"Richard Smith" wrote in message writes:

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That's Euler-Bernoulli beam - very clear and exact. You can have the
load it can take and the deflection at that load to great accuracy.
If you set-up the load on the finished article, you'd find the
deflection matched to within a millimetre or something like that.
The end supports cannot be anything like rigid enough against rotation
to benefit the load capacity and stiffness against deflection.
You've got a "simple supported beam" ("double-supported beam").
A fair and reasonable conservative assumption would be to put the
entire weight of the curtain in the middle of the "curtain rail" when
doing the Euler-Bernoulli calculation for what tube to specify.
So that truly is the "simply supported centrally-loaded beam" case.

I do a lot of these calculations. eg. http://www.weldsmith.co.uk/tech/struct/210314_ebbeam_drillplat/19_drillplat_calcs.html

Rich Smith -------------------------- https://www.archtoolbox.com/materials-systems/plumbing/standard-pipe-dimensions.html

https://amesweb.info/section/section-properties-calculator.aspx

https://amesweb.info/Beam/beam-deflection-calculator.aspx

Water pipe attached to a vertical wall with elbows, close nipples and floor flanges is Simply Supported because the threads can rotate within the flange.

Pipe and fence tubing longer than 10' is hard to find, and transport. A center support makes this problem MUCH simpler.

.....................

That's Euler-Bernoulli beam - very clear and exact. You can have the

I do a lot of these calculations. eg. http://www.weldsmith.co.uk/tech/struct/210314_ebbeam_drillplat/19_drillplat_calcs.html

Rich Smith -------------------------- https://www.archtoolbox.com/materials-systems/plumbing/standard-pipe-dimensions.html

https://amesweb.info/section/section-properties-calculator.aspx

https://amesweb.info/Beam/beam-deflection-calculator.aspx

Water pipe attached to a vertical wall with elbows, close nipples and floor flanges is Simply Supported because the threads can rotate within the flange.

Pipe and fence tubing longer than 10' is hard to find, and transport. A center support makes this problem MUCH simpler.