Stress distribution in bolt holes

[Polecat]

What is the proper stress distribution in a bolt hole in concrete resulting from a load imparted by a bolt in single shear bearing. Usually, a triangular distribution is assumed (so the average is 1/2 the max), but is there any evidence or testing to show that a parabolic distribution could also be assumed?

http://www.spiraleng.com

 

[BAretired]

It depends on the diameter of the hole, usually more than the diameter of the bolt. Theoretically, the stress is very high at the point of contact when load is first applied, but the material starts to yield and the stress assumes a value compatible with the strain of bolt and plate. In single shear, the bolt bends over the thickness of plate, so stress variation is not consistent across the plate thickness.

Why is it important to know?

BA

 

[dhengr]

Polecat:
Of course, the bearing line or surface is some sort of a curve in most cases, for the types of reasons that BA mentions. I don’t know that I would complicate the problem that way if I didn’t have a very good reason, so answer BA’s question. I probably wouldn’t call the curve a “ parabolic distribution ,“ I’d just say the bearing stress is max. at the faying surface and varies in some non-linear fashion as you move along the bolt. But, I would also argue that a triangular (trapezoidal?) distrib. is a darn good simplified representation of true situation, and should suffice for most situations. When you think about it, most of our common bearing situations are not uniform, as we normally assume they are: the deflection of a beam or bar joist causes a max. bearing load at the bearing edge toward the center of the beam, and it most likely isn’t exactly a linear distrib.; the bearing stresses under a WF column on a steel base pl. are generally max. right under the WF shape, etc. For your bolt question, look up Hertz bearing stresses for a pin in a hole, think about a beam on an elastic foundation and dig out your Advanced Strength of Materials and Theory of Elasticity text books and go to it.