Hi,everybody!

Who can tell me the way hand calculate the force as a result of piping thermal expansion!
Tell me the fomula!

Thanks!

I know I'm really just a graduate, but I'm thinking that your question is really ambiguous. The force due to pipe thermal expansion will depend highly on the piping geometry and boundary conditions.

Do you mean for a straight run of pipe anchored at both ends? If so, then it's probably gonna be huge!

Here's my guess : I'd calculate the expansion length first, based on the material's thermal coefficient of expansion, and the piping temperature. From that you get the pipe strain (change in length/length). Using the pipe material's Young's Modulus you can get the axial stress. Multiply this by the pipe cross-sectional area and you get the force.

Not sure if this is 100% correct, as the pipe could have a tendency to bend. A good estimate perhaps? Can't think why'd you want this though.

-Pete

First : In case of No restraints/one point restraint to thermal expansion, there will not be any thermal force.

If somehow the pipe has two end fixity, you can use these simple formulas:

Axial force= Axial stiffness ( =AE/L) *axial displacement.

Lateral force= Lateral stiffness (=12EI/L^3)*lateral displacement.

Bending moment = Bending stiffness(=EI/L)*Bending rotation in radian. To be conservative multiply this value by 4.

Torsional moment =(Torsional stiffness (=GJ/L)*torsional rotation in radian

E=modulus of elasticity,

G= SHEAR MODULUS= E/2(1+v), v=Poisson's ratio.

L=Length

I=Second Moment of area about Neutral axis.

J= Polar moment of area = 2I for pipe.

Anindya Bhattacharya

Assuming you're talking about a fixed-fixed case, then ...

Axial extension due to temperature:
delta = alpha * length * deltaT

Axial Compression due to an axial force:
delta = force * length / ( area * modulus )

Now, set the deltas equal to each other, and solve for the force:
alpha * length * deltaT = force * length / ( area * modulus )

alpha * deltaT * (area * modulus) = force


This is the force you will obtain from CAESAR II if you build a fixed-fixed model and apply a temperature. However, in the real world this force will not develop, due to buckling. (Pipe stress programs don't address buckling and other 2^nd order effects.)