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Elasticity problem

by physicist10
Tags: elasticity
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physicist10
#1
Jan7-13, 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. σn and σs.

σn is a multiple of (l, m, k) vector. For σs, 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!
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physicist10
#2
Jan7-13, 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. σn and σs.

σn is a multiple of (l, m, k) vector. For σs, 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!
Zirkus
#3
Jan7-13, 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=(σ1l, σ2m, σ3n). It has two components as you wrote, Tn and Ts. The magnitude of Tn is simply the dot product of T and n and its direction is along n as you wrote. Vector Ts 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.

Studiot
#4
Jan7-13, 11:01 AM
P: 5,462
Elasticity problem

zirkus
Let's first find the stress vector T
Whilst this thread properly belongs in the homework section, this needs comment.

What is a stress vector?
physicist10
#5
Jan7-13, 11:12 AM
P: 17
Quote Quote by Studiot View Post
Whilst this thread properly belongs in the homework section, this needs comment.

What is a stress vector?
Aha, he's probably talking about the traction vector.

However, this was very helpful. Thanks
Zirkus
#6
Jan7-13, 11:19 AM
P: 10
What is a stress vector?
We defined it similarly like the article on wiki does, so I won't rewrite it...Stress on Wikipedia
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.
physicist10
#7
Jan7-13, 11:42 AM
P: 17
Quote Quote by Zirkus View Post
We defined it similarly like the article on wiki does, so I won't rewrite it...Stress on Wikipedia
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.
Thanks Zirkus!


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