ASME PTB Example E E4.3.5 BPVC VIII
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- Γώργος Τρικούπη
- 6 χρόνια πριν
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1 Table of contents Table of contents... 1 Comparison Overview * Internal Design Pressure... 3 Example E Cylindrical Shell... 3 E LV Calculation * Example E Conical Shell... 6 E LV Calculation * Example E Spherical Shell... 9 E LV Calculation * Example E Torispherical Head E LV Calculation * Example E Elliptical Head E LV Calculation * Appendix : Material documentation Layout Input values: or Calculated values: or Critical values: or Estimated values: or Lauterbach Verfahrenstechnik GmbH 1 27-Feb-2014
2 Comparison Overview * Equation form Comments Results for examples E4.3.1 to 5 acc. ASME and Lauterbach Verfahrenstechnik GmbH The LV program uses formulas for thick shells acc.asme VIII Div.1 UG27/32 and App.1. Equations Value Conversion factor mm2in = MPa2psi = 'Results Ex. E4.3.1 LV and ASME Required thickness t acc. LV t1 = mm2in*#6(1) Required thickness tc ASME tc1asme = Difference in % Diff1 = (t1-tc1asme)/tc1asme* 'Results Ex. E4.3.2 LV and ASME Required thickness acc. LV t2 = mm2in*#15(7) Required thickness ASME tc2asme = Difference in % Diff2 = (t2-tc2asme)/tc2asme* 'Results Ex. E4.3.3 LV and ASME Required thickness t acc. LV t3 = mm2in*#25(8) Required thickness tc ASME tc3asme = Difference in % Diff3 = (t3-tc3asme)/tc3asme* 'Results Ex. E4.3.4 LV and ASME Allowable Pressure P acc. LV P4 = MPa2psi*#16(5) Allowable Pressure P ASME P4Asme = Difference in % Diff4 = (P4-P4Asme)/P4Asme* 'Results Ex. E4.3.5 LV and ASME Allowable Pressure P acc. LV P5 = MPa2psi*#16(9) Allowable Pressure P ASME P5Asme = Difference in % Diff5 = (P5-P5Asme)/P5Asme* 'Maximum difference between LV and ASME Dmax = Max( Diff1 ; Diff2 ; Diff3 ; Diff4 ; Diff5 ) * Form for equations Lauterbach Verfahrenstechnik GmbH 2 27-Feb-2014
3 4.3 Internal Design Pressure Example E Cylindrical Shell Determine the required thickness for a cylindrical shell considering the following design conditions. All Category A and B joints are Type 1 butt welds and have been 100% radiographically examined. Vessel Data: Material = SA-516, Grade 70, Normalized Design Conditions = 356 psig@300 F Inside Diameter = 90.0 in Corrosion Allowance = in Allowable Stress = psi Weld Joint Efficiency = 1.0 Determine the inside radius and adjust for corrosion allowance. Lauterbach Verfahrenstechnik GmbH 3 27-Feb-2014
4 E LV Calculation * Cylindrical shells Design pressure PD 356 psi = pd 356 psi Hydrostatic head DP 0 psi = Dp 0 psi Calculation pressure P0 356 psi = p0 356 psi Calulation temperature T0 300 F Outside diameter D0 98 in Design wall thickness te 4 in Wall thickness allowance c in Allowance (corrosion) c2 0 in Weld joint efficiency E 1 - Material: K02700-SA Class:-Size: Allowable stress S psi Results Outside radius R0 49 in Effective thickness t in Required thickness t(r0) t(r) thin shell acc. UG in in thick shell (not applicable) in in Minimum t = Min[t(R);t(R0)] t mm with allowances t+c1+c in Allowable excess pressure P 1633 psi Allowable excess pressure without hydr. head MAWP 1633 psi Remark: For calculation of openings according to UG-37: Required thickness t(e=1) mm Allowable unreinforced opening diameter da for welded, brazed, and flued connections acc. UG 36(c)3: da 89 mm for t 10 mm or: da 3 1/2 in for t 3/8 in da 60 mm for t > 10 mm or: da 2 3/8 in for t > 3/8 in For a vessel thickness > 2*t(E=1) the reinforcement of the vessel alone is sufficient for unreinforced openings, unless additional conditions acc. to UG-37 apply. * Thickness of shells under internal pressure ASME BPVC VIII UG-27 & APPENDIX-1, 2013 Edition Lauterbach Verfahrenstechnik GmbH 4 27-Feb-2014
