How to solve for the angle of principle stresses

[kfc12piece]

Hello everyone,

I want to start by saying this is my first official visit to the forum, however I have been using the forum for several years to help me through my classes, and I owe a big thanks to all who are involved for getting me through some tough times!

Now, on to my question...

I need some help on how to solve the equation for the angle of principle stress on a stress element. The equation is tan2∅=(shear stress/(stress in X-stress in Y)/2.

I don't understand how to solve for ∅ in this equation, since I don't understand what to make of the tan2∅ term. How do I punch that into a calculator to solve this equation? I also don't understand how I'm suppose to get two separate angles out of this equation (one for each of the principle stresses).

Any help would be much obliged.

 

[tiny-tim]

welcome to pf!

hello kfc12piece! welcome to pf!

(have a nicer phi: φ )

The equation is tan2∅=(shear stress/(stress in X-stress in Y)/2.

I don't understand how to solve for ∅ in this equation, since I don't understand what to make of the tan2∅ term. How do I punch that into a calculator to solve this equation? I also don't understand how I'm suppose to get two separate angles out of this equation (one for each of the principle stresses).

use the tan^-1 button …

that'll give you 2φ ​

eg if tan2φ = √3,

then 2φ = 60° (or 240° or 420° or …)

so φ = 30° (or 120°) ​

 

[Chestermiller]

The principal stresses are perpendicular to one another. So, once you know one angle, you know the other.