A reinforced concrete column consists of concrete filled with iron bars. Assume that iron occupies one-twentieth of the total cross-section area and Young's modulus of concrete is one-tenth of that of iron. The concrete column is under a compressive load `P`. Determine the fraction of load on the concrete.

Explanation

The concrete and iron sections are subjected to the same strain. If `sigma_(c)` and `sigma_(i)` denote compressive stress , `A_(c)` and `A_(i)` cross-section areas and `Y_(c)` and `Y_(i)` Young's moldulus respectively,
`(sigma_(c))/(Y_(c)) = (sigma_(i))/(Y_(i))`
Let `x` fraction of load `P` be shared by concrete then we have
`(xF)/(A_(c) Y_(c)) = (F-xF)/(Y_(i) A_(i))`
or `x = (A_(c) Y_(c))/(A_(i) Y_(i) + A_(c) Y_(c))`
On substituting `Y_(c) = (1)/(10) Y_(i), A_(i) = (1)/(20) A_(c)`, we get
`x = (A_(c) Y_(c))/((1)/(20) A_(c) xx 10Y_(c) + A_(c) Y_(c)) = (2)/(3)`