5 Equations: P0 = 0.1*p0 = = 0.1 * R0 = D0 / 2 = 1245 = 2489 / 2 t+c1+c2 = 23.8 = R = R0 - t0 = = 1146 = corroded inside radius 1) Thin shell: For P0 = 356 psi 0.385*S*E = 7700 psi and te = (R0-te) / 2 = ( )/2 = acc. UG-27 Eq.(1) with the inside radius R: P0*R * 1146 t(r) = = = S*E - 0.6*P * * S*E*t * 1 * P(R) = = = R + 0.6*t * or with the outside radius R0 acc. App.1-1 Eq.(1): P0*R * 1245 t(r0) = = = 22 S*E + 0.4*P * * S*E*t * 1 * P(R0) = = = R0-0.4*t * ) Thick shell: For P0 = 356 psi > 0.385*S*E = 7700 psi or te = > (R0-te) / 2 = ( )/2 = with the inside radius R acc. App.1-2: t(r) = R * ( Exp(P0/(S*E)) - 1 ) = 1146 * ( Exp( / ( * 1 ) - 1 ) P(R) = S*E*Log((R+t0)/R) = * 1 * Log(( )/ 1146 )) or with the outside radius R0 acc. App.1-2: t(r0) = R0 * ( 1 - Exp(-P0/(S*E)) ) = 1245 * ( 1 - exp( / ( * 1 ) ) P(R0) = S*E*Log(R0/(R0-t0)) = * 1 * Log( 1245 / ( )) Log(x) = Ln(x) Lauterbach Verfahrenstechnik GmbH 5 27-Feb-2014
6 4.3.2 Example E Conical Shell Determine the required thickness for a conical shell considering the following design conditions. All Category A and B joints are Type 1 butt welds and have been 100% radiographically examined. Vessel Data: Material = SA - 516, Grade 70, Normalized Design Conditions = 356 F Inside Diameter (Large End) = in Inside Diameter (Small End) = 90.0 in Length of Conical Section = 78.0 in Corrosion Allowance = in Allowable Stress = psi Weld Joint Efficiency = 1.0 Adjust for corrosion allowance and determine the cone angle. Lauterbach Verfahrenstechnik GmbH 6 27-Feb-2014
7 E LV Calculation * Conical sections with or without knuckle acc. to UG-32(g) Design pressure PD 356 psi = pd 356 psi Hydrostatic head DP 0 psi = Dp 0 psi Calculation pressure P0 356 psi = p0 356 psi Calculation temperature T0 300 F Final wall thickness te in Wall thickness allowance c1 0 in Allowance (corrosion) c in Effective thickness witout allowances t in Half-apex angle ( 30 without knuckle) α Outside diameter at the large end D in Inside diameter at the large end D in Outside diameter at the small end Dk 94 in Cone length L in Weld joint efficiency factor E 1 - Material: K02700-SA Class:-Size: Allowable stress S psi Calculation: Required thickness t in inc. allowances (te= in t+) t in Allowable excess pressure incl. hydrost. head P psi without hydrostatic head MAWP psi Remark: Geometrical conditions: valid Strength condition: Wall thickness acceptable For calculation of openings according to UG-37(a) in nomenclature for tr: Design diameter according to UG-37(a):tr(b) D1 in Required thickness t(e=1) in * Dished heads and cones under internal pressure ASME VIII UG-32 and APPENDIX-1 BPVC 2013 Edition Lauterbach Verfahrenstechnik GmbH 7 27-Feb-2014
8 Equations according to UG-32(g): cos( α ) = cos( ) = D = D0-2 * t0 / cos( α ) = 3812 = * / P0*D t =, 2*cos( α )*(S*E - 0.6*P0) t = = * * ( * * ) 2*S*E*t0*cos( α ) P =, D + 1.2*t0*cos( α ) P = = 2 * * 1 * * * * Rem.: App.1-5(d) or (e) indicates if a reinforcement ring is required. Lauterbach Verfahrenstechnik GmbH 8 27-Feb-2014
9 4.3.3 Example E Spherical Shell Determine the required thickness for a spherical shell considering the following design conditions. All Category A joints are Type 1 butt welds and have been 100% radiographically examined. Vessel Data: Material = SA -542, TypeD, Class 4a Design Conditions = 2080 psig@850 F Inside Diameter = in Corrosion Allowance = 0.0 in Allowable Stress = ps Weld Joint Efficiency = 1.0 Lauterbach Verfahrenstechnik GmbH 9 27-Feb-2014
