Calculating Bearing Stresses between Two Flat Surfaces

[adv_eng]

hello there ...

i am in the middle of stress-strain calculation..and got stuck-up at bearing/contact stresses
how to calculate bearing stresses in two flat plate...?
most of the engineering books has mentioned about bearing stresses/contact stresses between two circular bodies and which can be calculated by hertz theory...
but how about two flat surfaces...

 

[Studiot]

Some more information would be much better than guessing what your application is.

For instance what are the relative sizes of the two components?
What materials are we talking about?
How are the plates loaded?
What are the foundation/support conditions for the lower plate?

Have you head of punching shear?
Have you heard of St Vennant's principle?

 

[adv_eng]

well, i have two bodies in contact one is sphere and other is shaft...sphere is having slot (consider as female component) and one end of the shaft is machined in such a way that (consider male component) it could assmebly with the sphere slot ...now the overall picture would be like flat surface of the shaft is in contact with flat surface sphere slot..both the bodies are fixed in all DOF only rotation is free
now torque or moment is applied at circular end of the shaft and it will transfer to the sphere thro shaft-sphere connection (its a simplae assembly ..no welding no fastners )...now actual area in contact is somewhere around 0.113 in^2
and moment can be converted to the couple forces ...and that would be around 3000N
so we have force and we have area ...then what would be the suitable equation to calculate contact stresses in shaft-sphere connection...

i hope you clear with the problem...

 

[Studiot]

Punctuation is good. It allows the reader to draw breath.



As I understand what you are saying you are asking to analyse the action of a flat bladed screwdriver in the screwhead slot. Or perhaps the action of the square drive end of a socket extension piece in the socket.

Now that you have told us you are transmitting torque it changes the analysis fundamentally.

This is not a contact stress problem of normal (direct or axial) stresses.

There is a stress distribution in the shaft, increasing outwards from the axis of rotation.
The moment increase with distance from the axis.

Consequently there is a pressure distribution on the mating surface increasing which is maximum at the points most distant from the axis of twist.

For a screwdriver (thin rectangular section) these are the edges of the blade.
For a socket drive (square section) these are the corners (all four) of the square. This is why corners get rounded and hex drives are promoted for less substantial sections (more corners).
If you are only machining a single flat onto your shaft end it ewill be like the screwdriver.

I would assume a linear stress distribution from axis to edge (extreme fibre) as a first analysis.

 

[adv_eng]

lol...;)

case of screwhead slot and screwdriver is a perfect example of my problem...

now when you apply torque to screw driver then flat balde of screwdriver get in contact with screw slot...and there is my question how to find stresses at that contact ...??

you are saying "transmitting torque will change the fundamental of analysis" i agree with that ...but if you resolve the torque into couple forces then ...i think it makes the problem easier...? isn't it..?

and then if i calculates stresses by using formula .. stress = force/area...will that be a bearing stresses..?? what is your opinion..??

i am doing handcalculations, so trying to smplify the case... ! ! !


regards

 

[Studiot]

Last line of post#4

I would assume a linear stress distribution from axis to edge (extreme fibre) as a first analysis.