Stacked beams

[L-H]

Hi Guys,

When we have two wood beams (just for example), one beam sits on top of the other beam and there is an uniform load acting on top of the top beam, assume two beams have the same size and are laterally supported, can we assume each beam will carry 1/2 of the total load acting on top of beam A in order to check for bending ? How about shear ? Can the critical shear plane extends from the support all the way up to top of beam A as shown in the picture ? Does the critical shear plane depend on the composite action between two beams ? Like if there is no bonding between two beams, will the shear plane be different to that of the case when two beams are perfectly bonded together ?

 

[hokie66]

Two wood beams, one on the top of the other, with no bonding, will act the same as the two beams side by side (or one beam twice the width). No, you can't assume the shear acts as in your picture. That would be true only if the beams were as one.

 

[L-H]

Hi hokie66,
Thank you for your response. So how the critical shear plane looks like in the beams when they are not bonded together ?

 

[dik]

You would have two parabolic distributions... one for each beam.

Dik

 

[L-H]

Hi dik,

Thank you for your response. Can you please explain a bit more ? Parabolic distribution for the load on the beams ? How does it look ?

 

[civeng80]

What they are saying is that they are two separate beams. So half the load would be taken per beam and then beam theory applied.

 

[hokie66]

And shear on a rectangular beam is distributed parabolically, as dik said. Shear stress is maximum at mid-depth, and is 3/2 x V / A.

 

[TLHS]

Anyone remember the thread on this question where people started stacking model sized beams on top of each other and measuring deflections?

 

[KootK]

Anyone remember the thread on this question where people started stacking model sized beams on top of each other and measuring deflections?

I recall that bit of communal awesomeness: Link

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[L-H]

Hi hokie66,

I knew parabolic shear distribution on the section and the maximum stress which is equal to 3/2 V/A. But how much V each beam will get ? The amount of V the top beam will get equal to that of the bottom beam ? Let's say when we have one beam only with load w, span L and depth d. Then the value of shear V the beam will get is w(L/2-d) because the critical shear plane is at d distance from the support. So back to my original question and picture that i posted. Can I draw a line at 45 degree angle extend from the support to the top face of the top beam like that ? And calculate V for each beam based on that line ? That means the top beam will get smaller V compared to that of the bottom beam.

 

[hokie66]

No, I wouldn't do that. The beams will share the load equally, just as if they were side by side. So I would discount the 45 degree idea.

 

[rb1957]

I'm wondering if dik is referring to spanwise parabolic loads ? To me, two beams stacked one on top of the other doesn't sound like two beams side-by-side, but I can see what's meant (each beam carries 1/2 the load, bending in isolation). I'd've thought that the upper beam would pass a distributed load to the lower beam, as the upper beam deflects due to the load applied. Having nothing at all between the two beams sounds "unwise" ... I'd at least glue them together. Then you can see that they'd work together, each carrying 1/2 the bending stress field, yes?

I guess the question becomes are two beams stacked twice as stiff as 1, or 8x ?

another day in paradise, or is paradise one day closer ?

 

[jayrod12]

If you glue them together, then you've got horizontal shear transfer between them. They're more likely to act as a single composite unit at that point and you'd have a different shear distribution.

 

[hokie66]

The OP didn't ask about composite action, so we assumed they acted independently. So two beams stacked are twice as stiff as one.

rb1957,
No, dik means the shear stress distribution is parabolic across the section depth. Zero at top and bottom, maximum at mid-depth.