What are the Material Properties of a Twisted Shaft and Tensile Test Results?

[Malawaki]

Homework Statement

A shaft of 0.3 metres long and 45mm diameter twists 2 degrees under a torque of 7kNm.
On a tensile test the same material extends 0.015mm on a length of 110mm. If the tensile force producing this extension was 500N and the diameter of the test piece was 5mm determine the values of :
G, E, v, K

Any help/ guidance would be greatly appreciated

Kindest Regards

 

[radou]

Any help/ guidance would be greatly appreciated

Any attempts/elaborations/efforts from your side first would be appreciated even more.

 

[Malawaki]

My first thoughts on the question were to figure out v then with v= lateral strain/longditudinal strain i can only figure out one of these strains i then got stuck as v is in the other formula. Apoint in the right direction would be helpful

Regards

 

[radou]

If the applied load in the first case causes torsion, then you can use the relation $$\phi = \frac{M L}{G I}$$, where I is the polar moment of inertia and I = $$\frac{d^4 \Pi}{32}$$.

 

[Malawaki]

i take it that i re-arrange the formula to get G am I correct

Regards

 

[radou]

i take it that i re-arrange the formula to get G am I correct

Regards

Yes, you can calculate G, and I hope it works out.

 

[Malawaki]

Am i correct in saying that M is the bending moment and in this case it is = to 500 Newtons

 

[radou]

Am i correct in saying that M is the bending moment and in this case it is = to 500 Newtons

No, it seems to equal 7 kNm.

 

[Malawaki]

The answer i get is very small 4.22 x10-7

Is my working out right

7 x 0.32/ (0.045to the power 4 x pi / 32) x 2

 

[radou]

The answer i get is very small 4.22 x10-7

Is my working out right

7 x 0.32/ (0.045to the power 4 x pi / 32) x 2

Looks right, except the length of the shaft is 0.3 m

 

[Malawaki]

what is 4.22 x 10 -7 measured in and what forumula do i use next

Regards

 

[radou]

what is 4.22 x 10 -7 measured in and what forumula do i use next

Regards

Well, how is the shear modulus G defined?

Next, you can calculate the module of elasticity E. Further on, there is a neat relation between G, E and v, do you know it?

 

[Malawaki]

yes i do know what it is but the formual has two unknown values in it poisson's ratio and E. I also know that i have to calculate poissons ratio next and i know this is equal to lateral strain / longditudinal strain. But i don't know how to get these values from the question

Regards

 

[radou]

yes i do know what it is but the formual has two unknown values in it poisson's ratio and E. I also know that i have to calculate poissons ratio next and i know this is equal to lateral strain / longditudinal strain. But i don't know how to get these values from the question

Regards

You already calculated G. Now you can calculate E, since you know the force which caused the given extension at the tensile test. Then you can easily calculate v from the mentioned relation.

 

[Malawaki]

I think i am doing something wrong i calculated G which i feel is right with other collegues of mine but am i right in saying E = stress / strain then i get a value of V = .765 which can not be right

 

[radou]

Did you turn the torque from [kNm] to [Nm]?

 

[Malawaki]

I have solved that problem now calculating poissons ratio having difficulty transposing the formula to find v

 

[Malawaki]

Thanks for all the help i solved it in the end

Many thanks