Bearing Strength Vs Bearing Stress

[NewEngInField]

Bearing Stress Formula

fbr=P/(D)(t)

where:
Fbr= Bearing stress (Pa)
P= Force of Load (N)
D=Diameter of Bolt
t=thickness of plate


Bearing Strength

Rn=(2.4)(0.75)(d)(t)(Fu)

where:
Rn= Bearing Strength (N)
Pa= Yield Strength (Pa)
D=Diameter of Bolt
t=thickness of plate


My question is, what are the differences between both formulas. Assuming if I replace the value of bearing stress with yield strength, the value of calculated Force of load will not be the same as Bearing strength. Which of these formulas should I use to determine the limiting factor while designing?

 

[centondollar]

I suggest you to be more specific if you want good answers. What are you designing? Do you have a supervisor who should know these things and who can guide you? Are you supposed to adhere to some code?

That "Bearing strength" formula involves constants (2.4 and 0.75), the origin of which are unclear. The first formula is the simplified mechanics of materials approximation of bolt-plate bearing stress which ignores the fact that stress is non-uniform in the bolt-plate contact area. The second formula is a mystery to me.

 

[NewEngInField]

As Per requested my source for the bearing stress formula.

 

[driftLimiter]

The first equation you show is simply a resolution of the force P over the bearing area (D*t). There is no parameter in this equation that has to do with strength. This is an analysis equation. I suppose you could substitute some allowable level of stress in here. But this is not how it is done.

The second equation is part ofan AISC 360 formula (empirical).

Refer to AISC 360-10 Section J10. Bearing Strength at Bolt Holes.

The 2.4dtFu term is used as the maximum limit of the bearing strength at bolt holes that are not long slotted. Lets be clear this is the maximum strength, and this is for the connected material bearing. This check does not include the check of the bolt itself.

The 0.75 term included by the OP is the phi factor for LRFD.

TBH I think you have some homework to do. You want to understand the basics before you start designing. This guy will get you up and running on anything steel.Link

To answer your question directly, the second equation is the only one you would use to check the limit state of bearing at bolt holes. The difference mostly being that one of them is a simple cut of the section and resolves the force as a normal force on the projected bolt area. In reality the bearing is resisted by a combination of stresses that are in different directions. The AISC strength equations consider how the forces flow away from the bolt hole.