.859 : 6.905 : 13.81 : 11 1.183 : 0.4888 : 0.6667 :-0.02264 : 2.856 : 6.888 : 13.78 : 12 0.001522 : 0.6588 : 0.7618 : 0.4104 : 0.1327 : 0.2485 : 0.2485 : 0.7618 ---- Step 5 -------------------------------------------------------------- : omS : om*S : omC : om*C : gammab : :MaxDiff% 13 2.685 : -2.654 : 0 : 9.677 :-0.06025 : : : 14 2.685 : -2.654 : 0 : 9.682 :-0.06022 : : : 15 0.00149 : 0.00147 : 0 : 0.05101 : 0.04598 : 0 : 0 : 0.05101 ---- Step 5+6 for calculation case 7(O3) ----------------------------------- : gamma : Ps' : Pt' : Pgamma : PW 16 -0.04727 : -46322 : 860814 : -1252 : 231.6 : 201 : -421.4 : 17 -0.047 : -46387 : 862002 : -1254 : 230.9 : 200.6 : -421.5 : 18 0.5693 : 0.14 : 0.1379 : 0.1231 : 0.2825 : 0.1835 : 0.02733 : 0.5693 ---- Step 7+8+9 for calculation case 1 (D1) -------------------------------- : Q2 : Q3 : Fm : |Sig| : 19 -7037 : 0.09743 : 0.09737 : 25656 : 5582 : -1.081 : -4024 : 20 -7041 : 0.0976 : 0.0975 : 25540 : 5584 : -1.081 : -4024 : 21 0.04914 : 0.1718 : 0.1319 : 0.453 : 0.03138 : 0.01434 :0.007331 : 0.453 ---- Step 7+8+9 for calculation case 2(D2) --------------------------------- : Q2 : Q3 : Fm : |Sig| : 22 -318.7 : 0.07875 : 0.09004 : 1272 : 299.3 : -1.012 : 269.1 : 23 -319 : 0.0786 : 0.0901 : -1269 : 299 : -1.011 : -269 : 24 -0.09373 : 0.1949 :-0.06574 : 0.2504 : 0.1139 : 0.1316 : 0.02093 : 0.2504 ---- Step 7+8+9 for calculation case 3 (D3)--------------------------------- : Q2 : Q3 : Fm : |Sig| : 25 -7356 : 0.09646 : 0.09699 : 26929 : 5883 : -1.078 : -3755 : 26 -7363 : 0.09667 : 0.09717 : 26819 : 5884 : -1.078 : -3758 : 27 0.09987 : 0.2173 : 0.1902 : 0.4106 : 0.02614 : 0.0397 : 0.07611 : 0.4106 ---- Step 7+8+9 for calculation case 4(O4) --------------------------------- : Q2 : Q3 : Fm : |Sig| : |Tau| : Ftmin : Sigt1 :MaxDiff% 28 -3938 : 56.65 : 28.43 : 8888 : 6.624 : -213.1 : -599.6 : 29 -3940 : 56.63 : 28.41 : 8838 : 6.6 : -213.2 : -600.4 : 30 0.05713 : 0.03625 : 0.07466 : 0.5686 : 0.3574 : 0.02388 : 0.1412 : 0.5686 — Comparison Table Form for equations ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 50 5-Mar-2014 Appendix : Material documentation Section no 1: Boden/UHXbSection no 1: Mantel/UHXbSection no 1: Boden-Zeitst/UHXbSection no 1: Mantel- Zeitst/UHXbSection no 2: Boden/UHXbSection no 2: Mantel/UHXbSection no 2: Boden-Zeitst/UHXbSection no 2: Mantel-Zeitst/UHXbSection no 3: Boden/UHXbSection no 3: Mantel/UHXbSection no 3: Boden-Zeitst/UHXbSection no 3: Mantel-Zeitst/UHXbSection no 4: Boden/UHXbSection no 4: Mantel/UHXbSection no 4: Boden-Zeitst/UHXbSection no 4: Mantel-Zeitst/UHXbSection no 5: Boden/UHXbSection no 5: Mantel/UHXbSection no 5: Boden- Zeitst/UHXbSection no 5: Mantel-Zeitst/UHXbSection no 6: Boden/UHXbSection no 6: Mantel/UHXbSection no 6: Boden-Zeitst/UHXbSection no 6: Mantel-Zeitst/UHXbSection no 7: Boden/UHXbSection no 7: Mantel/UHXbSection no 7: Boden-Zeitst/UHXbSection no 7: Mantel-Zeitst/UHXbSection no 8: Boden/UHXbSection no 8: Mantel/UHXbSection no 8: Boden-Zeitst/UHXbSection no 8: Mantel-Zeitst/UHXb Material specification: Regulation: ASMET1A:2010Spec. No.: SA-516 Product: Plate Material code: K02700-SA-516-70-Class:-Size: Short name: Carbon steel Design conditions and dimensions: Temperature [°C]: 371,1111 Pressure [bar]: 0 Thickness [mm]: 77,79 Outside diameter [mm]: 1028,7 Material values for test and design conditions: Test condition Operating condition ---------------------------------------- Nominal design strength [N/mm²]: 138,00 123,78 Safety factor: 1,00 1,00 Allowable stress [N/mm²]: 138,00 123,78 Modulus of elasticity [kN/mm²]: 202 175,6222 Creep rupture strength for 100000 h [MPa]: Tensile strength and yield stress at ambient temperature: Diam./·········|Tensile str.···|···············|ReH············|Rupture········|Rupture········ Thick.·········|Rm min·········|Rm max·········|···············|elong.·········|elong·········· <= mm··········|MPa············|MPa············|MPa············|längs %········|quer %········· ---------------+---------------+---------------+---------------+---------------+--------------- ···············|···············|···············|···············|···············|··············· K-values as function of the temperature Diam./···|·········|·········|·········|·········|·········|·········|·········|········· Thickn.··|50°C·····|100°C····|150°C····|200°C····|250°C····|300°C····|350°C····|400°C···· <= mm····|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······ ---------+---------+---------+---------+---------+---------+---------+---------+--------- ·········|·········|138······|138······|138······|138······|136······|128······|101······ K-values as function of the temperature Diam./·····|···········|···········|···········|···········|···········|···········|··········· Thickn.