# Composite bars

1. Aug 1, 2016

1. The problem statement, all variables and given/known data
φ is the angle of twist , i dont understand why the angle of twist must be the same for 2 bars ...

2. Relevant equations

3. The attempt at a solution
They are made of different material , how could the angle of twist be the same for 2 bars ?

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2. Aug 1, 2016

### BvU

For a composite shaft, it is useful if the shaft pieces do not come apart at junctions (like point B) . That means $\phi_1 = \phi_2$ !

3. Aug 1, 2016

Why?

4. Aug 1, 2016

why the twisting angle are the same? they are different materials, when same twisting moment applied to them , both of them will have different twisting angle,right?

5. Aug 1, 2016

### BvU

What about T = T1 + T2 + T3 + .... ?

Can you check how 'twisting moment' is defined ?

6. Aug 1, 2016

ok,i noticed that the torsion(moment ) applied on both bar are not the same,but why are the twisting angle same?

7. Aug 1, 2016

### BvU

If they are not the same, then the parts of the shaft have rotated wrt one another. That's not good at all.
Are we talking about the same $\phi$ here ?
Work out (7.10) and (7.11) for your composite bar ABC. Surely, at point B you want $\phi$ from bar AB to be the same as $\phi$ from bar BC at point B ?

I think that's what he means: at point B $\phi$ from bar AB is $\phi_1$ and $\phi$ from bar BC is $\phi_2$.

8. Aug 1, 2016

so, the torsion here don't allow the parts of the shaft have rotated wrt one another?
It's not stated in the question, how do we know that?

9. Aug 1, 2016

### BvU

They mention a (one) composite shaft - not two separate shafts that happen to be in each other's neigborhood. . So they are welded (or glued or screwed, or ..) together.