Understanding Mohr's Circle: Shear Stress and Normal Stress Interactions

[chetzread]

Homework Statement

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress_principal.cfm
in this notes , i couldn't understand that why there exists an angle (θp) where the shear stress (τx'y' ) becomes zero , (only normal stress acting )
is there any proof on this ?

for the second part , why when we find max shear stress , there's also average normal stress acting ?

Homework Equations

The Attempt at a Solution

is the second diagram wrong ? when we find max shear stress , there should not be average normal stress acting ...[/B]

 

[Chestermiller]

Homework Statement

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress_principal.cfm
in this notes , i couldn't understand that why there exists an angle (θp) where the shear stress (τx'y' ) becomes zero , (only normal stress acting )
is there any proof on this ?

for the second part , why when we find max shear stress , there's also average normal stress acting ?

Homework Equations

The Attempt at a Solution

is the second diagram wrong ? when we find max shear stress , there should not be average normal stress acting ...[/B]

Are you familiar with the Cauchy stress relationship?

 

[chetzread]

Are you familiar with the Cauchy stress relationship?

no , i have never heard of that

 

[Chestermiller]

no , i have never heard of that

Then how can you possibly determine the components of the stress (traction) vector on a surface of arbitrary orientation?

The Cauchy stress relationship says that $$\tau=\sigma n$$
where n is a unit column vector normal to a surface of interest, $\sigma$ is the matrix of stress tensor components, and $\tau$ is the stress (traction) vector acting on the surface. Have you ever heard of anything like this?