Bean Deflection Problem

[Alexey881]

Hello, I am trying to find maximum bending moment developed in a fixed beam due to two equal (or unequal) equi-spaced forces.

[This scenario happens when ventilation mechanics trying to suspend the duct with rods to the ceiling. However istead of attaching to the ceiling they put a channel or an angle across a 6ft span of ceiling trusses. When you do seismic analysis, the rods may or may not develop the same forces which will subject the channel to bending.]

Are there any readily available formulas, which can be applied to these scenarios? Standard beam deflection diagrams do not seem to apply (Unless I can actually combine a reaction moment diagram at a support with the standard simply supported dual force diagram.)

Thanks.

 

[Alexey881]

Here's the picture

http://files.engineering.com/getfile.aspx?folder=86f1ac06-6233-4de7-aeef-62a37c480060&file=Beams.jpg

 

[jayrod12]

There's no quick formulae when you've got unequal magnitude and unequal locations on an indeterminate beam.

The fastest way would be to quickly set up a FEA solution using nodes at each support and each load. It wouldn't take too long to set up a spreadsheet where all you would have to do is change the locations of the input nodes and material properties for each problem.

Or get a software program that will do it for you.

 

[dik]

Yakov has a free excel spreadsheet that can easily accommodate the problem.

Dik

 

[Alexey881]

What if the distances are not unequal. For example between the wall and the rod (on both sides of the beam) the distance would be the same. The only variation is the distance between the rods.

So, if I wanted to set up excel, would I have to start with the beam formula and then integrate and accomodate boundary conditions? Assuming this is done I should be able to determine all the unknown reactions... ?

Also that link for Yakov did not work.

 

[bridgebuster]

The 9th edition of AISC has beam formulas; there is an example for a fixed beam with a single concentrated load. It'll work in your case. Use superposition.

If you don't have AISC just Google " formula for maximum moment".