bearing stress in slot

[mielke]

is there a simple equation to use to find the average bearing stress in a slot in a plate due to a bolt loading?

I've seen the equation STRESS=F/A and for small holes A=dt (where d=bolt diameter and t=thickness of the plate) but how do you apply this stress equation to a bolt acting on a slot? the area of contact goes down to a 1D line, is there an empirical correction for this?

Thanks!

 

[dhengr]

Mielke:
The equation S = F/(dt) is an idealized bearing stress after significant amount of bearing yielding has taken place btwn. the bolt and the plate hole, to fully seat the bolt in the deformed hole in the plate. Then almost the full dia. of the bolt is bearing at some stress level or another. When you ask about a bolt in a slot, in effect, you have a cylindrical element (the bolt shaft) bearing on a flat pl. edge of length ‘t.’ At first the bearing area is a line of length ‘t,’ but of course, that causes essentially infinite bearing stress on that line, or the immediate yielding of the plate on and near that line. Now you have some width of bearing, of length ‘t,’ but yielding and the width continues to grow until you reach equilibrium. Look up Hertz Bearing Stresses in a good Advanced Strength of Materials or Theory of Elasticity text book. Roark has some of this in his book too. There will be examples of a cylinder on a flat pl. (your bolt in the slot) and examples of a cylinder in a cylindrical hole and the closer you get to the dia. of the bolt matching the i.d. of the hole, the closer you come to S = F/(dt), but you never quite get there.

 

[dhengr]

Mielke:
BTW, yielding in bearing is generally higher than the yielding in tension or compression, for the same material, because the surrounding material tends to constrain the yielding material which is under bearing stress. It just can’t yield, move or strain, its confined. Also, when dealing with a bolted connection remember that one bolt hole & bolt in bearing yields first, to start to bring the next bolt into full bearing, and then the third bolt starts to bear, etc., in some indeterminate fashion. This is in good part a function of fabrication tolerances. It is an oversimplification to assume all bolts are bearing equally until there is considerable movement of the connection. A good riveted connection works better in this respect, because the hot rivets expand to fill the holes and thus come into play in better unison.

​

 

[desertfox]

Hi Miele

I think you can apply the same formula where the bolt diameter x plate thickness is the area resisting the load, the fact that the bolt only touches one side of a slot doesn't really matter because a bolt situated in a clearence hole can only make line or tangential contact in any case.
Of course a bolt under load if sufficient enough will ten to yield the clamped material slightly until a slight flat occurs which will reduce the said stress.
As dhengr states the formula is an idealised one and at best only gives an average stress.

 

[tbuelna]

To simplify things it can be analyzed as an elastic hertzian contact between a cylinder and a flat plate. This approach takes into account the relative stiffness of the materials in contact. A steel bolt bearing against an aluminum slot face would not give the same result as a steel bolt bearing against a steel slot face.

If you don't want any yielding at the contact you'll need to consider factors like misalignment between the bolt and slot face, which can create significant stress concentrations at the slot edge. In the end what you'll likely find is that the radial force at the bolt which keeps the bearing stress below yield is probably quite modest.

 

[desertfox]

Hi

Meant to provide this link

http://www.roymech.co.uk/Useful_Tables/Screws/Bolted_Joint.html

 

[sdz]

In structural engineering you are only allowed to use a bolt in bearing normal to the slot direction and then you can use the full capacity. If the load is in the slot direction you have to use friction grip bolts fully tensioned.

 

[tbuelna]

Using the cylindrical body of a bolt bearing directly against the flat side surface of a slot is a crummy way to transfer force. If it is necessary to have slotted holes for adjustability, it would help to use an elongated bushing in the slot that has a round hole in the center and flat sides. This provides a conformal contact for both the cylindrical bolt body and flat side surfaces of the slot, and greatly increases the bearing capacity of the fastener installation in that orientation before yield occurs.

 

[dhengr]

The way Mielke asked his question, I thought he wanted something more than just the std. AISC take on the matter. That’s what prompted my answers, the way I gave them. He didn’t say what sort of connection he had, how many bolts, etc. He asked about bearing of a pin/bolt in a hole or slot. Sdz has given the std. AISC prescription for bolts in short slots, in a connection. There will be considerable movement and deformation in that connection before it fails, unless the bolts are fully tensioned. Tbuelna’s approach is one that certainly finesses the problem and the high bearing stresses, but it would unlikely be affordable in a typical structural connection.

 

[MikeHalloran]

Unfortunately, Mielke didn't make it clear if the question has to do with structures or with mechanisms.

I have used something similar to what Tbuelna described, i.e. a sliding square-ish bronze block with a round bore to connect a crank and link to a linear mechanism, with reasonable stresses and decent life and not unreasonable costs for its market. Stuff like that becomes unaffordable in products like low-cost lawn furniture, where some brinelling is accepted, as is very limited life.

Come to think of it, I see fewer instances of screws in slots in modern consumer products, probably thanks to innovations like plastic structural connections and self-drilling screws.

I haven't noticed much innovation in larger structures since hook-knurled bolts. ... but I may have missed a meeting or two. ;-)






Mike Halloran
Pembroke Pines, FL, USA