Moment and uplift on bolt group due to force eccentric to both axis

[mecheng24]

I have the scenario drawn out in the attachment.

I want to find the max tensile force in the bolt. I am wondering if I can use the Case II approach in the Section “Eccentricity Normal to the Plane of the Faying Surface” in Part 7 of the Steel Construction Manual? This approach puts the NA right at the centroid of the bolt group as I have drawn.

I have 16 bolts total. But because half the bolts are in the compression block for moment in X and half the bolts are in compression for moment in Z, do I only consider 4 bolts (bolts #5,6,7,8) for this case? So uplift divided by 4 bolts, plus moment in X divided by 8 bolts, plus moment in Z divided by 8 bolts?

Or do I do uplift divided by 16 bolts and moment in X and Z divided by 8 bolts each? Or something different?

I have done an FEA on the scenario and the results are closer to the former conservative assumption.

 

[mecheng24]

case II excerpt from SCM for those unaware:

 

[rb1957]

I'm not sure how you 'crete people do things ... I'd do each moment separately and sum the results. I think you say the compression is carried by the concrete (at the centroid) and tension by the rebar ... so would you react the tension load on all the rebar ? (including the ones in the compression loaded concrete ?)

maybe a smart way would be to draw the moment vector through the centroid of the rebar (your origin) and say (a bit like the pope) this side is in compression and these rebar are in tension ?

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

 

[mecheng24]

rb1957,

Ok so divide the uplift by all 16 bolts. This is what I originally did but resulting force was much lower that what FEA gave me so it made me question it. Especially since SCM says that this method is supposed to be more conservative.

FWIW, i should have clarified. This is not connected to concrete but rather another steel plate.

Regards

 

[mike20793]

Does bending in both directions occur simultaneously or independent of each other?

 

[rb1957]

ok, so you're trying to react the tension and two moments on the 16 fasteners ? typical analysis allows the fasteners to react tension and compression; this makes it easy to superimpose the three loads.

I guess it's more precise to react the compression load as a face-to-face "bearing" ... this would be a triangular loading (zero on the NA, max furthest away). this would take quite a bit of iteration to find the true NA.

A further complexity is preload ... are the fasteners tightened down to prevent gapping under the tension load ? to an extent this simplifies the analysis ... now the entire face is in compression, so moment is reacted as a typical bending stress distribution, adding to and subtracting from the preload compression.

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

 

[mecheng24]

I guess that is what I am trying to get sorted out, do the bolts in the compression zone help resist uplift as well? The bolts are under preload, but I am trying to determine the maximum tensile force in the bolt to ensure it doesn't exceed the pretension.

Yes, I agree calculating the true NA of the bolt group would be ideal if I could figure out how to do that. That is something that has been in the back of my mind for a while but no luck so far.

 

[rb1957]

"do the bolts in the compression zone help resist uplift as well?" ... in my opinion, yes ... you've moved the load to the centroid of the bolt group.

the applied loads are reacted by a stress field which you can determine form saying the entire plate area reacts the loads (direct and moment). if the resulting stress exceeds the preload compression stress you've got gapping. so I'd use the plate area to determine the peak reaction stress, then peak stress = 16P/area >> required preload "P". I think you can use the plate area 'cause the preload is creating a compression stress that the load is working against.

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