# Limit State Of Serviceability-Design of Reinforced Concrete

## Limit State Of Serviceability

In Limit state of serviceability, the deflection limits as per IS 456-2000.The following criteria are adopted for attaining proper performance of beams and slabs

The final defection due to all loads including the effects of temperature.creep and shrinkage should not exceed span/250.This limitation is to control the cracks

The deflection occurring after the construction of finishes and partitions should not exceed span/350  or 20mm whichever is less.This limit is intended to avoid damage of partitions and finishes

## Deflection in Reinforced Concrete members may be divided into two types

### 1.Short term deflection in limit state of serviceability

Short term or instantaneous deflection caused by the service loads may be calculated by using the elastic theory using short-term modulus of elasticity and effective moment of inertia

For example

A simply supported beam supporting a point load at its centre has a maximum deflection of

Deflection= PL³/48EI

In this equation replace E by Ec and I by Ieff to get short-term deflection

This is the method for calculating the deflection.

### 2.Long-Term deflection in limit state of serviceability

It mainly consists of defection due to creep and deflection due to shrinkage.

Deflection due to shrinkage depends on

•   Support conditions
•   Shrinkage strain
•   Overall depth of section
•   Percentage of compression
•   Percentage of tension
1. Approximate value of shrinkage strain of concrete is 0.0003
2. Deflection due to creep depends only upon the permanent loads.
3. Deflection due to creep can be calculated by the following equation

Creep defection due to permanent loads

=Initial creep deflection due to permanent loads obtained using an elastic analysis with an effective modulus of elasticity Short term deflection due to permanent load using Ec