# What is limit state of serviceability ?

A structure should be serviceable and its important that it should serve the intended function throughout its life. When we follow the limit state of serviceability as per Indian Standards (IS 456: 2000), it is ensured that the comfort of people and aesthetic appearance of the structure is satisfactory. When a concrete structure is designed only on the basis of limit state of collapse, there is a chance that the structure will fail because of excessive crack and also the sections have comparatively smaller sections. Mainly in this we check for deflection and cracking of the structure.

## Limit State of Deflection

This further depends on :

1. Short term deflection – It is the deflection that occurs immediately after the placement of concrete. Immediately after the load is applied it may be full or partial load.
2. Long term deflection – It occurs after a longer period of time. It is mainly due to creep and shrinkage of concrete. It is always greater than the short term deflection.

### Causes for deflection

• Application of load more than estimated.
• Stress in reinforcement.
• Humidity and temperature
• Age of concrete
• Water cement ratio

## Limit State of Cracking

Crack develops when there is an increase in tensile stress on to the concrete. Cracks are basically starting point of failure. We should always maintain the safe zone by limiting the crack width to a maximum of 0.3 mm (even to 0.004 mm when the exposure condition is very severe). We should calculate the crack width as per the formula given in IS 456: 2000 (Annexure F).

$$W_{\mathrm{cr}}=\frac{3 a_{\mathrm{cr}} \varepsilon_{\mathrm{m}}}{1+\frac{2\left(a_{\mathrm{cr}}-C_{\min }\right)}{h-x}}$$

Where,

• acr is the distance from the point considered to the surface of the nearest longitudinal bar.
• Cmin is the minimum cover to the longitudinal bar.
• εm is the average strain in steel at the point considered.
• h is the overall depth of the section, and
• x is the depth of the neutral axis.