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

[EngDM]

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.

 

[BAretired]

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.

Well, I agree there are a lot of variables, but leaving a correctly sized gap will get the OP closer to equalizing reactions than what exists now.

 

[EngDM]

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.

Forgive my ignorance, but how would you go about solving this? Do you create a system of equations of a simply supported beam and 2 span continuous, and solving for reactions by unloading the 2 span equation's UDL by whatever desired deflection you want before the center post gets loaded?

 

[Tomfh]

I agree with XR250 regarding the practicality and politics of it, but in theory, yes, you can leave a gap above the post to roughly equalize your loads in the ultimate case.

 

[Tomfh]

Forgive my ignorance, but how would you go about solving this?

Apply the amount of load you want to shed as an upward point load on the beam. The associated deflection is the gap size you need.

 

[Celt83]

 

[BridgeSmith]

Forgive my ignorance, but how would you go about solving this? Do you create a system of equations of a simply supported beam and 2 span continuous, and solving for reactions by unloading the 2 span equation's UDL by whatever desired deflection you want before the center post gets loaded?

There's likely an iterative or direct theoretical solution, but it most likely would not reflect the reality of the real structure, with it's redundancies and restraints that would be difficult to quantify or model.

The only way I see to accomplish this is by adjusting the support under full dead load.

If I'm completely wrong on this, please correct me, but here goes. If the supports are rigid and set so that the unloaded beam bears on all 3 supports (minimal stress and deflection in the beam), then it is loaded uniformly, the center support should be carrying 62.5% of the total load, or thereabouts. You want it to be carrying 33.3% of the load. If we assume the beam is linearly elastic (Someone more familiar with LVLs please chime in on whether this is a valid assumption), then, if I'm thinking about this correctly, the reactions would equalize with the center support lowered to 47% of the deflection there with no center support (1 - .333/.625).

Since the beam is much stronger than required, when the full dead load has been applied, measure carefully from the floor to the beam, then the lower the center support until there is no load on it. Measure from the floor to the beam again to get the deflection, then raise the center support to take out 53% of the deflection. So, if it deflected 1" when the center support was removed, raise it back up about 9/16".

Obviously, this is not going to be very accurate, even if my assumptions are correct, and it will change some over time, due to creep of the various components.

If there are too many question marks with that approach, you probably need to consider acceptable ways to increase the distribution area of load from the post to the slab.

 

[BAretired]

As Celt83 demonstrated, the calculation is quite straightforward. And for those of you who are worried about accuracy, this procedure is just as accurate as any continuous beam calculation which you all do without worrying about accuracy. For any continuous beam, differential settlement of supports is a possibility because soil properties are not constant from one location to another.

 

[BAretired]

As Celt83 demonstrated, the calculation is quite straightforward. And for those of you who are worried about accuracy, this procedure is just as accurate as any continuous beam calculation which you all do without worrying about accuracy. For any continuous beam, differential settlement of supports is a possibility because soil properties are not constant from one location to another.

Understanding the structural problem is a damn sight easier than figuring how to respond to this forum.

 

[Tomfh]

Thinking more about this, the beam is 18" and spanning only 7foot. The deflections will be so small that it'll be impossible to tune the reactions.

 

[BridgeSmith]

Thinking more about this, the beam is 18" and spanning only 7foot. The deflections will be so small that it'll be impossible to tune the reactions.

That's a good point, and you're right.

 

[BridgeSmith]

Well, at least Celt83 confirmed that my assumption regarding the deflection for equal reactions being 47% (technically 46.6667%) was correct (7/1152 / 5/384 = .46667).

 

[BAretired]

If the deflection is so small as to be deemed negligible, why not consider the beam to be a rigid body? If the central post takes too much load, the slab it rests on only needs to deflect a tiny amount to equalize the three reactions. The load will distribute to the three supports in accordance with the stiffness of the soil below. The only way you could do better would be to build a proper footing under the grade slab at the central column, definitely the best solution.

 

[canwesteng]

You don't even need a gap, without any jacking the post will already only see live loads. Another option instead of a slab is a big steel base plate to spread load out over the SoG

 

[EngDM]

You don't even need a gap, without any jacking the post will already only see live loads. Another option instead of a slab is a big steel base plate to spread load out over the SoG

This might be the best solution; or at least it is the least intrusive.

Thinking more about this, the beam is 18" and spanning only 7foot. The deflections will be so small that it'll be impossible to tune the reactions.

I guess I thought that if the beam doesn't deflect since it is so stiff, then it won't transfer loads to 18.75%/62.5%/18.75% since there is no differential deflection other than what is provided by the supports, which are all the same in this case.

 

[Tomfh]

I guess I thought that if the beam doesn't deflect since it is so stiff, then it won't transfer loads to 18.75%/62.5%/18.75% since there is no differential deflection other than what is provided by the supports, which are all the same in this case.

The beam is so stiff, and the imprecision in the timber connections so much, that you’ve got no real way of knowing how the load is actually shared between the 3 supports. At least with 2 supports you have 50/50.