| CALC : Pipe : Diameter 006 : Multi Layer Pipe EI Modulus or Bending Stiffness - E Modulus x I Modulus : Calculator
Description : Calculate pipeline EI modulus or bending stiffness, EA modulus or xxial stiffness and thermal expansion force coefficient EAα for multi-layer pipelines.
Discussion : Only include the layers which will contribute to the modulii. Generally external coating layers do not contribute. Goto the setup page to change the number of layers.
Calculation Steps :
- Outside layer modulii
- Inside layer modulii
- Total modulii values
Input Variables :
- αi = Pipeline Inner Layer Thermal Expansion Coefficient
- αo = Pipeline Outer Layer Thermal Expansion Coefficient
- D = Pipe Nominal Diameter
- Ei = Pipeline Inner Layer Youngs Modulus E
- Eo = Pipeline Outer Layer Youngs Modulus E
- WTi = Pipeline Inner Layer Wall Thickness
- WTo = Pipeline Outer Layer Wall Thickness
Output Variables :
- EA = Pipeline EA Modulus
- EAα = Pipeline Thermal Expansion Force Coefficient
- EAαi = Pipeline Inner Layer EAα Coefficient
- EAαo = Pipeline Outer Layer EAα Coefficient
- EAi = Pipeline Inner Layer EA Modulus
- EAo = Pipeline Outer Layer EA Modulus
- EIi = Pipeline Inner Layer EI Modulus
- EIo = Pipeline Outer Layer EI Modulus
- EIp = Pipeline Nominal EI Modulus
- IDi = Pipeline Inner Layer Inside Diameter
- ODo = Pipeline Outer Layer Outside Diameter
Calculation :
ODo[0] = D
IDi[0] = D
Loop i
j = i - 1
ODo[i] = ODo[j] + 2 WTo[i]
EIo[i] = Eo[i] π / 64 ( ODo[i] 4 - ODo[j] 4 )
EAαo[i] = αo[i] Eo[i] π / 4 ( ODo[i] 2 - ODo[j] 2 )
EAo[i] = Eo[i] π / 4 ( ODo[i] 2 - ODo[j] 2 )
End of i Loop
Loop i
j = i - 1
IDi[i] = IDi[j] - 2 WTi[i]
EIi[i] = Ei[i] π / 64 ( IDi[j] 4 - IDi[i] 4 )
EAαi[i] = αi[i] Ei[i] π / 4 ( IDi[j] 2 - IDi[i] 2 )
EAi[i] = Ei[i] π / 4 ( IDi[j] 2 - IDi[i] 2 )
End of i Loop
EIp = ArraySum( EIi ) + ArraySum( EIo )
EAα = ArraySum( EAαi ) + ArraySum( EAαo )
EA = ArraySum( EAi ) + ArraySum( EAo )
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