10 E LV Calculation * Spherical shells Design pressure PD 2080 psi = pd 2080 psi Hydrostatic head DP 0 psi = Dp 0 psi Calculation pressure P psi = p psi Calulation temperature T0 850 F Outside diameter D0 157 in Design wall thickness te 4 in Wall thickness allowance c1 0 in Allowance (corrosion) c2 0 in Weld joint efficiency E 1 - Material: K31835-SA-542-D-Class:4a-Size: Allowable stress S psi Results Outside radius R in Effective thickness t0 4 in Required thickness t(r0) t(r) thin shell acc. UG in in thick shell (not applicable) in in Minimum t = Min[t(R);t(R0)] t mm with allowances t+c1+c in Allowable excess pressure P 2231 psi Allowable excess pressure without hydr. head MAWP 2231 psi Remark: For calculation of openings according to UG-37: Minimum required thickness for openings t(e=1) mm Allowable unreinforced opening diameter da for welded, brazed, and flued connections acc. UG 36(c)3: da 89 mm for t 10 mm or: da 3 1/2 in for t 3/8 in da 60 mm for t > 10 mm or: da 2 3/8 in for t > 3/8 in For a vessel thickness > 2*t(E=1) the reinforcement of the vessel alone is sufficient for unreinforced openings, unless additional conditions acc. to UG-37 apply. * Thickness of shells under internal pressure ASME BPVC VIII UG-27 & APPENDIX-1, 2013 Edition Lauterbach Verfahrenstechnik GmbH Feb-2014
11 Equations P0 = 0.1*p0 = = 0.1 * R0 = D0 / 2 = 1994 = 3988 / 2 t+c1+c2 = = R = R0 - t0 = = 1892 = corroded inside radius 1) Thin shell: For P0 = 2080 psi 0.665*S*E = psi and te = *(R0-te) = 0.356*( ) = acc. UG-27 Eq.(3) with the inside radius R: P0*R * 1892 t(r) = = = *S*E-0.2*P0 2* * 1-0.2* *S*E*t0 2* * 1 * P(R) = = = R + 0.2*t * or with outside radius R0 acc. App.1-1 Eq.(2): P0*R * 1994 t(r0) = = = *S*E+0.8*P0 2* * * *S*E*t0 2* * 1 * P(R0) = = = R0-0.8*t * ) Thick shell: Für P0 = 2080 psi > 0.665*S*E = psi or te = > 0.356*(R0-te) = 0.356*( ) = with inside radius R acc. App.1-3: t(r) = R * ( Exp(0.5*P0/(S*E)) - 1 ) = 1994 * ( exp(0.5* / ( * 1 ) - 1 ) P(R) = 2*S*E*Log((R+t0)/R) = 2* * 1 * Log(( )/ 1892 ) or with outside radius R0 acc. App.1-3: t(r0) = R0 * ( 1 - Exp(-0.5*P0/(S*E)) ) = 1994 * ( 1 - exp(-0.5* / ( * 1 ) ) P(R0) = 2*S*E*Log(R0/(R0-t0)) = 2* * 1 * Log( 1994 /( )) Log(x) = Ln(x) Lauterbach Verfahrenstechnik GmbH Feb-2014
12 Example E Torispherical Head Determine the maximum allowable working pressure (MAWP) for the proposed seamless torispherical head. The Category B joint joining the head to the shell is a Type 1 butt weld and has been 100% radiographically examined. Vessel Data: Material = SA -387, Grade 11, Class 1 Design Temperature = 650 F Inside Diameter = 72.0 in Crown Radius = 72.0 in Knuckle Radius = in Thickness = in Corrosion Allowance = in Allowable Stress = psi Weld Joint Efficiency = 1.0 Modulus of Elasticity at Design Temperature = 26.55E + 06 psi Yield Strength at Design Temperature = psi Adjust for corrosion allowance Lauterbach Verfahrenstechnik GmbH Feb-2014
13 E LV Calculation * Input: Type of head (1=Kloepper-, 2=Korbbogen-, 3=Torispherical, 4=Semi-spherical, 5=Elliptical 2:1) 3 Torispherical Design pressure PD 136 psi = pd 136 psi Hydrostatic head DP 0 psi = Dp 0 psi Calculation pressure P0 136 psi = p0 136 psi Calculation temperature T0 650 F Final wall thickness te in Wall thickness allowance c1 0 in Allowance (corrosion) c in Effective thickness witout allowances t0 0.5 in Outside diameter of cylindrical shell D in Inside diameter of cylindrical shell (= D0-2t0) D in Outside crown radius L in Inside crown radius (= L0-t0) L in Knuckle radius r 