Allowable Shear Stress 3

[Tagger]

I have difficutly in finding the Ultimate Shear stress in material properties. Basically steels (i.e. 4140, 1045, etc). If given only Yield and Ultimate strength of a material, how do you determine the shear stress (psi or MPa) where the material starts to yield (permanent deformation). I would like to determine the allowable shear stress for a particular material. I've seen a formula where Sv allow = 0.22Sy (Sv allow is allowable shear stress and Sy is Yield Strength of material). Machinery's Handbook say to use 4000 psi for main power tranmitting shafts, to 8500 psi for small short shafts. Can you use these numbers for plate? What I am trying to determine is the force required to shear a bolt through it's hole assuming the bolt will not break, and what allowable shear (psi) to use for a 4140 steel plate.

 

[Lcubed]

Ultimate shear strength of your steel is about 0.62 x Ultimate Tensile Strength. Yielding in shear will start at about 0.577 x Tensile Yield Strength. Some tests have shown that calculated shear stresses in manufacturing shearing operations reach about 70 percent of ultimate tensile strength as the punch shears through the workpiece, but this is not truly pure shear stress.

You are not dealing with pure shear when you pull a bolt through a plate. There is a combination of bending, shear, bearing (which is different from compression), and tension. The zone of load application will change continuously. You will probably need to do some testing.

 

[vonlueke]

Tagger: Are you asking about "shear tear out" strength of the plate (bolt is loaded in transverse shear and bolt shank tears out toward edge of plate)? Or are you asking about bolt head "pull through" (bolt is loaded in tension and bolt head pulls through plate in bolt axial direction)? The former of these checks uses only plate shear strength (either Ssy or Ssu).

Bearing stress, on the other hand, for bolt loaded in transverse shear toward plate edge, is a different calculation, and it's compared only to the plate bearing strength Sbry or Sbru. Though this stress state is a combination of stresses, published bolt hole bearing strength values are empirical and convert this complex stress state to an equivalent bearing strength uniformly distributed over the projected bolt area, D*t. If a published bearing strength value is unavailable, for ductile metals it can generally be approximated as 1.5 times Sty or Stu, for edge distance to bolt hole diameter ratio e/D_h = 2.0.

For ductile metals, shear yield strength Ssy can be taken as 0.577 Sty. And shear ultimate strength Ssu = 0.62 Stu sounds plausible in the absence of a published Ssu value. You then divide the material strength value by the factor of safety (FS) required for your project (or built into your code) to obtain the shear allowable stress for your plate, or, instead, multiply your applied stress by FS, then compare this factored stress to Ssy or Ssu.

As far as the tensile ultimate strength Stu of, say, steel AISI 4140, I think the strength can vary widely depending on the condition and temper, and can be as low as 620 MPa. And AISI 1045 could perhaps be as low as, say, 560 MPa, depending on the condition. But I defer to Materials or Metallurgical experts for typical strength values of specific steel alloys, as they are more knowledgeable of the forms and tempers most commonly available.

 

[Lcubed]

Oops! I probably should have made it clear that, since Tagger spoke of "a bolt THROUGH its hole", I was commenting on the case of pulling the bolt axially through a plate instead of loading the bolt transversely and tearing it out through the edge of the plate.

Shear strength of the plate would be useful in the axial pull-through case if the plate is supported in such a way that the plate cannot deflect and the bolt acts much like a punch shearing out a hexagonal slug with a circular hole in the center, but I didn't interpret his question as indicative of that situation.

 

[vonlueke]

And here's a clarification to my above post: Where I say "1.5 times Sty or Stu," I meant to say "1.5 Sty or 1.5 Stu."

 

[Tagger]

Thanks for the replies guys. To clarify: What I was talking about is what you said Lcubed in your second post in the second paragraph. The bolt is "pulled" through the bolt hole axially shearing the material of the plate with the bolt head. Therefore I would use plate shear strength according to vonlueke, thus 0.577Sy (Sy = yield strength) is equal to the shear yield strength of a ductile material. For Cast Iron it would be basically the point where it fractures.

 

[boo1]

Tagger, allowable shear (0.22*Fu) comes from AISC code for threaded fasteners, threads excuded from shear plane.

 

[TVP]

Tagger,

You can get some general information on the shear strength of some metals from MIL-HDBK-5H. It is freely available from one of the following sites:

http://assist2.daps.dla.mil/quicksearch/

**HUGE DOWNLOAD!**

or

http://euler9.tripod.com/

**Much smaller, available as individual chapters**

 

[vonlueke]

Tagger: To clarify, in the first paragraph, last sentence, of my first post, notice I used the word "former." I was referring there to the bolt transverse shear tear out. I didn't cover axial pull-through strength; this is covered in the second paragraph in each of the above posts by Lcubed.

Notice the caveat Lcubed mentions in the second paragraph of his second post. If the plate is very well supported--e.g., if there are two or three walls surrounding the bolt head through which the tensile load to the bolt head is applied--then axial plate "punch-through" shear strength might govern. However, the majority of applications might not have two or three walls in tension closely surrounding the bolt head, and thus the plate pull-through strength is more likely governed not by pure shear but by the mixed-mode failure described in the second paragraph of Lcubed's first post. Due to the difficulty in analyzing this, notice he suggested testing might be necessary.

I have an idea on how one might approximate this scenario using FEA, but since it would be a detailed discussion, will not go into that unless you are definitely interested in trying to approximate the combined pull-through stress using FEA.