# What is the stress within the column?

1. Nov 8, 2007

### mathcrzy

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

A marble column of cross-sectional area 1.7 m2 supports a mass of 30,000 kg.
(a) What is the stress within the column?
(b) What is the strain?

Elastic modulus for marble E (N/m^2) 50e9
shear modulus (G)

2. Relevant equations

a)stress=F/A=N/m^2
b) dont know

3. The attempt at a solution

a) 30000*9.8/1.7=172941 N/m^2 (this is right)
b)

2. Nov 8, 2007

### hotcommodity

The strain will be given by the change in the length of the column divided by its initial length: $$\frac{\Delta L}{L_0}$$.

Its relation to the stress is given by: $$\frac{F}{A} = Y \frac{\Delta L}{L_0}$$. That is, the stress is equal to the modulus times the strain. Now its just algebra.

3. Nov 8, 2007

### mathcrzy

how do you find the length of the column?

4. Nov 8, 2007

### hotcommodity

You don't need it. You can just treat $$\frac{\Delta L}{L_0}$$ as a single term, does that make sense?

5. Nov 8, 2007

### mathcrzy

so just solve for that term then? what would Y be? the elastic or shear modulus?

F=30000*9.8
A=1.7
Y=?

6. Nov 8, 2007

### hotcommodity

You would use the elastic modulus, we're speaking in terms of tensile stress and strain. If we were using shear stress and strain, we would use the shear modulus.

Last edited: Nov 8, 2007
7. Nov 8, 2007

### mathcrzy

so-

(30000*9.8/1.7)/50e9=3.5e-6

8. Nov 8, 2007

### hotcommodity

Looks good to me, don't forget to put your answer for part a into significant figures.