Bulk and Shear Modulus Calculations

[oxon88]

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?

 

[SteamKing]

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.

 

[Chestermiller]

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

 

[oxon88]

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

G = 250 / (2(1-0.32)

G = 250/1.36

Shear Modulus, G = 183.82

 

[SteamKing]

Still going without units, I see.

 

[oxon88]

I guess the units would be Pascals, Pa?

 

[oxon88]

can anyone help me with this?

 

[Chestermiller]

can anyone help me with this?

You're still trying to figure out the units?

Chet

 

[oxon88]

I believe the unit for bulk modulus will be pascals.

I'm still trying to get the shear modulus.

 

[Chestermiller]

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.

 

[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