- To find steel member takes more load than Concrete in R.C.C.
- Equivalent or Transformed Concrete Area
- Insights on Composite Member Subjected to Bending

If you need proper lead on this article, you can visit the article: What is Working Stress Method? Assumptions, Features, Merits & Demerits.

## Reinforced Concrete Members Subjected to Direct Loading

This analysis is performed to study how much load is taken by steel and concrete in a R.C structure when subjected to external loading. The analysis also gives a relation to determine, the equivalent concrete area to be used if steel is minimized.

Consider a reinforced concrete section (R.C.C) as shown in the figure-1 below. For convenient analysis and better understanding, the steel and concrete has been illustrated separately. The given measurements are: 1. Area of Steel Asc

2. Area of Concrete Ac

3. The load Applied on the Whole Unit W

4. The load taken by Steel Ws

5. The load taken by Concrete Wc

Fig.1. Steel and Concrete ( RC Structure) Illustrated separately under the Action of Load W |

Then,

Strain in Steel = Strain in Concrete

Eq.1 |

In the above relation, e

_{st}and e_{c }are the strain in steel and concrete. Stress in steel and concrete is given by Ïƒ_{st }and Ïƒ_{c}respectively. Then we have relationship between stress and strain as: Strain (e) = Stress/Modulus of Elasticity (E). Where, Stress is again given by load (W) divided by Area of cross-section (A). Est and Ec are the modulus of elasticity of Steel and concrete.Also Read: What is Stress and Strain?

We know that,

**Modular Ratio (m) = Es/Ec**

From the Equation-1, it can be given that,

Relation-2 |

_{}

_{}

_{}

From the above relation, we can conclude:

**Es/Em = m= modular ration between steel and Concrete**

## How to Prove Steel Member is Subjected to Greater load than Concrete?

From the Equation 1, it is clear that Wst + Wc = W, Where 'W' is the total Load. Hence the following relation can be obtained:

Eq.4

Also, Est = mEc, by substituting in Eq.4, we get:

Suppose the areas Ast = Ac; Then we get the relation,

For a modular ration value m=18, the areas Ast = Ac; When substituting in eq.6, we get:

**Wc = W/19;**

This proves that the steel member us subjected to a greater load than the concrete.

## What is Equivalent or Transformed Concrete Area of Steel reinforcement?

We know that:

Total Load = Load in Steel + Load in Concrete\

W = Wst + Wc

W = Ïƒ

_{st}Ast + Ïƒ_{c}Ac Eq.7But we know that:

Ïƒ

_{st}= (Es/Ec)Ïƒ_{c}= mÏƒ_{c}Substituting the above relation in Eq.7, we get

W= mÏƒ

_{c}Ast + Ïƒ_{c}Ac;Hence,

Here,

**Equivalent Concrete Area = Ae = Actual Concrete Area + m x steel area = mAst + Ac ( Denominator of the Above Equation)**

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