Why is the angle of twist the same for both bars if they're different materials?

[chetzread]

Homework Statement

φ is the angle of twist , i don't understand why the angle of twist must be the same for 2 bars ...

Homework Equations

The Attempt at a Solution

They are made of different material , how could the angle of twist be the same for 2 bars ?

 

[BvU]

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

 

[chetzread]

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

Why?

 

[chetzread]

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

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?

 

[BvU]

What about T = T₁ + T₂ + T₃ + ... ?

Can you check how 'twisting moment' is defined ?

 

[chetzread]

What about T = T₁ + T₂ + T₃ + ... ?

Can you check how 'twisting moment' is defined ?

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

 

[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 abouthttp://www.colorado.edu/engineering/CAS/courses.d/Structures.d/IAST.Lect07.d/IAST.Lect07.pdf 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 $\phi_2$.

 

[chetzread]

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 abouthttp://www.colorado.edu/engineering/CAS/courses.d/Structures.d/IAST.Lect07.d/IAST.Lect07.pdf 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 $\phi_2$.

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?

 

[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.