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Max deflection of a fixed beam with two poinht loads

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Tygra_1983

Student
Joined
Oct 8, 2021
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125
Location
GB
Hi there,

Does anyone here know the formula for the max deflection of a beam that has two fixed ends and has two point loads of equal magnitude and spacing? I cannot find one anywhere.

Kind regards.
 
One approach is to use superposition. That is the deflected shape (and stresses) for each load case at each station along the beam can be added together, because it is a linear system.

The other approach would be the usual that unfortunately seems to be missing from many courses, construct a shear force diagram, then a BM diagram, then a slope diagram, then a deflection diagram.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
The thing is for what I want to do I need a formula. I have tried double integration, but can't seem to land on the correct answer.
 
Its okay, I tried double integration again and I now have the correct answer.
 
Are you familiar with Conjugate Beam Theory? I have found it to be a very useful method for any loading. It is an example of applying area/moment theory.

For two point loads with fixed ends, GregLocock's method is probably the easiest. Just superimpose the expressions for each point load as shown below.

Capture_r5smyk.jpg
 
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