Question

strengths

Answer 1

give me a few. Having technology issues.

Answer 2

I don't necessarily have a solution. The values I get for T are wrong.

Answer 3

That was what I was about to ask (whether your answer was accepted).

Your assumption that phi_A=phi_B seems reasonable to me, except that that would result from no bonding between the two materials.

I was wondering is there must be some common shear stress at the bonding surface. This way, each material would have a different torque. I will give it some thoughts along those lines. You could do the same if you are convinced of the approach.

Give me a few minutes before I get back to you.

Answer 4

Sure, I will review my work again.

Answer 5

I think it's a unit error for me.

Answer 6

when dealing with mm we have to be in KN and MPa?

Answer 7

You can use N, mm, N/mm = MPa.
kN is not consistent with MPa.

Answer 8

That's with equal twist angles, right? Let me see what I get. I just got started!

Answer 9

yes

Answer 10

Yes, I get the same,
T1=605415; T2=294585; in N-mm
Are those numbers that were rejected? If so, we need to review the concept.

Answer 11

yeah it rejects the values.

Answer 12

Wait, they are asking for shear stresses, not torques. So we have one more step to do.
The tau looked like a T in the answer box! lol

Answer 13

it's in mega pascals though.

Answer 14

oh lol

Answer 15

wow... I am dyslexic.

Answer 16

Yeah, but I got T1 and T2 (that addes up to 900).
We need shear stresses!

Answer 17

so I got T_stress = 84.33 MPa

Answer 18

(605,415)*(45mm)/(pi/32*(45^4-30^4) = 84.33

Answer 19

I got tau_1=42.17 and tau_2=55.57 in MPa using tau=Tr/J where r is max. r.
I think you used diameter instead of radius. :(

Answer 20

WOrking on the next part.

Answer 21

so I took angle of twist formula for Tb - angle of twist formula for Ta. That doesn't give me the correct answer. Tb is rotating positive and Ta is rotating negative.

Answer 22

wait a min.

Answer 23

I get phi=0.023098

Answer 24

are we using the steel core or bronze?

Answer 25

using T1*L/(G1J1).

Answer 26

They should be the same, ... our assumption.

Answer 27

Did both, they are the same.

Answer 28

I was assuming the angle twist for the steel and bronze were the same.

Answer 29

But I got the same answer as you now. Hmmmm

Answer 30

I would agree with you that angle of twist is different because steel is harder than bronze.

Answer 31

Does that sound bad? lol

Answer 32

I would imagine the bronze would twist more since it's not as strong as steel.

Answer 33

Yes, the 900 was applied on the outside, but the bonding transmits the torque T2 to the iron core. Because of the bonding/shear stress between them, they have the same twist angle.

Answer 34

How much time you have left?

Answer 35

I have to leave in about 45 minutes, give or take a few minutes.

Answer 36

Okay well lets look at the morhse circle problem. Let me make a new thread really quick.

Answer 37

To finish off this one, I think also that the bronze on the outside is more bulky, so it actually took more torque than the core. J1 is about four times greater than J2.

Answer 38

ok

Answer 39

The Ta = 605,415N-mm is for both bronze and steel center? It's both of those metals combined? It's not the torque on the bronze alone?

Answer 40

It is just for the outer sheath. The balance, 394.6 is for the core.
So they end up having equal angles of twist.

Answer 41

Were the first two answers correct?

Answer 42

*294.6

Answer 43

Those answers were correct. It's just for the outer sheath?

Answer 44

So the concept is good. Then the identical twist angles should be good as well.

Answer 45

T1 is for outer, T2 is for core, only.

Answer 46

T1 is greater because it's just the size of the bronze? Doesn't have anything to do with properties?

Answer 47

Actually, and conceptually, since the 900 was applied on the outer, of which T2 was transmitted (in opposite direction) to the core.
Yes, properties as well. That's why J1=4J2, but T1 < 4T2, because bronze is less strong.

Answer 48

Okay, I think I get it now. I am confusing myself. It makes sense to me now why T1 > T2

Answer 49

Good! It's good engineering practice to check if things make sense! congrats!

Answer 50

okay hold on here. So the bronze core is going to torque less or more?

Answer 51

More, right? So that is why T1 is so large ?

Answer 52

I believe you mean steel core! The J is 1/4 of the bronze sleeve, but it attracts >1/4 of the torque because of the G.

Answer 53

It's like a statically indeterminate problem. Stiffness attracts forces.
J1=4 J2, so one would expect T1=4 T2 (if the materials are the same). Agree?

Answer 54

If that is the steel core that makes more sense. I thought you were saying T1 is bronze not steel.

Answer 55

I would imagine it be more difficult to twist steel than bronze.

Answer 56

Yes, T1 is outside (bronze), larger J, but smaller G.

Answer 57

Okay sounds good. Making other thread.

Answer 58

Geometry makes a difference too! :)

Answer 59

ok!