Beam Deflection
Beam Deflection
(OP)
Hi there,
I am struggling with working out maximum deflection in a beam.
It has two point loads, at L/4 on each side and a distributed load at L/2.
I know max deflection for a distributed load but I am not sure how I calculate both at the same time.
Do I have to treat this problem as three seperate beams? Calculate for each 'cross section' and add deflections? Really haven't got a clue.
The beam is simply supported with pin and roller boundary constraints.
Ty in advance.
I am struggling with working out maximum deflection in a beam.
It has two point loads, at L/4 on each side and a distributed load at L/2.
I know max deflection for a distributed load but I am not sure how I calculate both at the same time.
Do I have to treat this problem as three seperate beams? Calculate for each 'cross section' and add deflections? Really haven't got a clue.
The beam is simply supported with pin and roller boundary constraints.
Ty in advance.






RE: Beam Deflection
another day in paradise, or is paradise one day closer ?
RE: Beam Deflection
RE: Beam Deflection
Superposition will get you a better answer.
DaveAtkins
RE: Beam Deflection
RE: Beam Deflection
The beam is 6m long, Point loads at 1.5m & 4.5m and a distributed load across the length.
Should I calculate the deflection at 1.5m with the point load and multiply it by 2 or calculate deflection at 1.5m and 4.5m seperately?
RE: Beam Deflection
Properties of Conjugate Beam
The length of a conjugate beam is equal to the length of the actual beam.
The load on the conjugate beam is the M/EI diagram of the loads on the actual beam.
A simple support for the real beam remains simple support for the conjugate beam.
The point of zero shear for the conjugate beam corresponds to a point of zero slope for the real beam.
The point of maximum moment for the conjugate beam corresponds to a point of maximum deflection for the real beam.
BA
RE: Beam Deflection
Pa(3l2 - 4a2)/24EI + 5wl4/384EI
BA
RE: Beam Deflection
another day in paradise, or is paradise one day closer ?
RE: Beam Deflection
I worked out deflection to be ~6mm however, ANSYS modelling suggests it should be arround 14. Of course there may be error in my model on ANSYS.
RE: Beam Deflection
It is the deflection at midspan for two loads 'P', each at a distance 'a' from each support plus a uniform load 'w' across the entire span. It is also the maximum deflection for that combination of loads.
BA
RE: Beam Deflection
So that is the beam. It has a cross section of (0.3x0.35m)
Am I correct in thinking deflection is as follows:
2{Pa(3l2 - 4a2)/24EI} + (5wl4/384EI)
or do I just make P the value of the sum of the point loads?
This help is really appreciated. Helping my understanding a lot.
RE: Beam Deflection
Δ = Pa(3l2 - 4a2)/24EI + 5wl4/384EI
where Δ is the deflection at midspan (also the maximum deflection in the beam)
The first term takes into account the fact that there are symmetrical loads P placed 'a' away from each support. The second term is the deflection due to a uniformly distributed load.
BA
RE: Beam Deflection
RE: Beam Deflection
BA
RE: Beam Deflection
RE: Beam Deflection
BA
RE: Beam Deflection
RE: Beam Deflection
another day in paradise, or is paradise one day closer ?
RE: Beam Deflection
RE: Beam Deflection
The following picture shows the formula I am following for natural frequencies. This doesn't take in to account mass does it?
The values for natural frequencies vary hugely compared to ansys.
RE: Beam Deflection
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Beam Deflection
It does in so far as the uniformly distributed self-weight of the beam (the A and ρ terms - section area and density - in the denominator), but does not include added lumped-masses within the span.