
#1
Jan713, 07:54 AM

P: 17

Hello, I am struggling with this problem. It is probably the easiest problem ever...
What I did: The plane has 2 stress components. σ_{n} and σ_{s}. σ_{n} is a multiple of (l, m, k) vector. For σ_{s}, I made up a vector (a, b, c) which is orthogonal to (l, m, k). And I equated all vectors. I'm probably doing something wrong. Any help is appreciated! 



#2
Jan713, 08:57 AM

P: 17

1. The problem statement, all variables and given/known data
2. Relevant equations General plane formulas. 3. The attempt at a solution I thought that the plane has 2 stress components. σ_{n} and σ_{s}. σ_{n} is a multiple of (l, m, k) vector. For σ_{s}, I made up a vector (a, b, c) which is orthogonal to (l, m, k). And I equated all vectors. I'm probably doing something wrong. Any help is appreciated! 



#3
Jan713, 10:31 AM

P: 10

Hello, I am not an expert on elasticity but this really looks quite straightforward. Let's first find the stress vector T (I'm using T instead of σ to avoid confusion with the stress tensor). You will get it by multiplying the (diagonal) stress tensor by your normal vector as T=(σ_{1}l, σ_{2}m, σ_{3}n). It has two components as you wrote, T_{n} and T_{s}. The magnitude of T_{n} is simply the dot product of T and n and its direction is along n as you wrote. Vector T_{s} has to be the complement to the total stress vector.
And for the second part  the shear stress will be maximum if vector T lies in your plane, e.g. the dot product of T and n is zero. 



#4
Jan713, 11:01 AM

P: 5,462

Elasticity problemWhat is a stress vector? 



#5
Jan713, 11:12 AM

P: 17

However, this was very helpful. Thanks 



#6
Jan713, 11:19 AM

P: 10

Most likely there are other methods or other terminology, I'm not a native speaker so i can't tell the subtle differences that well, sorry about that. 



#7
Jan713, 11:42 AM

P: 17




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