Ledger bolt spacing from chord force

[StrEng007]

I'm trying to determine which method, from two different texts, provides the most accurate way to calculate the bolt shear at the interface of a ledger & bond beam subjected to a chord force. One method produces a shear value that is exactly two times the other.

Method 1:
1)Chord force, C= M/d
2)Bolt shear between ledger and bond beam, v=VQ/I, where V=wl/2. This is reduced to v=V/d (lb/ft).

The shear flow is being reduced to V/d since the force is being resolved into the chord steel. A unit area of 1.0in² is being used in Q and I.
The chord force is not used to calculate the shear in the bolts.

Method 2:
1)Chord force, C= M/d
2)Bolt shear between ledger and bond beam, v=C/(0.5*l) (lb/ft)

The maximum chord force is divided by a length of 1/2 of the wall.

A third method I've seen but have not been able to find in text:
1)Chord force, C= M/d
2)Bolt shear between ledger and bond beam, v=4C/l

Method 3 is mathematically equivalent to Method 1:
(wl/2)x(1/d) = (wl²/8)x(1/d)*(4/l)

This shows that shear flow in an element is equivalent to the distributed load magnitude required to create a chord force equivalent to M/d at the center span.

Which is the most adopted method?

 

[KootK]

I think that the difference is, fundamentally, about whether you feel it is more appropriate to use an elastic shear flow model (VQ/It) or a plastic redistribution model (composite beams) where all you need to do is "develop" either side of peak moment.

I have a slight preference for the elastic model. In my opinion, once you go plastic, you then don't have the ability to generate the composite action moment that you're assuming is available as you move inwards from the reaction. That, because you're fastened for less than the peak VQ/It demand. I have a related thread of my own that you could check out for additional information on that Link. Probably TMI for your purposes here.

May I ask what references you're using? Pretty good chance I have them and I'd like to look into it further.

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.

 

[KootK]

And the easy derivation of the elastic case is:

Delta_T/ft = Delta_M/ft * 1/d = V * 1/d = V/d

With [Delta_T/ft] being the answer that we seek.

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.