Deflection of Stacked Beams with Different Beam Sections 7

[Logan82]

Hi,

What would be the equation of the deflection of the two beams stacked stacked on each other? I am looking for the deflection at a distance "a" from the support.

Assumptions:
- The two beams are not linked to another, they are just stacked.
- We can assume that there is no friction.
- The two loads are symmetrical.
- The two beam shapes are different.

I know that:
- The deflections are equal (Δ1 = Δ2).
- The equation of the deflection if there was one beam would be:
Δ_x = (P*x*(3*L*a-3*a^2-x^2))/(6*E*I)
Since we are looking for the deflection at x = a, then:
Δ_a = (P*a*(3*L*a-4*a^2))/(6*E*I)

 

[BridgeSmith]

If you want them to act as composite before they deflect significantly enough to engage the bolts in bearing, they have to be tensioned as slip critical. Otherwise, you won't get full composite action; you'll only get partial composite action that doesn't kick in until there's enough deflection to start engaging the bolts in shear, which will start with the ones near the ends of the beam, and will never engage the ones near the middle. That is, until the ones at the end start shearing off. I doubt your client would be too happy if that happened.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[KootK]

@Logan82: any change you'd be willing to post a sketch of the beam support condition?

Even if the bolts are designed for shear flow, if they are not slip critical, it's difficult to know which will be engaged first. It's tempting to say it would be the bolts at the peak shear locations but even that is somewhat uncertain.

My gut feel is that, even if the bolts are bearing bolts not designed for shear flow, nothing would likely come apart. Many of the bolt failure mechanisms are ductile-ish.

I probably would just stitch weld the beams together unless if proved economically prohibitive to do so for some reason.

Lateral torsional buckling for such a setup might be interesting, although perhaps drifting too far into the pedantic. Any intermittent stiffeners along the length of the beam? Any kickers/fly bracing?

 

[Logan82]

@Logan82: any change you'd be willing to post a sketch of the beam support condition?

It looks approximately like this (simplified):

Lateral torsional buckling for such a setup might be interesting, although perhaps drifting too far into the pedantic. Any intermittent stiffeners along the length of the beam? Any kickers/fly bracing?

There are stiffeners between the top and bottom flange of the top beam. Also, for the bottom beam only, there are a total of 3 beams used for lateral support between the supports (as well as one beam for lateral support at each support as shown in the sketch).

Weld the flanges together with intermittent fillet welds is another option. There are also some clamps but IDK if I would rely on those permanently for this application.

Why wouldn't it be permanent?

Say I install new slip critical bolts. Before that, I clean the surface free of rust with sand-blast (but with rough surface due to the consequence of corrosion), would you say that would be enough to meet the minimum surface class (class A)?

However, I don't think that bolting or welding the two beams together could create a composite beam in this specific situation, since there are shims between the two beams in some places of that have a thickness of up to 20 mm. The shims were put in place to level the beam since there is a rolling path on top.