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Pipe Under Clamping Force

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Pipe under clamping force
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  Line Number  H90625Specification EBTPipe Stress due to clamping forces and check combined circumferantial stress:Ref:  1. Roark's Formulas for Stress and Strain, 7th Edition, Table 9.2 Case 1 2. Pressure Vessel Design Manual, 3rd Edition, Dennis Moss 3. ASME B31.3-2006Required clamping force calculatedW' 2700NSafety factor against the calculated force for clampingSF1.5Clamping Force on the pipe cross sectionW = SF * W' =4050NInternal maximum operating pressure of the pipeP11.3MPaPipe SizeDN100  with additive reinforcement around Pipe ScheduleSch120  add 12.7 mm around ( DN125 Sch 120 ) Pipe Material A 106BMaximum operating temperature of the pipe123CB31.3 Basic Allowable tensile stress of the pipe material at the oper.temp.S  A 137.89MPaYield strength of pipe material at maximum operating temperatureS Y 217MPaB31.3 Quality factor from Table A-1A or A-1BE q 1B31.3 Coefficient from Table 304.1.1, valid for t <= D / 6Y0.4B31.3 Weld joint reduction factor per para. 302.3.5(e)W1Pipe ODD o 114.3mmPipe OD with reinforcementD 2 139.7mmPipe thicknessWT11.13mmReinforcement thiskness thicknessT 2 12.7mmManufacture negative tolerance in wall thicknessTol12.5%Sum of mechanical allowances including corrosionC4.5mmPipe remaining thickness:t = ( 1 - Tol / 100) * WT - C =5.24mm  Assumed Pipe only carries the pressure stresses Reinforcement remaining thicknessT = ( 1 - Tol / 100) * T 2  =11.11mm  Assumed the reinforcement carries the crashing force. D 2  / 6 =23.28mmPipe calculation internal diameter D i  = D o  - 2 t =103.82mmRadius of centroid of cross section of reinforcementR = ( D 2  - T ) / 2 =64.29mmShort clamp beam heightH 125mmfor 125 PFC Considered effective length in the calculationB = H + 1.56 SQRT( R T ) =166.7mmConsidered cross section area in the effective lengthA = B * T =1852mm   Moment of resistance of the considered cross sectionZ = B * T / 6 =3431mm Area moment of inertia of the considered cross sectionI = B T / 12 =19063mmShape factor for the considered cross sectionF1.20Poisson ratio of the material  n 0.3Distance between centroidal axis and neutral axis of cross sectione0mmMaterial elasticity modulusE195970MPaShear modulus od elasticityG = E / [ 2 ( 1 + n  ) ] =75373MPa a  = I / ( A R ) =0.00248946250544971.xls.ms_office1 of 6  Line Number  H90625Specification EBT b  = F E I / ( G A R ) =0.00776711k 1  = 1 - a  + b  =1.00527765k 2  = 1 - a  =0.99751054Maximum positive momentMax + M = M  A  = 1 / p  * W R k 2  =82678NmmMaximum negative momentMax - M = M B  = - ( 0.5 - k 2  / p  ) W R =-47517Nmm0.78 SQRT( R t )H0.78 SQRT( R t )  W B = H + 1.56 SQRT (R t)  W Change in the horizontal diameter   D D H  = W R 3  / E I * [ k 1  / 2 - k 2  + 2 k 2 2  / p  ] =0.04mmChange in the vertical diameter   D D V  = - W R 3  / E I * [ p  k 1  / 4 - 2 k 2 2  / p  ] =0.04mmBending stress at A due to clamping action  s bA  = M  A  / Z =24.1MPaBending stress at B due to clamping action  s bB  = M B  / Z =-13.8MPaB31.3 Circumf. Stress due to internal pressureS = P ( D o  - 2 t Y ) / ( 2 t E q  W ) =118.8MPaOKAY   t  / S A t  / S  Y Maximum combined circumferantial stress at A  s tA  = ABS ( s bA  ) + S =142.9MPaFAIL1.0360.658Maximum combined circumferantial stress at B  s tB  = ABS ( s bB  ) + S =132.6MPaOKAY0.9620.611 A B 250544971.xls.ms_office2 of 6  Line Number  H90625Specification EBTPipe Stress due to clamping forces and check combined circumferantial stress:Ref:  1. Roark's Formulas for Stress and Strain, 7th Edition, Table 9.2 Case 1 2. Pressure Vessel Design Manual, 3rd Edition, Dennis Moss 3. ASME B31.3-2006Required clamping force calculatedW' 2700NSafety factor against the calculated force for clampingSF1.5Clamping Force on the pipe cross sectionW = SF * W' =4050NInternal maximum operating pressure of the pipeP11.3MPaPipe SizeDN100Pipe ScheduleSch120Pipe Material A 106BMaximum operating temperature of the pipe123CB31.3 Basic Allowable tensile stress of the pipe material at the oper.temp.S  A 137.89MPaYield strength of pipe material at maximum operating temperatureS Y 217MPaB31.3 Quality factor from Table A-1A or A-1BE q 1B31.3 Coefficient from Table 304.1.1, valid for t <= D / 6Y0.4B31.3 Weld joint reduction factor per para. 302.3.5(e)W1Pipe ODD o 114.3mmPipe thicknessWT11.13mmManufacture negative tolerance in wall thicknessTol12.5%Sum of mechanical allowances including corrosionC4.5mmPipe remaining thickness:t = ( 1 - Tol / 100) * WT - C =5.24mmD o  / 6 =19.05mmPipe calculation internal diameter D i  = D o  - 2 t =103.82mmRadius of centroid of cross sectionR = ( D o  - t ) / 2 =54.53mmShort clamp beam heightH 125mmfor 125 PFC Considered effective length in the calculationB = H + 1.56 SQRT( R t ) =151.4mmConsidered cross section area in the effective lengthA = B * t =793mm   Moment of resistance of the considered cross sectionZ = B * t / 6 =692mm Area moment of inertia of the considered cross sectionI = B t / 12 =1814mmShape factor for the considered cross sectionF1.20Poisson ratio of the material  n 0.3Distance between centroidal axis and neutral axis of cross sectione0mmMaterial elasticity modulusE195970MPaShear modulus od elasticityG = E / [ 2 ( 1 + n  ) ] =75373MPa a  = I / ( A R ) =0.00076912 b  = F E I / ( G A R ) =0.00239965k 1  = 1 - a  + b  =1.00163053k 2  = 1 - a  =0.99923088250544971.xls.ms_office3 of 6  Line Number  H90625Specification EBT Maximum positive momentMax + M = M  A  = 1 / p  * W R k 2  =70244NmmMaximum negative momentMax - M = M B  = - ( 0.5 - k 2  / p  ) W R =-40180Nmm0.78 SQRT( R t )H0.78 SQRT( R t )  W B = H + 1.56 SQRT (R t)  W Change in the horizontal diameter   D D H  = W R 3  / E I * [ k 1  / 2 - k 2  + 2 k 2 2  / p  ] =0.25mmChange in the vertical diameter   D D V  = - W R 3  / E I * [ p  k 1  / 4 - 2 k 2 2  / p  ] =0.28mmBending stress at A due to clamping action  s bA  = M  A  / Z =101.5MPaBending stress at B due to clamping action  s bB  = M B  / Z =-58.0MPaB31.3 Circumf. Stress due to internal pressureS = P ( D o  - 2 t Y ) / ( 2 t E q  W ) =118.8MPaOKAY   t  / S A t  / S  Y Maximum combined circumferantial stress at A  s tA  = ABS ( s bA  ) + S =220.2MPaFAIL1.5971.015Maximum combined circumferantial stress at B  s tB  = ABS ( s bB  ) + S =176.8MPaFAIL1.2820.815 A B 250544971.xls.ms_office4 of 6
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