How to Calculate Principal Stresses in a Stressed Component?

[cabellos]

Principal stresses help please?

I am looking through past paper examinations and have come a across a question:

At a certain critical point in a stressed component, calculations show that the stresses are sigma(x) = 220MPa sigma(y) = -95MPa and shear = 60MPa

Find the maximum and minimum direct stresses (principal stresses) in the component at that point?

How do i go about this problem?

Thankyou.

 

[radou]

Well, do you know any related formulae? To be more specific, there is exactly one formula you need to apply.

 

[cabellos]

Ah yes i think I have a solution to this problem now using the general formula for plane stresses.

There is a second part to the question where it now asks to find the angle which the maximum stresses make with the direction sigma(x)?

Does this involve the 2D Mohr Circle?

 

[radou]

Ah yes i think I have a solution to this problem now using the general formula for plane stresses.

There is a second part to the question where it now asks to find the angle which the maximum stresses make with the direction sigma(x)?

Does this involve the 2D Mohr Circle?

You can simply use tg(2A) = Txy / (Nx - Ny), where A is the angle of the principal stress, Nx and Ny are normal stresses and Txy is the shear stress.

Have on mind that tg2(A + Pi/2) = tg(2A).