Are you asking what's the longest length of a steel rod that can hang without breaking under its own weight? This doesn't involve strain at all - you just need to find the ultimate yield stress of the material, and set that equal to F/A, where F (force) is due to the weight of the material being hung. For a steel rod the weight is length x cross-sectional area x density x g. If we let L = length and r = density you get:

stress = F/A = LArg/A = Lrg

The yield stress of steel is about 400 MPa, and the density is about 7.8 g/cm^3. You can get similar data for other materials here:

http://www.askmehelpdesk.com/islam/q...ik-573046.html . So:

stress = Lrg

400 x 10^6 N/m^2 = L (7.8 g/cm^3 x 1 Kg/1000g x 10^6 cm^3/m^3) x 9.8 m/s^2 = L x 76.4 x 10^3 N/m^3

Rearrange to solve for L:

L = 400 x 10^6/76.4 x 10^3 = 5.2 x 10^3 m.

Hence a rod that is greater than 5.2 Km in length would break under its own weight. Of course this assumes that the acceleration due to gravity 'g' is constant, which for a rod only 5 Km in length is a reasonable assumption. But if you had a really tall space elevator you would have to take into account the fact that 'g' gets smaller as you increase your disnace from the ground.