Shear flow into fastners of built up sections

[SPJ1]

Hi,

I am doing a project where I am strengthening an existing structure that is insufficient. The current structure utilises a channel for a beam and as a method of strengthening it I am fastening an addition channel to it back-to-back (webs vertical).

I am struggling to visualize how to calculate the spacing of the fasteners, I have reviewed the methods of fastening together flanges to webs etc using Tau = VQ/I.

The main part I’m struggling with is to calculate Q as the sections as the sections are side by side and there is no eccentricity of the sections in y direction. Is my method of approach correct or should I calculate the shear stress in the section at the bolt location using sigma = M/Z and calculate a force on the bolt from there?

Also is there any pros or cons to fastening at both the top and bottom of the web as opposed to just fastening in the centre of the web?

I have attached a rough drawing to illustrate

Thanks in advance

 

[Ingenuity]

Related discussion here: Thread 507-408049 Composite wood beam shear flow design. Albeit different materials, similar concepts.

 

[atrizzy]

This is not a VQ/IT problem since you're not introducing a horizontal joint. If the goal is for the two channels to share a given line load and if that line load is applied from one direction only (and if the channels are approximately the same stiffness) then you need only provide enough fasteners to supply half the load from one channel to the other via simple shear in the fasteners.

Furthermore, if the line load is applied from both directions evenly (and again, if the channels are approximately the same stiffness) you could technically get away without any fastening at all. Just think of it as 2 joists closely spaced. Of course, you'd still want to connect them nominally.

 

[dhengr]

SPJ1:
I agree with Atrizzy’s approach to the problem, with a couple additional comments. The load comes in on the existing beam member now, so you must bolt to distribute something a little more than half the load to the new member, to make them act together. This will cause some amount of torsional loading on those light cold formed steel channels, not a particularly good thing. You might try to rearrange the load application a bit so it comes into the new beam more centered and/or applied to both members directly, then the torsion issue goes away and the bolting becomes even less critical, except to hold the two channels together. I’d bolt only on the centerline, except out at the bearings you should apply some bolts t&b. The biggest issue is that you should unload the existing beam, maybe even camber it a little bit, by jacking it up a little more than just straight (no deflection, rather a little camber). Then apply, drill and bolt the new member in place, to that same cambered shape. This allows both members to take all the loading when it is reapplied. If you just bolt the new member in place with the existing member, as is, the new member will only pick up new loads, additional loads. The existing member will pick up some of those new loads too, along with all the existing loads, and may then be overloaded.

 

[KootK]

I agree with atrizzy's conclusion but not the rationale supllied for it. All manner of VQ/IT problems do not involve horizontal joints. For similar material built up sections, the litmus test for whether or not VQ/IT comes into play is whether or not the centroids of the various components are aligned vertically (normal strong axis bending). When they align, there's no VQ/IT. When they don't, shear flow needs some attention. A common example of a vertical joint with shear flow would be a 2x8 sistered to a 2x10 with the bottom edges aligned.

I'd be inclined to stagger the bolts about the center-line as I expect that you'll be depending on the existing joist to provide lateral torsional bracing to the new joist and staggered bolts will do a better job off that. Besides, what does it hurt? Same number of bolts.

One note of caution. If your new member doesn't make it out to the bearings independently, then you'll need to transfer 100% of the end shear out of the new joists and into the existing joists locally. Hopefully you're getting out to the bearings.

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.

 

[SPJ1]

Thanks for all the help guys I appreciate it