Calculating Bearing Stresses between Two Flat Surfaces

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In summary, the conversation is discussing the calculation of bearing stresses between two flat surfaces, specifically in the context of a spherical object with a slot and a shaft that can be assembled together. The conversation also touches on the application of torque and its effect on the stress analysis, with a mention of using linear stress distribution as a first analysis. Further details and clarification are needed to accurately determine the suitable equation for calculating the contact stresses in this scenario.
  • #1
adv_eng
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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...
 
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  • #2
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?
 
  • #3
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...
 
  • #4
Punctuation is good. It allows the reader to draw breath.

:wink:

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.
 
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  • #5
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
 
  • #6
Last line of post#4

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

1. What is a bearing stress?

A bearing stress is a type of stress that occurs when two flat surfaces are in contact with each other and one surface is subjected to a force that is perpendicular to the surface. This stress is caused by the compression of the material between the two surfaces.

2. How do you calculate bearing stress?

To calculate bearing stress, you need to know the applied force, the contact area between the two surfaces, and the material properties of the surfaces. The formula for bearing stress is stress = force / area. This will give you the stress in units of pressure, such as pounds per square inch (psi) or newtons per square meter (N/m2).

3. What factors can affect bearing stress?

Bearing stress can be affected by several factors, including the magnitude and direction of the applied force, the surface roughness and flatness of the two surfaces, and the material properties of the surfaces. Uneven loading or surface imperfections can also impact the distribution of stress between the two surfaces.

4. How does bearing stress differ from other types of stress?

Bearing stress is unique in that it occurs between two flat surfaces in contact with each other, whereas other types of stress, such as tensile or compressive stress, occur within a material. Bearing stress is also considered a surface stress, as it is only present at the interface between the two surfaces.

5. Why is it important to calculate bearing stress?

Calculating bearing stress is important for ensuring the structural integrity of components and structures that rely on the contact between two flat surfaces. It allows engineers and scientists to determine if the material can withstand the applied forces without failing or deforming. It also helps in selecting the appropriate materials and design for a given application to prevent failure due to excessive bearing stress.

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