Hi!
I am having difficulty solving this problem (see the attachment).I have the following issues:
1. For the application of principle stress formulas, the normal stresses are uniform where as in this case we have a linear distribution. Is there a way we can it into a uniform load. To my opinion we'll have a concentrated load applied at 2/3 of the length.
2. What is meant by principle stress at the origin? The question demands principle stress at a point, should it be a plane?
Please suggest any reading material or a book that might help me solve this. A regular book is not quite helping me.
P.S- I am conceptually weak
Regards
Is it in equilibrium? If so then you can solve by finding the resultant force and its C.G. position. Corresponding to the C.G. positions, shift the load along the centre line of the section which will result a couple which will generate another stress components. After that you can easily find the principal stresses.
I refer you to Theory of elasticity By Timoshenko. There are also some useful online resources. it is a typical elasticity problem with boundaries as functions of coordinate. In short, You can find the solution in terms of calculating "Airy stress function", in terms of sigma(x,y). After that, you can find the stresses at each point by evaluating Airy stress function in the desired point and easily find principal stresses.
https://books.google.com/books?id=ialLYAAACAAJ&dq=theory+of+elasticity+timoshenko&hl=en&sa=X&ved=0ahUKEwj_2r6gybDLAhUJKyYKHTjaAUYQ6AEINTAC
https://en.wikiversity.org/wiki/Introduction_to_Elasticity
This looks straightforward. From the equation supplied the shear stress is Sxy=2.5. From the boundary tractions Sx=5 and Sy=0. Just need to shove these values into the equation for the principal stresses...
You are dealing with the plane stress problem. Its solution is straightforward (see comments by Angus Ramsay).
Consider an infinitely small rectangle at the origin. If you rotate the rectangle, the normal stresses at its edges will vary continuously passing through maximum and minimum. These are the principal stresses.
Please find my comments in the attachment.
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