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2 span continuous - Always a 25% increase under UDL? 1

EngDM

EngDM

Structural
Aug 10, 2021
630
Hey all,

I am wondering if the 25% increase in reaction of the center support (compared to taking just trib widths) under a 2 span continuous beam, loaded via UDL, always occurs.

If the member was VERY stiff compared to the load, I'd imagine that the supports would be loaded more uniformly into a 25%/50%/25% split instead of 18.75%/62.5%/18.75%.

Furthermore, if you had a compressible support, for instance a wood post, as soon as the central post compresses at all wouldn't it re-distribute loads to the outer posts and find a nice equilibrium as a system.

I'm trying to get an exististing slab to work for a new mezzanine that is adding point loads from openings, but the LVL used was very deep for the load it actually carries (2ply 18" lvl only spanning 7ft). I'm considering adding a central post to alleviate the load on the slab edge, but then the central post gets loaded even heavier than without it.
 
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If the beam works as simply supported, you could sever the top 1/2 of the beam at the middle support and turn it into two beams.

As far as I understand it, doesn't matter how stiff the beam versus column is, the statics is the statics and for a UDL continuous equal span beam the centre support always takes more. Strictly due to the continuity of the beam.
 
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If you model the supports as springs, rather than true rigid supports, the beam stiffness will play a role in determining the reactions.
Not sure if it is appropriate to treat the supports as a spring in your situation though.
 
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Relative stiffness of the beam and support will play a role. If you have access to a frame program like MASTAN2, RISA, Elements, Robot, Visual Analysis, etc. it should be pretty quick to model the beam and supporting columns to better approximate the reactions.
 
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Celt83 said:
Relative stiffness of the beam and support will play a role. If you have access to a frame program like MASTAN2, RISA, Elements, Robot, Visual Analysis, etc. it should be pretty quick to model the beam and supporting columns to better approximate the reactions.
Click to expand...
What do you take for spring constants if I were to model it in a 2d analysis program?
 
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it’s an engineering judgement thing. You need to judge how much some extra centre load will matter. Can your structure redistribute the load gracefully?. If it’s say for checking punching shear at a centre support you need to be more careful than say checking allowable bearing stress under a raft
 
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Maybe what I am picturing, of all 3 supports taking equal load since the beam is rigid, is unrealistic. It only seems to model out that way with a really low spring stiffness and very high beam stiffness.

The LVL sits on steel stud posts.
 
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EngDM said:
What do you take for spring constants if I were to model it in a 2d analysis program?
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Easiest to model the columns, but in this case since the beam column joints are pins in theory you could replace them with springs of AE/L
A = Area of Column
E = Young's Modulus of Column
L = Height of Column
 
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You won’t get equal load as you would with simply supported spans. Why are you fussing it? Does it not work with the theoretical higher load?
 
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Celt83 said:
Easiest to model the columns, but in this case since the beam column joints are pins in theory you could replace them with springs of AE/L
A = Area of Column
E = Young's Modulus of Column
L = Height of Column
Click to expand...
This is no doubt the best answer, however since lvl is bearing on the post, sometimes bearing deformation can exceed the one you calculate with AE/L of column, in this case due to wood grain orientations. Other way could be, if you know your peak load and anticipated support settlement, then K = Peak Load/ Settlement. This can reduce some reaction on middle support if that is something you are trying to achieve rather than simply supported solution.
 
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EngDM said:
Maybe what I am picturing, of all 3 supports taking equal load since the beam is rigid, is unrealistic. It only seems to model out that way with a really low spring stiffness and very high beam stiffness.

The LVL sits on steel stud posts.
Click to expand...
Even using two simple beams, the middle support takes twice as much as each exterior support. If you want to equalize the reactions, move the exterior supports inward to create a cantilever at each end. Alternatively, omit the central support, leaving only two supports equally spaced from each end, each carrying half the total load. Sheesh!
 
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BAretired said:
Even using two simple beams, the middle support takes twice as much as each exterior support. If you want to equalize the reactions, move the exterior supports inward to create a cantilever at each end. Alternatively, omit the central support, leaving only two supports equally spaced from each end, each carrying half the total load. Sheesh!
Click to expand...
I understand there are different ways to get my desired outcome if it were a new build. However this has already been built and covered, and now I have to try and get it to work for what they did on site. Adding a central, or a pair of columns, seems like it would be the easiest without them having to tear everything apart.

The thing that is failing is the slab on grade, since these mezzanine beams were built right on the edge of the slab on grade where it meets the grade beam, so my point loads are on a free edge of slab. I can get the slab to work for the punching/rupture of unreinforced concrete if the supports all share 33%, otherwise I need to consider other solutions.
Tomfh said:
You won’t get equal load as you would with simply supported spans. Why are you fussing it? Does it not work with the theoretical higher load?
Click to expand...
Correct. See above.
Tomfh said:
it’s an engineering judgement thing. You need to judge how much some extra centre load will matter. Can your structure redistribute the load gracefully?. If it’s say for checking punching shear at a centre support you need to be more careful than say checking allowable bearing stress under a raft
Click to expand...
Slab on grade.

Part of the issue is these 5" slab on grades are put in with little thought to future construction or use. I have ran into many a slab lately that just don't work for anything other than an area load when using unreinforced concrete methods such as PCA.
 
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As others have stated, kerf the top of the beam - assuming the deflection on the remaining halves still works.
 
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I'm guessing the "put in a footing" option has already been ruled out as a possibility?
 
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XR250 said:
As others have stated, kerf the top of the beam - assuming the deflection on the remaining halves still works.
Click to expand...
Yea but then the central post takes 50% of the load based off trib widths. This is the same loading as if I had a simple span.
dold said:
I'm guessing the "put in a footing" option has already been ruled out as a possibility?
Click to expand...
Yea thats a big no go, no matter how much I'd prefer this.

The slab is doweled in to the existing grade beam there. As I have currently checked it, the rupture plane doesn't consider any load that may be transmitted through the dowels into the grade beam. Not something I would typically rely on, but I may have to explore this option.
 
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You can model it with the supports as springs, as noted above, but you might as well not bother; the axial stiffness of the posts is much greater than the bending stiffness of the beam, so your reactions would only change by a tiny fraction of a percent.

One thing you could do to equalize the loading across the 3 posts would be to reduce the support of the center post, either by lowering it or adding a compressible material between the beam and the post. However, this will substantially increase the moments and stresses in the beam, and increase the sag of the beam, which you may have to make up for by shimming above the beam. This is only an option if the beam has excess capacity.
 
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BridgeSmith said:
One thing you could do to equalize the loading across the 3 posts would be to reduce the support of the center post, either by lowering it or adding a compressible material between the beam and the post. However, this will substantially increase the moments and stresses in the beam, and increase the sag of the beam, which you may have to make up for by shimming above the beam. This is only an option if the beam has excess capacity.
Click to expand...
Interesting. I've never seen a detail of this before.

My beam is only loaded to like 11% capacity (contractor installed it to be same as joist depth) so I have ample load to work with.

I ended up just running the SOG in safe to get the moment in the slab, instead of just trying to get plain concrete to work since it was getting to the point where it was just easier to do that.

Do you have a detail of this used in a residential/commercial application? I'm not sure what product you'd even use for this.
 
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Leave a large enough gap over the central post such that all three reactions are equal when the beam is fully loaded. Use a connection designed to permit deflection but to prevent post from falling over.
 
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I think it is a fool's errand to try to get something to work as expected like Bridgesmith suggested (in wood construction anyway). Too many other variables in play and good luck getting your contractor on board.
 
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