4.5 in Weld joint efficiency E 1 - Material: K11789-SA Class:1-Size: Elasticity modulus ET 2.660E+7 psi Elastic limit Sy psi Reduce allowable *) stress for Rm20 > 485 MPa? Yes (Yes/No) Tensile strength at 20 C Rm psi Allowable stress: at working temperature acc. ASME-table ST psi at 20 C S psi acc. UG-32(e) or App. 1-4(c) S psi *) According to App. 1-4(c) the allowable stress must be reduced to 138 * ST /S20 (=20 ksi*...) for Rm20 > 485 MPa (70 ksi) Calculation: Ratio L/r Factor M Required thickness without allowance t in inc. allowances (te= in t+) t in Allowable excess pressure incl. hydrost. head P psi without hydrostatic head MAWP psi Geometrical conditions: valid Strength condition: Final wall thickness 15,875 < 15,9403 = required thickness * Dished heads and cones under internal pressure ASME VIII UG-32 and APPENDIX-1 BPVC 2013 Edition Lauterbach Verfahrenstechnik GmbH Feb-2014
14 Required thickness for openings acc. to UG-37(a) in nomenclature for tr: Using UG-32 with E=1 t(e=1) = in acc. section (a) in the crown region t1(e=1) = in Allowable unreinforced opening diameter da for welded, brazed, and flued connections acc. UG 36(c)3: da 89 mm (3.5 in.) for t 10 mm (3/8 in.) da 60 mm (2 3/8 in.) for t > 10 mm (3/8 in.) Remark: Equations: P0*L*M * 1832 * t = = = 2*S*E-0.2*P0 2* * * *S*E*t0 2 * * 1 * 12.7 P = = L*M + 0.2*t * * 12.7 For openings in the crown region with: Opening diameter di in Distance between opening center and head center e in Available reinforcement width acc. UG37: Available reinforcement width of the crown b' in Diameter of the crown region dka in Angle of the knuckle region phi Arc length of the knuckle region b in dka = (2*L+te)*(D/2-r)/(L-r) phi = Arccos( (D/2-r)/(L-r) ) b' = (dka-di)/2 - e b = (r+te)*phi Lauterbach Verfahrenstechnik GmbH Feb-2014
15 Example E Elliptical Head Determine the maximum allowable working pressure (MAWP) for the proposed seamless 2:1 elliptical head. The Category B joint joining the head to the shell is a Type 1 butt weld and has been 100% radiographically examined. Vessel Data: Material Design Temperature = = SA-516, Grade 70, Norm. 300 F Inside Diameter = 90.0 in Thickness = in Corrosion Allowance = in Allowable Stress = psi Weld Joint Efficiency = 1.0 Modulus of Elasticity at Design Temperature = = 28.3E + 06 psi Yield Strength at Design Temperature = psi Determine the elliptical head diameter to height ratio, k, and adjust for corrosion allowance. Lauterbach Verfahrenstechnik GmbH Feb-2014
16 E LV Calculation * Ellipsoidal heads acc. UG-32(d) and Appendix 1-4(f) Design pressure PD psi = pd psi Hydrostatic head DP 0 psi = Dp 0 psi Calculation pressure P psi = p psi Calculation temperature T0 300 F Final wall thickness te in Wall thickness allowance c1 0 in Allowance (corrosion) c in Effective thickness witout allowances t0 1 in Outside diameter of cylindrical shell D in Inside diameter of cylindrical shell (= D0-2t0) D in Outer height of head (minor semi-axis) h in Inside depth of head (minor semi-axis= h0-t0) h 22.5 in Weld joint efficiency E 1 - Material: K02700-SA Class:-Size: Elasticity modulus ET 2.829E+7 psi Elastic limit Sy psi Reduce allowable *) stress for Rm20 > 485 MPa? Yes (Yes/No) Tensile strength at 20 C Rm psi Allowable stress: at working temperature acc. ASME-table ST psi at 20 C S psi acc. UG-32(e) or App. 1-4(c) S psi *) According to App.1-4(c) the allowable stress must be reduced to 138 * ST / S20 (=20 ksi*...) for Rm20 > 485 MPa (70 ksi) and K > 1 Results: Ratio D/2h 2 - Factor K 1 - Factor K1 acc. Table UG-37 K Required thickness t 1 in incl. allowances (te= in t+) t in Allowable excess pressure incl. hydrost. Head P psi without hydrostatic head MAWP psi Required thickness for openings acc. to UG-37(a) in nomenclature for tr: Using UG-32 with E=1 t(e=1) 1 in Section (c) in the centre circle < 0.8*D t1(e=1) 0.9 in Equivalent spherical diameter 2*K1*D0 Dk in Geometrical conditions: valid Strength: Wall thickness acceptable * Dished heads and cones under internal pressure ASME VIII UG-32 and APPENDIX-1 BPVC 2013 Edition Lauterbach Verfahrenstechnik GmbH Feb-2014
