Max deflection of a fixed beam with two poinht loads

[Tygra_1983]

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.

 

[GregLocock]

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


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[Tygra_1983]

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.

 

[Tygra_1983]

Its okay, I tried double integration again and I now have the correct answer.

 

[BAretired]

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.