····|450°C······|500°C······|550°C······|600°C······|650°C······|700°C······|800°C······ <= mm······|MPa········|MPa········|MPa········|MPa········|MPa········|MPa········|MPa········ -----------+-----------+-----------+-----------+-----------+-----------+-----------+----------- ···········|67.1·······|33.6·······|12.9·······|···········|···········|···········|··········· Modulus of elasticity in dependence of the temperature: Static modulus of elasticity in [kN/mm²] at the temperature of -75···|-200··|-125··|25····|100···|150···|200···|250···|300···|350···|400···|450···|500···|550··· ------+------+------+------+------+------+------+------+------+------+------+------+------+------ 209···|216···|212···|202···|198···|195···|192···|189···|185···|179···|171···|162···|151···|137··· Coefficient of linear expansion: Thermal coefficient of expansion between 20°C and Density|100°C··|200°C··|300°C··|400°C··|500°C··|600°C··|700°C··|800°C··|Heat···|Heat··· (20 °C)|·······|·······|·······|·······|·······|·······|·······|·······|cond.··|capac.· kg/dm³·|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|W/Km···|J/kgK·· -------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------- 7,85···|12,1···|12,7···|13,3···|13,8···|14,4···|-······|-······|-······|·······|······· ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 51 5-Mar-2014 Section no 1: Rohre/UHXbSection no 1: Rohre-Zeitst/UHXbSection no 1: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXbSection no 2: Rohre/UHXbSection no 2: Rohre-Zeitst/UHXbSection no 2: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXbSection no 3: Rohre/UHXbSection no 3: Rohre-Zeitst/UHXbSection no 3: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXbSection no 4: Rohre/UHXbSection no 4: Rohre-Zeitst/UHXbSection no 4: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXbSection no 5: Rohre/UHXbSection no 5: Rohre-Zeitst/UHXbSection no 5: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXbSection no 6: Rohre/UHXbSection no 6: Rohre- Zeitst/UHXbSection no 6: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXbSection no 7: Rohre/UHXbSection no 7: Rohre-Zeitst/UHXbSection no 7: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXbSection no 8: Rohre/UHXbSection no 8: Rohre-Zeitst/UHXbSection no 8: Rohre bei Bodentemp. /Tubes at tubesheet temp./UHXb Material specification: Regulation: ASMET1A:2010Spec. No.: SA-214 Product: Wld. tube Material code: K01807-SA-214--Class:-Size: Short name: Carbon steel Design conditions and dimensions: Temperature [°C]: 371,1111 Pressure [bar]: 0 Thickness [mm]: 2,11 Outside diameter [mm]: 25,4 Material values for test and design conditions: Test condition Operating condition ---------------------------------------- Nominal design strength [N/mm²]: 78,60 71,91 Safety factor: 1,00 1,00 Allowable stress [N/mm²]: 78,60 71,91 Modulus of elasticity [kN/mm²]: 202 175,6222 Creep rupture strength for 100000 h [MPa]: Tensile strength and yield stress at ambient temperature: Diam./·········|Tensile str.···|···············|ReH············|Rupture········|Rupture········ Thick.·········|Rm min·········|Rm max·········|···············|elong.·········|elong·········· <= mm··········|MPa············|MPa············|MPa············|längs %········|quer %········· ---------------+---------------+---------------+---------------+---------------+--------------- ···············|···············|···············|···············|···············|··············· K-values as function of the temperature Diam./···|·········|·········|·········|·········|·········|·········|·········|········· Thickn.··|50°C·····|100°C····|150°C····|200°C····|250°C····|300°C····|350°C····|400°C···· <= mm····|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······ ---------+---------+---------+---------+---------+---------+---------+---------+--------- ·········|·········|78.6·····|78.6·····|78.6·····|78.6·····|78.1·····|74.7·····|62.3····· K-values as function of the temperature Diam./·····|···········|···········|···········|···········|···········|···········|··········· Thickn.····|450°C······|500°C······|550°C······|600°C······|650°C······|700°C······|800°C······ <= mm······|MPa········|MPa········|MPa········|MPa········|MPa········|MPa········|MPa········ -----------+-----------+-----------+-----------+-----------+-----------+-----------+----------- ···········|47.6·······|27.1·······|10.6·······|···········|···········|···········|··········· Modulus of elasticity in dependence of the temperature: Static modulus of elasticity in [kN/mm²] at the temperature of -75···|-200··|-125··|25····|100···|150···|200···|250···|300···|350···|400···|450···|500···|550··· ------+------+------+------+------+------+------+------+------+------+------+------+------+------ 209···|216···|212···|202···|198···|195···|192···|189···|185···|179···|171···|162···|151···|137··· Coefficient of linear expansion: Thermal coefficient of expansion between 20°C and Density|100°C··|200°C··|300°C··|400°C··|500°C··|600°C··|700°C··|800°C··|Heat···|Heat··· (20 °C)|·······|·······|·······|·······|·······|·······|·······|·······|cond.··|capac.· kg/dm³·|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|W/Km···|J/kgK·· -------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------- 7,85···|12,1···|12,7···|13,3···|13,8···|14,4···|-······|-······|-······|·······|······· ASME PTB-4-2013 Example E4.18.5 BPVC VIII-1 2013 Lauterbach Verfahrenstechnik GmbH 52 5-Mar-2014 Section no 1: mittlere W-dehn. Mantel/UHXbSection no 2: mittlere W-dehn. Mantel/UHXbSection no 3: mittlere W- dehn. Mantel/UHXbSection no 4: mittlere W-dehn. Mantel/UHXbSection no 5: mittlere W-dehn. Mantel/UHXbSection no 6: mittlere W-dehn. Mantel/UHXbSection no 7: mittlere W-dehn. Mantel/UHXbSection no 8: mittlere W-dehn. Mantel/UHXb Material specification: Regulation: ASMET1A:2010Spec. No.: SA-516 Product: Plate Material code: K02700-SA-516-70-Class:-Size: Short name: Carbon steel Design conditions and dimensions: Temperature [°C]: 287,78 Pressure [bar]: 0 Thickness [mm]: 4,76 Outside diameter [mm]: 892,18 Material values for test and design conditions: Test condition Operating condition ---------------------------------------- Nominal design strength [N/mm²]: 138,00 136,49 Safety factor: 1,00 1,00 Allowable stress [N/mm²]: 138,00 136,49 Modulus of elasticity [kN/mm²]: 202 185,9776 Creep rupture strength for 100000 h [MPa]: Tensile strength and yield stress at ambient temperature: Diam./·········|Tensile str.···|···············|ReH············|Rupture········|Rupture········ Thick.·········|Rm min·········|Rm max·········|···············|elong.·········|elong·········· <= mm··········|MPa············|MPa············|MPa············|längs %········|quer %········· ---------------+---------------+---------------+---------------+---------------+--------------- ···············|···············|···············|···············|···············|··············· K-values as function of the temperature Diam./···|·········|·········|·········|·········|·········|·········|·········|········· Thickn.··|50°C·····|100°C····|150°C····|200°C····|250°C····|300°C····|350°C····|400°C···· <= mm····|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······|MPa······ ---------+---------+---------+---------+---------+---------+---------+---------+--------- ·········|·········|138······|138······|138······|138······|136······|128······|101······ K-values as function of the temperature Diam./·····|···········|···········|···········|···········|···········|···········|··········· Thickn.····|450°C······|500°C······|550°C······|600°C······|650°C······|700°C······|800°C······ <= mm······|MPa········|MPa········|MPa········|MPa········|MPa········|MPa········|MPa········ -----------+-----------+-----------+-----------+-----------+-----------+-----------+----------- ···········|67.1·······|33.6·······|12.9·······|···········|···········|···········|··········· Modulus of elasticity in dependence of the temperature: Static modulus of elasticity in [kN/mm²] at the temperature of -75···|-200··|-125··|25····|100···|150···|200···|250···|300···|350···|400···|450···|500···|550··· ------+------+------+------+------+------+------+------+------+------+------+------+------+------ 209···|216···|212···|202···|198···|195···|192···|189···|185···|179···|171···|162···|151···|137··· Coefficient of linear expansion: Thermal coefficient of expansion between 20°C and Density|100°C··|200°C··|300°C··|400°C··|500°C··|600°C··|700°C··|800°C··|Heat···|Heat··· (20 °C)|·······|·······|·······|·······|·······|·······|·······|·······|cond.··|capac.· kg/dm³·|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|10E-6/K|W/Km···|J/kgK·· -------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------- 7,85···|12,1···|12,7···|13,3···|13,8···|14,4···|-······|-······|-······|·······|·······