17 Allowable unreinforced opening diameter da for welded, brazed, and flued connections acc. UG 36(c)3: da 89 mm (3.5 in.) for t 10 mm (3/8 in.) da 60 mm (2 3/8 in.) for t > 10 mm (3/8 in.) Remark: Equations according to UG-32: P0*D*K * 2292 * 1 t = 25.4 = 2*S*E - 0.2*P0 2* * 1-0.2* *S*E*t0 2 * * 1 * 25.4 P = = K*D + 0.2*t0 1 * * 25.4 Geometry of an equivalent torispherical head: Equivalent spherical inside radius = K1*D L = in Knuckle inside radius acc. Table r = in Lauterbach Verfahrenstechnik GmbH Feb-2014
18 Appendix : Material documentation Section no 2: Schale/UG27Section no 3: Boden/UG32 Material specification: Regulation: ASMET1A:2010Spec. No.: SA-516 Product: Plate Material code: K02700-SA Class:-Size: Short name: Carbon steel Design conditions and dimensions: Temperature [ C]: 148,8889 Pressure [bar]: 30,49 Thickness [mm]: 101,6 Outside diameter [mm]: 2489,2 Material values for test and design conditions: Test condition Operating condition Nominal design strength [N/mm²]: 138,00 138,00 Safety factor: 1,00 1,00 Allowable stress [N/mm²]: 138,00 138,00 Modulus of elasticity [kn/mm²]: ,0667 Creep rupture strength for 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 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 Modulus of elasticity in dependence of the temperature: Static modulus of elasticity in [kn/mm²] at the temperature of 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 ,85 12,1 12,7 13,3 13,8 14, Lauterbach Verfahrenstechnik GmbH Feb-2014
19 Section no 4: Schale/UG27 Material specification: Regulation: ASMET1A:2010Spec. No.: SA-542 Product: Plate Material code: K31835-SA-542-D-Class:4a-Size: Short name: 2.25Cr-1Mo-V Design conditions and dimensions: Temperature [ C]: 454,44 Pressure [bar]: 30,49 Thickness [mm]: 101,6 Outside diameter [mm]: 3987,8 Material values for test and design conditions: Test condition Operating condition Nominal design strength [N/mm²]: 168,00 144,29 Safety factor: 1,00 1,00 Allowable stress [N/mm²]: 168,00 144,29 Modulus of elasticity [kn/mm²]: ,5062 Creep rupture strength for 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 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 Modulus of elasticity in dependence of the temperature: Static modulus of elasticity in [kn/mm²] at the temperature of 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 ,1 12,7 13,3 13,8 14, Lauterbach Verfahrenstechnik GmbH Feb-2014
20 Section no 5: Boden/UG32 Material specification: Regulation: ASMET1A:2010Spec. No.: SA-387 Product: Plate Material code: K11789-SA Class:1-Size: Short name: 1.25Cr-0.5Mo-Si Design conditions and dimensions: Temperature [ C]: 343,33 Pressure [bar]: 30,49 Thickness [mm]: 15,88 Outside diameter [mm]: 1860,55 Material values for test and design conditions: Test condition Operating condition Nominal design strength [N/mm²]: 118,00 118,00 Safety factor: 1,00 1,00 Allowable stress [N/mm²]: 118,00 118,00 Modulus of elasticity [kn/mm²]: ,4002 Creep rupture strength for 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 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 Modulus of elasticity in dependence of the temperature: Static modulus of elasticity in [kn/mm²] at the temperature of Static modulus of elasticity in [kn/mm²] at the temperature of 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 ,85 12,1 12,7 13,3 13,8 14, Lauterbach Verfahrenstechnik GmbH Feb-2014
