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

Click For Summary

Discussion Overview

The discussion revolves around the material properties of a twisted shaft and the results from a tensile test. Participants are attempting to determine values for shear modulus (G), modulus of elasticity (E), Poisson's ratio (v), and bulk modulus (K) based on given parameters from the problem statement. The conversation includes elements of mathematical reasoning and homework-related inquiries.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a problem involving a shaft that twists under torque and a tensile test, seeking help to calculate G, E, v, and K.
  • Another participant suggests using the relation for torsion to find G, mentioning the polar moment of inertia.
  • There is a discussion about the correct interpretation of the bending moment, with some confusion regarding its value.
  • Participants express uncertainty about the units of their calculated values and the next steps in their calculations.
  • One participant notes a potential error in their calculation of E and Poisson's ratio, indicating a value that seems incorrect.
  • Another participant asks whether the torque was converted to the correct units for calculations.
  • Several participants confirm the calculations of G and discuss how to derive E and v from known values.
  • One participant expresses difficulty in transposing the formula to find Poisson's ratio.
  • Ultimately, one participant reports having solved the problem after receiving assistance.

Areas of Agreement / Disagreement

Participants generally agree on the approach to calculate G and E, but there are multiple competing views regarding the interpretation of the bending moment and the correct values for Poisson's ratio and other parameters. The discussion remains unresolved on certain calculations and interpretations.

Contextual Notes

Participants express uncertainty about the definitions and relationships between the material properties, particularly regarding the calculations of Poisson's ratio and the interpretation of strain values. There are also unresolved mathematical steps in deriving the necessary values.

Malawaki
Messages
13
Reaction score
0

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
 
Physics news on Phys.org
Malawaki said:
Any help/ guidance would be greatly appreciated

Any attempts/elaborations/efforts from your side first would be appreciated even more. :wink:
 
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
 
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}.
 
i take it that i re-arrange the formula to get G am I correct

Regards
 
Malawaki said:
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.
 
Am i correct in saying that M is the bending moment and in this case it is = to 500 Newtons
 
Malawaki said:
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.
 
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
 
  • #10
Malawaki said:
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
 
  • #11
what is 4.22 x 10 -7 measured in and what forumula do i use next

Regards
 
  • #12
Malawaki said:
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?
 
  • #13
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
 
  • #14
Malawaki said:
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.
 
  • #15
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
 
  • #16
Did you turn the torque from [kNm] to [Nm]?
 
  • #17
I have solved that problem now calculating poissons ratio having difficulty transposing the formula to find v
 
  • #18
Thanks for all the help i solved it in the end

Many thanks
 

Similar threads

Angle of Twist and Peak Torsional Shearing Stress
  • · Replies 6 ·
Replies
6
Views
4K
Tensile Tests Load-Extension into Stress-Strain
  • · Replies 2 ·
Replies
2
Views
30K
Mechanics of material shaft coupling
  • · Replies 3 ·
Replies
3
Views
3K
Tensile Test Specimen Point of Failure
  • · Replies 5 ·
Replies
5
Views
8K
Stress/Strain What is the property in a material
  • · Replies 3 ·
Replies
3
Views
2K