Has anyone ever seen this formula?
Has anyone ever seen this formula?
(OP)
I am looking at some calcs submitted that are showing the deflection of a column with an eccentric axial load (equal end moments). The equation being used is Pe(L^2)/(16EI). I could certainly go through the problem and use Castigliano's method or something similar, but it seems like so much work to verify this. I have looked in teh AISC manual and my mechanics of materials book and I can't find this (either with eccentric axial load or just end moments - assuming this would be virtuallly identical since the axial load contributes little to deflection).
Has anyone ever come across an equation like this or know where I might be able to find this or something similar?
Has anyone ever come across an equation like this or know where I might be able to find this or something similar?






RE: Has anyone ever seen this formula?
RE: Has anyone ever seen this formula?
That is the deflection at mid height.
It matches the formula that I have for an end moment on a beam where M=Pe
csd
RE: Has anyone ever seen this formula?
csd- what reference do you have that formula?
RE: Has anyone ever seen this formula?
That formula represents indeed the midspan deflection of a simply supported beam with a moment Pe at one end.
However:
1)the maximum deflection is not at midspan in that case, it is at 0.577L and the max.deflection is f=PeL2/15.57EI (of course this doesn't make a big difference, but to be correct...): to check this see Roark 5th ed. Table 3 Case 3e, or go to the first site below under Beams -> Simply supported -> Conc.moment
2)StructuralEIT is calling for a beam (or column) with a constant eccentricity of the load all over the length (equal end moments): in this case the bending moment is constant in the beam, and the maximum deflection is exactly twice, or f=PeL2/8EI; this comes from the superposition of two moments, one at each end, and of course the max.deflection is now at midspan and is two times the deflection with one end moment.
prex
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RE: Has anyone ever seen this formula?
ML^2/9*(sqrt 3 EI) which is exactly what prex mentioned.
I am a little loss with the second point he made though.
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RE: Has anyone ever seen this formula?