Solid Mechanics Stiffness Question

[adlinkie1]

Homework Statement

A 0.5m high and 100mm diameter post is to be made from concrete reinforced by 10mm diameter steel rods. How many steel rods should be used if the axial stiffness of the post is to be at least 2000kN/mm?

Homework Equations

n = number of steel rods
D = diamater of the post
d = Diameter of the steel rods

A Concrete= $$\stackrel{piD 2}{4}$$ - n $$\stackrel{pid 2}{4}$$
A Steel = n $$\stackrel{pid 2}{4}$$k (Stiffness) = F/(EA)

The Attempt at a Solution

Strain compatibility is assumed
$$\frac{E SteelA Steel}{L}$$ = $$\frac{E ConcreteA Concreete}{L}$$

Substitute in Areas, and cancel where possible, I am left with n = $$\frac{4D²}{5d²}$$ which = 80, which is not right but i am struggling to see what I have done wrong.

 

[pongo38]

In your equ k=F/EA, what are the units of k on the LHS and what are the units of F/EA on the RHS? Isn't there something missing?