Surface area of Rectangular / Round transition

Apr 2012

This is my first post on this forum. I am creating an excel spreadsheet that will calculate me the weights of sheet metal HVAC ductwork and I am creating the equations for weight myself. I have some equations which I cannot figure out.

For calculation of weight I need the surface area.

I need to calculate the surface are of rectangular to round transition when I have these parameters:
rectangular base - a x b
diameter of upper round base (frustum) - d
- perpendicular length between base plane (a x b) and truncated plane (d) - l

- there are three types of these transitions, first one is symmetrical, where the center of round base is symmetrical with the center of rectangular base

1.jpg - in this picture the base is square, but I need rectangular base.

-or there may be some offset of upper round base from the center of lower base (asymmetrical transition)

- 3rd type is when the round base is adjacent to the line going up from one side of lower base (axb) (perpendicular transition).

Could you please help me create formulas for surface area of these transitions?

Thank you very much.
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