Group Abstract Group Abstract

Message Boards Message Boards

0
|
9.9K Views
|
2 Replies
|
1 Total Like
View groups...
Share
Share this post:

Solving simple trigonometric equation (Mohr's circle)

Posted 12 years ago

Intro: I am working towards constructing Mohr's circle for stresses at a point. This involves the Plane Stress Transformation equations, one of them being stress=(sigmax+sigmay)/2 + (sigmax-sigmay) Cos[2 phi]/2 + tau Sin[2 phi].

I want to determine the angle (preferably in the form Tan[2 phi]) at which the the stress is maximum, i.e. the principle direction of stress. Using this value I can then determine the principle stresses.

Problem: I do the following:

sol=Solve[D[stress,phi]==0,phi] hoping it will give me the following:{phi -> (1/2) ArcTan[2 tau / (sigmax-sigmay)]} but to no avail. It gives a screen full of ConditionalExpressions instead which I don't know how to begin to use.

Question: How to 'solve' for phi in the above conditions (i.e. when the differential of stress is 0)?

Thank you inadvance.

POSTED BY: T Fitz
2 Replies
Posted 12 years ago
POSTED BY: Bill Simpson
Posted 12 years ago

Bill Simpson, your guess was correct.

I modified it slightly to the following:

sol = Simplify[Solve[D[stress, phi] == 0, phi] /. C[1] -> 0,
    Element[tau,Reals] && Element[sigmax,Reals] && Element[sigmay,Reals]]

To account for the more general case of there being negative stresses and shears (e.g. tension and whatnot)

Thank you

POSTED BY: T Fitz
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard