Dear MANKO,
Recall basic beam theory.
Imagine you have a pipe whose top wall temp. is Tt and Bottom wall temp. is Tb.Let Tb >Tt.
You can easily see that at a distance y from the neutral axis, the temp. differential w.r.t neutral axis will be ( considering linear temp. variation )=y * (Delta T/d)
Where y is the distance from neutral axis, Delta T is the temperature differential ( Tb-Tt)and d is the depth of the section.
Now , BENDING MOMENT= integration of the differental moments due to through thickness variation in strain.
Strain at a distance y from the neutral axis will be equal to alpha *y * (Delta T/d).
If you integrate, you will get the moment=alpha * (Delta T/d) *E*I
So using the stiffness method, along with a fixed end force , with thermal bowing, you will have a fixed end moment also.
Regards
Anindya Bhattacharya
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anindya