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

[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.

 

[jayrod12]

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.

 

[HDStructural]

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.

 

[Celt83]

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.

 

[EngDM]

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.

What do you take for spring constants if I were to model it in a 2d analysis program?

 

[Tomfh]

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

 

[EngDM]

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.

 

[Celt83]

What do you take for spring constants if I were to model it in a 2d analysis program?

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

 

[Tomfh]

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?

 

[canwesteng]

Could saw the flanges of the LVL at the support maybe

 

[Taimoor957]

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

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.

 

[BAretired]

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.

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!