Question

A load of 400kN is Applied on a concrete column 250mm x 250mm.
The column is reinforced with six numbers of sixteen dia bars. If the modular ratio is 18, find stress in steel and concrete.
If the stress in concrete does not exceed 4N/m^2, find the area of steel required to resist 600kN.

Answer 1

This is an engineering question. In the future please post in the engineering section. Solicit help from other sections if you wish, but by referring to the original post.

Modular ratio is the ratio between the modulus of elasticity between the two materials, evidently steel is the higher one.

IF the steel bars are bonded perfectly to the concrete, then both materials will experience the same strain due to some axial load. This in turn means that steel bars will be stressed 18 times that of the adjacent concrete.

It is not specified, but will be assumed that the load is applied in compression, and without eccentricity.

Also 4 N/m^2 appears too low for concrete. Even 4 N/mm^2 (i.e. MPa) is less than 25% of usual allowable stress.

Let
area of concrete = Ac
Area of steel = As
Then equivalent area of concrete = AC+18As
Allowable concrete stress, \(\sigma_{all}\)
Axial load = P
So we have the inequality
\(P/ (Ac+18As)=\sigma_{all}\)
and solve for As.

Be sure to use consistent units. N, mm, and MPa would be a set of consistent units, so is kN, kPa and m.

Since there is an ambiguity with units of \(\sigma_{all}\), I will not venture a numerical solution.

Answer 2

BTW, congrats for having produced numerous tutorials. Please keep up the good work!

Answer 3

To be precise, Ac should be the gross dimension less the area occupied by steel bars.

Answer 4

@mathmate
thank you so much dear.
Help is really appreciated.
I was busy these days, though I did the solution.

Thanks again!

Answer 5

I didn't engineering section existed.
Okay, I will give it there.
but be sure to help me if I need any.

Answer 6

No problem. Tag me any time if you wish!