#### IS 456 Provisions for Design of Footings :The **IS 456** is the code of practice for plain and reinforced concrete in India, which provides guidelines and standards for the design of various structural elements, including **footings** and **pedestals**.

The stability and safety of a structure depend upon the proper performance of its foundation, which is why footings and pedestals play a crucial role in transferring loads from the superstructure to the ground safely and efficiently.

In this article, we will explore the important provisions and guidelines outlined in IS 456 regarding the design of footings and pedestals. This includes load considerations, structural design, soil pressure, and reinforcement detailing.

## Types of Footings

Footings are primarily used to transfer the load from columns or walls to the soil below. IS 456 categorizes footings into two main types:

**One-way footings**: These are typically used for walls where the load distribution is primarily in one direction.**Two-way footings**: Used under columns where the load is distributed in both directions.

The general aim of footing design is to ensure that the bearing pressure on the soil does not exceed its **safe bearing capacity (SBC)**. Additionally, the footing must be designed to handle the applied loads without experiencing excessive settlement or failure due to bending, shear, or punching shear.

## Load Combinations for Footing Design

The **IS 456** standard outlines the load combinations to be used for the design of footings. These combinations account for different types of loads that may act on the footing, such as dead load, live load, and wind or earthquake loads. The design must consider both serviceability and limit state conditions.

### 1. **Service Loads**

The service loads represent the loads that the structure will normally experience. The foundation’s size is based on service loads, and the three primary load combinations to be considered are:

**Dead Load (DL) + Live Load (LL)**:

1.0 DL + 1.0 LL**Dead Load (DL) + Wind Load (WL) or Earthquake Load (EL)**:

1.0 DL + 1.0 WL**Dead Load (DL) + Live Load (LL) + Wind Load (WL) or Earthquake Load (EL)**:

1.0 DL + 0.8 LL + 0.8 WL/EL

### 2. **Limit State Design**

For reinforced concrete (RC) structures, the design must be based on **factored loads**. IS 456 provides the following load combinations for the limit state design:

**1.5 (DL + LL)****1.2 (DL + LL + WL)****1.5 (DL + WL)****0.9 DL + 1.5 WL**

These combinations ensure that the footing can safely handle a wide range of load conditions, including extreme situations like earthquakes or strong winds.

## Structural Design of Footings

The design of footings generally involves determining the required area, thickness, and reinforcement based on load considerations and soil properties. The foundation must be proportioned so that the pressure on the soil is uniform and does not exceed the safe bearing capacity.

### 1. **Area of Footing**

The required area of the footing is calculated using the formula:

Area of footing= Service load on column(wall)/Safe bearing capacity of soil The area is based on service loads, and the structural design of the footing is done using factored loads.

### 2. **Thickness of Footing**

The thickness of the footing must be sufficient to resist shear forces and bending moments. The footing should also provide enough structural rigidity to ensure uniform settlement.

### 3. **Reinforcement Design**

The steel reinforcement provided must meet the minimum requirements outlined in IS 456. The minimum percentage of steel for footings is specified as:

**0.15%**for Fe 250 steel**0.12%**for Fe 415 steel The reinforcement should be sufficient to handle the applied bending moments and shear forces.

## Soil Pressure on Foundations

In the design of foundations, the pressure distribution on the soil is an important factor. For most designs, the soil is assumed to behave elastically, and the foundation is considered rigid. For uniform pressure distribution, the center of gravity (CG) of the load system must coincide with the CG of the loaded area.

If the load is eccentric or moments are present, the pressure distribution will be non-uniform, and special consideration must be given to ensure that the maximum soil pressure does not exceed the safe bearing capacity.

### Cases of Pressure Distribution

**Vertical Load with Moment**: When both vertical load and moment act on the column, the pressure distribution varies from a maximum value at one side to a minimum value at the other. This can be expressed as

where P is the vertical load,

M is the moment,

B is the breadth of the footing

L is the length of the footing.

**Eccentric Load**: If the vertical load acts with an eccentricity e, the resulting moment M is

## Conventional Analysis of Footings

IS 456 recommends analyzing footings for both vertical loads and moments. The design should ensure that the footing remains stable and that the pressures on the soil are within permissible limits. The ratio of maximum to minimum pressure should ideally not exceed 2, especially in clay soils where differential settlements can cause significant problems.

## Design of Independent Footings

### 1. **Types of Footings**

IS 456 specifies three types of reinforced concrete individual footings:

**Rectangular footings****Sloped footings****Stepped footings**These footings may rest on soil, rock, or piles. The minimum thickness of footings on soil or rock should be at least 150 mm, and for footings on piles, the minimum thickness should be 300 mm.

### 2. **Bearing Strength and Reinforcement**

The load transferred by the column to the footing is through **bearing pressure**. According to IS 456, the permissible bearing stress under direct compression is limited to **0.45 ( f_{ck} )**, where ( f_{ck} ) is the characteristic compressive strength of concrete. If this limit is exceeded, additional reinforcement is required to transfer the load effectively.

### 3. **Design Sections**

IS 456 specifies the sections to be considered for the design of footings:

**Section for bending moment**: At the face of the column**Section for one-way shear**: At a distance equal to the effective depth of the footing from the face of the column**Section for punching shear**: Around the column at a distance of ( d/2 )

## Shear Design in Footings

### 1. **One-Way Shear**

One-way shear (also known as wide-beam shear) is checked along a vertical plane extending across the width of the footing. The shear stress is calculated as:

where (V) is the shear force,

(b) is the width of the footing,

and (d) is the effective depth.

The depth of the footing must be sufficient to resist one-way shear without the need for shear reinforcement.

### 2. **Punching Shear**

Punching shear is the tendency of the column to “punch” through the footing. The shear stress is calculated along a perimeter around the column, and the footing is checked to ensure that the shear strength exceeds the applied punching shear.

## Bending Moment Design

The bending moment in footings is due to the reaction forces from the applied loads. IS 456 recommends that the bending moment be calculated at specific sections, such as the face of the column for reinforced concrete columns. The steel reinforcement required to resist the bending moment must be placed accordingly, ensuring that the footing is safe against flexural failure.

## Minimum Depth and Steel Detailing

IS 456 provides guidelines for the minimum depth and detailing of reinforcement in footings:

**Minimum depth**: The depth of the footing must be sufficient to ensure safety against shear and bending without the need for additional shear reinforcement.**Steel detailing**: The minimum percentage of reinforcement is 0.12% for Fe 415 steel. The maximum spacing of bars is limited to three times the effective depth or 300 mm, whichever is smaller.

For two-way rectangular footings, reinforcement is provided in both directions. In the shorter direction, more reinforcement is concentrated near the column, in a region known as the **column band**.

## Conclusion

The design of footings and pedestals as per IS 456 ensures that structures are safe, stable, and capable of withstanding applied loads without failure. Key considerations include the calculation of load combinations, soil pressure, reinforcement requirements,