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4. How to Design Spread Footings

# How to Design Spread Footings

Footings are structural members used to support columns and other vertical elements to transmit their superstructure loads to the underlying soils.

Figure 1 illustrates the design workflow process, which the SkyCiv Foundation adapts workflow process. Wherein these checks such as (1) Soil Bearing, (2) Shear, (3) Flexural, (4) Development Length, and (5) Stability Checks are important parameters required to satisfy the result without exceeding a value of 1.00 in the Demand-Capacity Ratio or DCR. Figure 1: Workflow of SkyCiv Foundation.

## How to Design Spread Footing

This section discusses the design procedure of spread footing in reference to American Concrete Institute 318-2014.

### Soil Bearing Check

The Soil Bearing Check mainly determines the geometric dimensions of an isolated footing from the superstructure (service or unfactored) loads. The actual bearing pressure mainly determines by the equation below:

$$q_{a} = \frac{ P}{A } \pm \frac{ M_{x} }{ S_{x} } \pm \frac{ M_{y} }{ S_{y} }$$
However, the equation above is only applicable if the eccentricities are within the kern ( $$\frac{L}{6}$$ ) of the foundation where bearing pressure is present in the whole area.

When the eccentricities exceeded the kern, The detailed bearing pressure pattern article explains here.

To satisfy the foundation geometric dimensions, the allowable bearing capacity of the soil should greater than governing base pressure under the footing.

$$\text{Allowable Bearing Capacity} > \text{ Actual (Governing) Bearing Pressure on the Foundation}$$

Note: No tension in Bearing Pressure in the Foundation Design.

### Shear Check

The Shear Check determines the thickness or depth of the foundation based on the shear load induced from the superstructure loads. There are two primary shear checks, as follows:

1. One-way (or Beam) Shear
2. Two-way (or Punching) Shear

#### One Way (or Beam) Shear

The critical section for one-way shear extends across the width of the footing and is located at a distance d from the face of a column. Figure 2: One-way Shear

##### Imperial (psi)

$$V_{c} = 2 \lambda \sqrt{ f^{‘}_{c} } b_{w} d$$

##### Metric (MPa)

$$V_{c} = 0.17 \lambda \sqrt{ f^{‘}_{c} } b_{w} d$$

To satisfy the One Way (or Beam) Shear, the $$V_{c}$$ should not be greater than $$V_{u}$$..

$$\phi V_{c} > V_{u} = \text{ Actual (Governing) Shear of the Foundation}$$

#### Two Way (or Punching) Shear

The critical section for two-way shear design is located in $$\frac{d}{2}$$ away from a concrete column face. Where $$V_{c}$$ equation is defined as follows: Figure 3: Two-way Shear

##### Imperial (psi)

$$V_{c} = \left( 2 + \frac{4}{\beta} \right) \lambda \sqrt{ f^{‘}_{c} } b_{o} d$$

$$V_{c} = \left( \frac{\alpha_{s} d }{ b_{o} } + 2 \right) \lambda \sqrt{ f^{‘}_{c} } b_{o} d$$

$$V_{c} = 4 \lambda \sqrt{ f^{‘}_{c} } b_{o} d$$

##### Metric (MPa)

$$V_{c} = 0.17 \left( 1 + \frac{2}{\beta} \right) \lambda \sqrt{ f^{‘}_{c} } b_{o} d$$

$$V_{c} = 0.083 \left( \frac{ \alpha_{s} d }{ b_{o} } + 2 \right) \lambda \sqrt{ f^{‘}_{c} } b_{o} d$$

$$V_{c} = 0.33 \lambda \sqrt{ f^{‘}_{c} } b_{o} d$$

The governing $$V_{c}$$ will be taken least value.

To satisfy the Two Way (or Punching) Shear, the $$V_{c}$$ should not be greater than $$V_{u}$$.

$$\phi V_{c} > V_{u} = \text{ Actual (Governing) Shear of the Foundation}$$

### Flexural Check

The Flexural Check determines the required reinforcement of the foundation based on the moment or bending load induced from the superstructure loads. The Design procedure for moment strength considers a one-way flexural member first in one principal direction. Figure 4: Critical Moment Section Line

Step 1. Calculate the Actual Moment on the foundation $$M_{u}$$.

$$M_{u} = q_{u} \left( \frac{ l_{x} – c }{ 2 } \right) l_{z} \frac{ l_{x} – c }{ 2 }$$

Step 2. Calculate the required minimum reinforcement of the foundation

Step 3. Calculated the Depth of equivalent rectangular stress block, a.

$$a = \frac{ A_{s} f_{y} }{ 0.85 f_{c}^{‘} l_{z} }$$

Step 4. Calculate the Moment Capacity of the foundation $$\phi M_{n}$$.

$$\phi M_{n} = \phi A_{s} f_{y}\left( d – \frac{a}{2} \right)$$

To satisfy the flexural requirement, the $$\phi M_{n}$$ should not be greater than $$M_{u}$$..

$$\phi M_{n} > M_{u}$$

### Development Length Check

The Development Length Check determines a reinforcement shortest embedment length required for a reinforcing bar to develop its full yield strength in concrete.

### Stability Check

There are two main types of Stability Check in the foundation, as follow:

1. Overturning
2. Sliding

#### Overturning Check

Overturning Check is a stability check against the Moment of the superstructure load. Generally, this factor of safety for the overturning moment is  1.5-3.0.

$$\text{Overturning Factor of Safety} < \frac{ \sum M_{R} }{ \sum M_{OT} }$$

Note:

• $$\sum M_{R}$$ – Resisting Moment
• $$\sum M_{OT}$$ – Overturning Moment

#### Sliding Check

Sliding Check is a stability check against Horizontal Force induced by the superstructure load. Generally, this factor of safety for the overturning moment is  1.5-3.0.

$$\text{Sliding Factor of Safety} < \text{Sliding Force}$$

1. Soil Bearing Check is mainly influenced by the spread footing dimension which is subjected to the superstructure (unfactored) loads and allowable soil pressure.
2. Shear Check is mainly influenced by the depth of the spread footing where the spread footing performs one-way and two-way checks.
3. Flexural Check is mainly influenced by the reinforcement schedule of the spread footing.
4. Development Length Check and
5. Stability Checks are mainly influenced by the spread footing dimensions.

Based on the information above, those adjustments will increase design capacity per checks of the spread footing.

Please note that some parameters such as materials strength, factor, and subjected loads are also part of increased design capacity influence.

## Design Code Modules

The SkyCiv Foundation have these currently available design codes:

• American code (click here for a detailed discussion of the design codes)
• Australian code (click here for a detailed discussion of the design codes)

## References

1. Building Code Requirements for Structural Concrete (ACI 318-14) Commentary on Building Code Requirements for Structural Concrete (ACI 318R-14). American Concrete Institute, 2014.
2. McCormac, Jack C., and Russell H. Brown. Design of Reinforced Concrete ACI 318-11 Code Edition. Wiley, 2014.
3. Taylor, Andrew, et al. The Reinforced Concrete Design Handbook: a Companion to ACI-318-14. American Concrete Institute, 2015.
4. Darwin, David and Dolan, Charles. Design of Concrete Structures 16 Edition. McGrawHill, 2021. 