Please help me in unserstandin gthe concept of thermal bowing.


Manko

Dear Manko,

The phenomenon of thermal bowing is usually related to the analysis of piping rather than pressure vessels. You might also check the CAESAR II Piping forum for more information.

Here is a scenario that could cause this effect.

Imagine a horizontal run of un-insulated piping that is carrying a relatively cool product. Also, the pipe is only partially filled with liquid. Assuming this pipe is outdoors, the sun may shine on the system heating the top of the pipe up. After a short while a thermal gradient around the circumference will be established. Since the temperature is not uniform, the pipe will "bow" in reaction to the gradient. From the "delta T" a moment can be computed and applied to the ends of the piping element to simulate this effect.

Hopefully this brief explanation has give you some insight into such types of problems.

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