From mechanics x=FL/AE where x is the thermal movement.Also x=eL where e is the dimensionless coeffecient of thermal expansion in mm/mm or in./in..For a pipe of length L fixed at both ends with area A and moddulus of Elasticity E..The thermal force would be F=AEx/L since x=el,this will reduce to F=AEe which cancels out L.This means that the axial force is independent of length L.When we form the stifness matrix of a piping system thermally do we consider this fixed end joint thermal load vector as independent of length L or is there other mathematical representation that this fxed end thermal force is dependent of the lenght.Thanks in advance for your opinion.

Best Regards,

Hi Borzki
You are right , for two fixed point beam force is independent of length.
That's why caesar also show the same load even if length change.
Here only missing points are , buckling, local buckling & stiffness of the end point.

But when L shape configuration is used situation changes, bending comes into picture to other leg of piping, when length of one leg increase that Delta L create more bending, tends to failure as well as create more load at end points.

Regards

Habib

Thanks Habib for your reply