Composite wood beam Shear flow Design

[sticksandtriangles]

Hello,

I have a condition where I am trying to ensure composite bending for an existing piece of wood sistered on each end with (2) LVLs.

See Below:

I know that the composite action is based on shear flow: v=VQ/I.
I wanted to design the fasteners to ensure composite action and wanted to confirm my design assumption of Q:

I also wanted to confirm that the equation, v=VQ/I, is showing me that adding more screws, e.g. maybe (4) rows of screws,

would not reduce my demand on the the upper screws.

I always note things where adding more does not help the situation. Let me know if I am missing something in the mix here.

Thanks for your thoughts in advance!

 

[KootK]

I actually believe this to be a much simpler problem. I think that you just need to design the fasteners to transmit the portions of the vertical applied load that will be going to each ply in proportion to that ply's relative stiffness. No VQ/It. I'd probably go with two rows of staggered fasteners around the third points of the section. One row would theoretically work but it's nice to give more stability to the edges of the LVL's. If you're feeling fancy, you might account for:

1) some of the load already being locked into the existing beam.
2) any effect due to jacking if you decide to go that route.

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.

 

[sticksandtriangles]

Thanks for the response.
Any reason as to why you feel like this is a much simpler problem that does not need to consider the shear flow idea?

When I sized this beam, I needed to have all portions of it acting compositely for it to work. If one side was unevenly loaded, I wanted to ensure that all portions of the member would be loaded based on the relative stiffness of the individual elements.

 

[MacGruber22]

I second KootK. Consider a solid section equal to the 3 pieces you have. Draw the differential cube element (stress tensor) and look at the stress equilibrium for beam action on that element. Eliminate all of the null stresses and you can see that the plane you are trying to apply VQ/I doesn't have a stress (normal or shear) associated with flexural behavior.

"It is imperative Cunth doesn't get his hands on those codes."

 

[KootK]

Think of it like this:

1) the goal of composite design is to get your parts to share a common flexural strain diagrams. Here, that diagram is your classic double triangle with the neutral axis at mid height. VQ/It is the shear force that must be transferred between parts to force them to strain this way when they would normally not do so of their own accord.

2) In your case, with equal depth members sharing a common centroidal axis, the strain diagrams will match naturally so long as the three members are made to travel vertically in unison and therefore assume the save curvatures at their respective centroidal axes.

3) The nailing, as I described it previously, would be sufficient to force the three plies to deflect vertically in unison.

Any chance you're convinced by that? Or is it diagram time?


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.

 

[sticksandtriangles]

That seems to make sense.
These guys would naturally deflect the same way


Thanks!

 

[sticksandtriangles]

That also explains why every example on shear flow I found was about transfer loads to sections above and below the NA, not sharing the same neutral axis.

I did simplify my post to show the new LVLs and the existing wood member to be the same depth, in reality the new wood member is about 1" deeper than the LVLs that are going to be sistered.

I suspect this to be insignificant, but for the sake of argument how would one solve for the resulting shear flow that would need to be accounted for?

 

[BAretired]

If the existing beam is carrying all of the load now, it would be advisable to shore it up in order to relieve it of stress before attaching the two new plies.

If load is applied from the top as it would be from joists bearing on the existing beam, then the connection does not transfer any shear provided the joists bear on the new plies in all locations.

If load is applied only to the existing beam as in the case of a wall bearing on the beam, then the connections to the new plies are required to transfer a shear based on the relative stiffness of each of the three plies which must all deflect together.

In both cases, shear flow is not a factor.


BA

 

[KootK]

That also explains why every example on shear flow I found was about transfer loads to sections above and below the NA, not sharing the same neutral axis.

Exactly. I'd considered this, initially, as a way to support my assertion. It didn't really seem proofy enough however.

...in reality the new wood member is about 1" deeper than the LVLs that are going to be sistered. I suspect this to be insignificant, but for the sake of argument how would one solve for the resulting shear flow that would need to be accounted for?

You're probably going to be sorry that you asked. This thread deals with this question ad nauseum: Link. In particular, see my sketch in green part way down.

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.

 

[sticksandtriangles]

Koot, I'm going to ignore that link . I'll just design for the proportion of shear each member will see based off stiffness.

Thanks for the link though. I think my searching skills need to be refined as I swear I searched for threads related this topic and found nothing.

 

[KootK]

Yeah, it's nuts how complex a common thing like sistering can get if you stare at it long enough. It gets even worse if the sistered pieces don't make it to bearing.

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.

 

[pcronin]

The beams will share load based on equivalent stiffness. The deflection of the beams will be the same and you can ratio equivalent thickness based on modular ratio of modulus of elasticity.

If loading from the top full width, you just need to tie them together to prevent separation. If framed into the face, you have to develop the shear load through the members to have them act together.

Shear flow is to develop load to top and bottom flanges of a composite section.

 

[UtahAggiePE]

you may want to stagger the pattern to prevent splitting in wood