# Homework Help: Bulk and shear modulus

1. Dec 4, 2014

### oxon88

1. The problem statement, all variables and given/known data
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.

2. Relevant 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?

2. Dec 4, 2014

### SteamKing

Staff Emeritus
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.

3. Dec 4, 2014

### Staff: Mentor

What's your equation for the shear modulus in terms of Young's modulus and poisson's ratio?

4. Dec 4, 2014

### oxon88

G = E / (2(1-V))

G = 250 / (2(1-0.32)

G = 250/1.36

Shear Modulus, G = 183.82

5. Dec 4, 2014

### SteamKing

Staff Emeritus
Still going without units, I see.

6. Dec 4, 2014

### oxon88

I guess the units would be Pascals, Pa?

7. Apr 9, 2015

### oxon88

can anyone help me with this?

8. Apr 9, 2015

### Staff: Mentor

You're still trying to figure out the units?

Chet

9. Apr 9, 2015

### oxon88

I believe the unit for bulk modulus will be pascals.

I'm still trying to get the shear modulus.

10. Apr 9, 2015

### Staff: Mentor

Did you not read you own post #4?

The units in all these cases is GPa.

11. Apr 9, 2015

### oxon88

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

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