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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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