Bulk and Shear Modulus Calculations

Click For Summary

Discussion Overview

The discussion revolves around the calculations of bulk and shear modulus for a material given its Young's modulus and Poisson's ratio. Participants are working through the equations and attempting to verify their calculations, focusing on both theoretical understanding and practical application in a homework context.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a calculation for the bulk modulus using the formula K = E / 3(1-2ν) and arrives at a value of 231.48.
  • Another participant questions the clarity of the shear modulus calculation and suggests there is a formula similar to that of the bulk modulus.
  • A participant provides a formula for the shear modulus as G = E / (2(1-ν)) and calculates it to be 183.82.
  • There is a discussion about the units for bulk and shear modulus, with some participants asserting that the units are Pascals or GPa.
  • Another participant proposes an alternative formula for shear modulus as G = E / (2(1 + ν)) and calculates it to be 94.7 GPa, suggesting the previous calculation was incorrect.

Areas of Agreement / Disagreement

Participants express differing views on the correct formula for shear modulus and the resulting calculations. There is no consensus on the correct value or formula, leading to an unresolved discussion.

Contextual Notes

Participants have not fully clarified the assumptions behind their calculations or the implications of using different formulas for shear modulus. The discussion reflects uncertainty regarding the correct approach and the significance of units in the calculations.

oxon88
Messages
176
Reaction score
1

Homework Statement


A material which has a Young’s modulus of elasticity of 250 GN m–2 and
a poisons ratio of 0.32, calculate:

(a) the bulk modulus of the material

(b) the shear modulus of the material.

Homework Equations


E=3(1−2ν)K

3. The Attempt at a Solution


a)

E = 3(1−2ν)K

K = E / 3(1-2*0.32)

K = 250/(3(1-2*0.32)

250 / K = 1.08

bulk modulus, K = 231.48

Are my working for A correct? I'm stuck with working out the shear modulus, please can anyone help?
 
Physics news on Phys.org
oxon88 said:

Homework Statement


A material which has a Young’s modulus of elasticity of 250 GN m–2 and
a poisons ratio of 0.32, calculate:

(a) the bulk modulus of the material

(b) the shear modulus of the material.

Homework Equations


E=3(1−2ν)K

3. The Attempt at a Solution


a)

E = 3(1−2ν)K

K = E / 3(1-2*0.32)

K = 250/(3(1-2*0.32)

250 / K = 1.08

bulk modulus, K = 231.48

Are my working for A correct? I'm stuck with working out the shear modulus, please can anyone help?

You are missing the units for the bulk modulus.

It's not clear why you can't calculate the shear modulus. There's a nifty formula for that, similar to the one for calculating the bulk modulus.
 
What's your equation for the shear modulus in terms of Young's modulus and poisson's ratio?
 
G = E / (2(1-V))

G = 250 / (2(1-0.32)

G = 250/1.36

Shear Modulus, G = 183.82
 
Still going without units, I see.
 
I guess the units would be Pascals, Pa?
 
can anyone help me with this?
 
oxon88 said:
can anyone help me with this?
You're still trying to figure out the units?

Chet
 
I believe the unit for bulk modulus will be pascals.

I'm still trying to get the shear modulus.
 
  • #10
oxon88 said:
I believe the unit for bulk modulus will be pascals.

I'm still trying to get the shear modulus.
Did you not read you own post #4?

The units in all these cases is GPa.
 
  • #11
I think the answer in post 4 is incorrect, the formula is not correct. I think it should be

G = E / (2(1 + ѵ))

G = 250/(2(1+0.32))

G = 250/2.64

G = 94.7

Shear Modulus, G = 94.7 GPa
 
  • Like
Likes   Reactions: Chestermiller

Similar threads

Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
3K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 4 ·
Replies
4
Views
1K
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 5 ·
Replies
5
Views
10K
  • · Replies 8 ·
Replies
8
Views
3K