Heel and tow effect reversed

[franc11]

Hi,

Head scratching question here.

If you bolt two plates, one over the other, with two rows of fasteners like this : (note that the two plus sign over one another means the lengths of the bolt linking one plate over the other...hope it's clear)


+++++++++++++++++
+ +
+ + v (1)
++++++++++++++++++++++++
^ (2)



If you try to peel off the plate (1), you will have a heel and toe effect, meaning that it's possible that the right fastener would be in tehnsion and the left fastener would be "in compression" meaning the bolt won't see any loads.

Here's my question. If we inverse the load (2)is it possible to have another king of heel and tow effect meaning that the right fastener would be "in compression" meaning it wont see any loads and the left fasteners would see tension. Is it something possible or the two fasteners will always be in tension?

 

[rb1957]

imagine you're applying load to the upper plate by pulling up; the right edge of the upper plate digs into the lower plate (the "toe" loading), increasing the tension loads on the left fasteners. note, the upper plate is pulled away from the the left edge of the lower plate.

now imagine you're loading the lower plate by piulling down; the left edge of the lower plate digs into the upper plate, and separates on the right side ... the opposite loads as above.

 

[franc11]

I get you on this, but my point is, if you apply the load up on the lower plate like shown with (2) is there any way that the right fastner could NOT be in tension, considering that the pivot would be the right edge of the upper plate.

 

[rb1957]

actually, i thought about this on the way home, and i think my post is a crock !

assume both plates are similar thickness. then, consider applying a load up on the left side of the upper plate, and the reaction is on the right side of the lower plate. then there is a plane of symmetry (between the bolts) so this is going to act like a fully fixed reaction. thus i think you'll have tension in left bolt, and no contact at the edge of the lower plate.

heel and toe ideally sets up when you have an angle fixed to a more substantial substrate with a single line of fasteners and a tension load, and is just a simple static solution to the situation where the load is offset from the reaction; the "toe" reaction provided moment equilibrium.

this example (with two bolts, presumably preloaded) is a more complex real world example. a lot of the external energy is taken up in splitting the clamped faces; again a simlification is to assume a gapped joint.

but returning to your question, if you apply a "compression" (down) load and lets assume a simple reaction (ie not think about the clamping forces) I'd say that the bolt reactions could be simply the opposite of the tension case ... the two bolts react the directly applied force (presumably equally) and they react the external moment as a couple. in this case you don't need a "toe" reaction for equilibrium; one could possibly develop depending on the stiffness of the plates and the plasticity of the plates.

any clearer ??

 

[corus]

You have to think about the contaxct that is being made, or not as the case may be. In both cases of load application, contact could be made at the end of either plate, providing a reaction force, and hence a balancing moment when coupled with the forces in the bolts. The bolts would be in tension in both cases 1 and 2.

corus

 

[vonlueke]

franc11: For load case 2, it's possible, in rare instances, that the right-hand bolt could be in "compression" (meaning zero bolt applied load) if the upper plate is very flexible compared to the lower plate, because then the upper plate might bend at, e.g., the left-hand bolt.

But typically, if both plates are of reasonable stiffness, the right-hand bolt will be subjected to a small or negligible amount of applied tension, because the pivot will typically occur anywhere from, say, the right-hand bolt to near the right-hand edge of the upper plate. (In rigid-body mechanics, the pivot occurs at the right-hand edge of the upper plate).

 

[RPstress]

I more or less concur with vonlueke: the problem will have passably predictable outcomes as described for common geometry.

However, it is stiffness dependent, being affected by the plate edge overhangs, the plate bending stiffness, the fastener stiffness and the amount of preload, etc. You could easily design a system which had both bolts in tension (thick, stiff plates with a big overhang) or just one in tension.

NB: if the bolts are preloaded, then the problem is non-linear even with no yielding.