Steel Beam on Slab - Concentrated Moment
Steel Beam on Slab - Concentrated Moment
(OP)
I'm looking for a little guidance on how to analyze this situation.
This will be applied to a job eventually, but for now I'm just trying to get the concept right.
For discussion sake I'll add some dimensions...
I have a 10' steel beam, 8' of the beam sits flat on a slab (I assume the slab is perfectly rigid) and is not fastened to the slab in any way, and there is a 2' cantilever. At the end of the canitlever is a concentrated moment. The cantilever supports gravity loads. The concentrated moment is applied so that the tip of the beam deflections upward. (see attached sketch)
I can picture how the beam will deflect...not all 8' of the beam will remain in contact with the slab, the remaining area of the beam in contact with the slab will resist the vertical load and the concentrated moment.
I would like to know how much of the beam remains in contact with the slab and what the pressure distribution will look like.
My approach right now is...
Take the vertical load, this is the resulant of the pressure between the beam and the slab.
Sum the moments at the far left of the beam (the end that is on the slab) and use this to get the location of my resultant.
And from there I'm guessing I have a triangular pressure distribution...
I'm just not sure if this is the right way to go. Does this sound about right?
This will be applied to a job eventually, but for now I'm just trying to get the concept right.
For discussion sake I'll add some dimensions...
I have a 10' steel beam, 8' of the beam sits flat on a slab (I assume the slab is perfectly rigid) and is not fastened to the slab in any way, and there is a 2' cantilever. At the end of the canitlever is a concentrated moment. The cantilever supports gravity loads. The concentrated moment is applied so that the tip of the beam deflections upward. (see attached sketch)
I can picture how the beam will deflect...not all 8' of the beam will remain in contact with the slab, the remaining area of the beam in contact with the slab will resist the vertical load and the concentrated moment.
I would like to know how much of the beam remains in contact with the slab and what the pressure distribution will look like.
My approach right now is...
Take the vertical load, this is the resulant of the pressure between the beam and the slab.
Sum the moments at the far left of the beam (the end that is on the slab) and use this to get the location of my resultant.
And from there I'm guessing I have a triangular pressure distribution...
I'm just not sure if this is the right way to go. Does this sound about right?






RE: Steel Beam on Slab - Concentrated Moment
RE: Steel Beam on Slab - Concentrated Moment
RE: Steel Beam on Slab - Concentrated Moment
Otherwise, this is more like an inverse beam on an elastic foundation.
Mike McCann
MMC Engineering
http://mmcengineering.tripod.com
RE: Steel Beam on Slab - Concentrated Moment
If the reaction is distance x from the c.g. of load, then:
2*w*x = M, so x = M/2w.
If 1'>x>9' equilibrium is not possible. If 1'<x<9' then the moment is zero at the reaction point and all points to the left.
Moments, curvatures and deformations can all be calculated in the usual manner.
Spreading the reaction over a nominal width will not make much difference but it could be included by treating the slab as an elastic foundation.
BA
RE: Steel Beam on Slab - Concentrated Moment
I guess at the end of the day as long as the reaction falls a reasonable distance from the edge of the slab its okay.
When I first looked at this I figured the slab would be so much stiffer than the beam that it wouldn't have much influence, but maybe it does...
If I were to assume that the slab was perfectly rigid, what do you think the pressure distribution would look like? I thought it would be triangular, with the point of zero pressure being where the beam lifted from the slab...but that would mean that I could get the length of bearing from just the equations of equilibrium, ignoring the stiffness of the beam...which can't be the case because if both beam and slab were infinitely stiff then the resultant would just be a point load at the far left of the beam.
I picture the pressure distribution being a trapezoid...a maximum pressure starting at the far left and staying constant for some distance, and then a linear drop to zero, at which point the beam lifts from the slab. I guess this is the part where I get a little lost running the numbers...
RE: Steel Beam on Slab - Concentrated Moment
The slope of the beam is zero at the reaction point and increases by an amount equal to the area under the M/EI diagram.
The deflection of the beam at any point can be found using area-moment principles.
Theoretically, liftoff occurs at the reaction point.
BA