Shear and Tensile Strengths
Shear and Tensile Strengths
(OP)
Hello everyone,
I have searched and searched this site as well as the web for the relationship between shear and tensile strengths of metals. I typically use 1/2 of tensile to estimate the shear strength. However, I remember a professor telling us that there is a definate relationship that can be used to determine the shear strength of a metal if the tensile strength is known. It MUST be a metal, and it goes back to the 45 degree shear plane theory.
I want to say the relationship to tensile to shear is 1/sqrt(2) which is .707. This makes sense to me due to the geometry of the 45 degree shear plane, but I keep seeing this .577 factor pop up too. I cannot figure out where this is coming from. The .577 has something to do with the Mohr circle, but I am not as familiar with it, so I cannot reproduce this .577 result. Can someone do a quick derivation of this so I can stop thinking about it?
Thanks
I have searched and searched this site as well as the web for the relationship between shear and tensile strengths of metals. I typically use 1/2 of tensile to estimate the shear strength. However, I remember a professor telling us that there is a definate relationship that can be used to determine the shear strength of a metal if the tensile strength is known. It MUST be a metal, and it goes back to the 45 degree shear plane theory.
I want to say the relationship to tensile to shear is 1/sqrt(2) which is .707. This makes sense to me due to the geometry of the 45 degree shear plane, but I keep seeing this .577 factor pop up too. I cannot figure out where this is coming from. The .577 has something to do with the Mohr circle, but I am not as familiar with it, so I cannot reproduce this .577 result. Can someone do a quick derivation of this so I can stop thinking about it?
Thanks





RE: Shear and Tensile Strengths
Plug into the von Mises equation for the principal stress the shear yield stress (set the other two principal stresses equal to 0 because you can assume pure shear) and solve, you will obtain the following
shear stress to cause yield = tensile yield strength/sqrt (3)
RE: Shear and Tensile Strengths
Thanks for the info. I see where it is coming from now (I think). The reason it is sqrt(3) rather than sqrt(2) is b/c of 3 principle stresses, correct? I was thinking 2d world, which is why I kept going back to 1/root2.
Thanks!
RE: Shear and Tensile Strengths