21 Section no 6: Boden/UG32 Material specification: Regulation: ASMET1A:2010Spec. No.: SA-516 Product: Plate Material code: K02700-SA Class:-Size: Short name: Carbon steel Design conditions and dimensions: Temperature [ C]: 148,89 Pressure [bar]: 30,49 Thickness [mm]: 28,58 Outside diameter [mm]: 2343,15 Material values for test and design conditions: Test condition Operating condition Nominal design strength [N/mm²]: 138,00 138,00 Safety factor: 1,00 1,00 Allowable stress [N/mm²]: 138,00 138,00 Modulus of elasticity [kn/mm²]: ,0666 Creep rupture strength for 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 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 Modulus of elasticity in dependence of the temperature: Static modulus of elasticity in [kn/mm²] at the temperature of 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 ,85 12,1 12,7 13,3 13,8 14, Lauterbach Verfahrenstechnik GmbH Feb-2014
Weight [lb] = (Do-t)*π*L*t*40.84/ (60-1)*3.1416*100*1*40.84/144 = (20000*1*1)/(29+0.6*1) = Pipe and Shell ver 4.
![Weight [lb] = (Do-t)*π*L*t*40.84/ (60-1)*3.1416*100*1*40.84/144 = (20000*1*1)/(29+0.6*1) = Pipe and Shell ver 4.](/thumbs/76/73791559.jpg "Weight [lb] = (Do-t)*π*L*t*40.84/ (60-1)*3.1416*100*1*40.84/144 = (20000*1*1)/(29+0.6*1) = Pipe and Shell ver 4.")
1 Pipe and Shell ver 4.08 Page 1 of 2 2 Host Shell Description 3 Options: 4 Interior ip? - Calculate interior pressure 5 No Exterior ep? - Calculate exterior pressure 6 Rolled Plate pr? - Pipe or rolled
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Current Sensing Chip Resistor SMDL Series Size: 0201/0402/0603/0805/1206/1010/2010/2512/1225/3720/7520. official distributor of
Product: Current Sensing Chip Resistor SMDL Series Size: 0201/0402/0603/0805/1206/1010/2010/2512/1225/3720/7520 official distributor of Current Sensing Chip Resistor (SMDL Series) 1. Features -3 Watts
Type. Capacities. 441, 442 Full nozzle DIN. Flanged Safety Relief Valves spring loaded. The-Safety-Valve.com LWN E
Type 441, 442 Full nozzle DIN Flanged Safety Relief Valves spring loaded Capacities The-Safety-Valve.com LWN 468.3-E Approvals Approvals DN O 5 65 8 Actual Orifice diameter d [mm] 23 37 46 Europe Coefficient
No Item Code Description Series Reference (1) Meritek Series CRA Thick Film Chip Resistor AEC-Q200 Qualified Type
Qualified FEATURE Excellent Mechanical Strength and Electrical Stability Ideal for Pick and Place Machinery Stable High Frequency Characteristics Miniature, High Board Density Equivalent Specification
If we restrict the domain of y = sin x to [ π 2, π 2
Chapter 3. Analytic Trigonometry 3.1 The inverse sine, cosine, and tangent functions 1. Review: Inverse function (1) f 1 (f(x)) = x for every x in the domain of f and f(f 1 (x)) = x for every x in the
B37631 K K 0 60
Multilayer Ceramic acitors High; X5R and X7R Chip Ordering code system B37631 K 7 5 K 6 Packaging 6 ^ cardboard tape, 18-mm reel 62 ^ blister tape, 18-mm reel Internal coding acitance tolerance K ^ ± %
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται
Multilayer Chip Inductor
Features -Monolithic structure for high reliability -High self-resonant frequency -Excellent solderability and high heat resistance Construction Applications -RF circuit in telecommunication and other