**A walkthrough of the calculations to design an isolated footing (AS 3600 2018)**

The foundation is an essential building system that transfers column and wall forces to the supporting soil. The engineer might opt for a shallow or deep foundation system based on the soil characteristics and building loads.

**SkyCiv FoundationDesign Module** includes analyzing and designing isolated footing conforming to the Australian Standards (AS 3600 2009 & 2018).

**Want to try SkyCiv’s Foundation Design software? **Our tool allows users to perform load-carrying calculations without any download or installation!

## Design of an Isolated Footing

**Dimension Requirements**

To determine the dimensions of an isolated footing, service or unfactored loads, such as permanent action (**G**), imposed action** **(

**Q**), wind action

**(**

**), earthquake action**

**W**_{u}**(**

**)**

**E**_{u}**and**

**,****will be applied using Load Combinations, as defined by AS 3600. Whichever Load Combination governs will be considered the design load, and is compared to the allowable soil pressure as shown in Equation 1.**

**S**_{u}\(\text{q}_{\text{a}} = \frac{\text{P}_{\text{n}}}{\text{A}} \rightarrow \) Equation 1

q_{a} = allowable soil pressure

P_{n} = service level design loads

A = foundation area

The footing dimensions can be initially estimated by solving the foundation area (A) using Equation 1.

\(\text{A} = \frac{\text{P}_{\text{n}}}{\text{q}_{\text{a}}} \rightarrow \) Equation 1a

**One-way Shear**

The** one-way shear **limit state, also known as **flexural shear**, recognizes that the footing may fail in shear similar to a wide beam along a critical shear plane located at a distance “d” from the face of the column (Figure 1), based on **AS3600 Clause 8.2.7.1**

Figure 1. Critical Shear Plane of One-way Shear

The **One-way ****Shear** **Demand **or **V _{u}** is calculated assuming the footing is cantilevered away from the column where the red area is indicated in Figure 1.

The **One-way ****Shear** **Capacity **or** ϕVu _{c}** is defined as the Ultimate shear strength and calculated using Equation 2 per

**AS3600-09 Cl 8.2.7.1**.

\( \phi \text{V}_{uc} = \phi \beta_{1} \times \beta_{2} \times \beta_{3} \times b_{v} \times d_{o} \times f_{cv} \times A_{st}^{\frac{2}{3}} \rightarrow \) Equation 2 (**AS3600 Eq. 8.2.7.1**)

ϕ = shear design factor

β_{1}= 1.1(1.6 – d_{o}/1000) ≥ 1.1 or 1.1(1.6(1-d_{o}/1000) ≥ 0.8

β_{2} = 1, for members subject to pure bending; or

=1-(N^{*}/3.5A_{g}) ≥ 0 for member subject to axial tension; or

=1-(N^{*}/14A_{g}) for members subject to axial compression

β_{3} = 1, or may be taken as –

2d_{o}/a_{v} but not greater than 2

a_{v} = distance for the section at which shear is being considered to the face of the nearest support

f_{cv} = f’c^{1/3} ≤ 4 MPa

A_{st} = cross-sectional area of longitudinal reinforcement

Shear Demand and Shear Capacity must meet the following equation to meet the design requirements of AS 3600-09:

\(\text{V}_{\text{u}} \leq \phi\text{V}_{\text{uc}} \rightarrow \) Equation 3 (per **AS3600 Cl. 8.2.5**)

SkyCiv Foundation, in compliance with Equation 3, calculates the one-way shear utility ratio (Equation 4) by taking Shear Demand over Shear Capacity.

\( \text{Utility Ratio} = \frac{\text{Shear Demand}}{\text{Shear Capacity}} \rightarrow \) Equation 4

**Two-way Shear**

The **Two-way Shear** limit state, also known as **punching shear,** extends its critical section to a distance “d/2” from the face of the column and around the perimeter of the column (Figure 2) based on **AS3600 Clause 9.2.3(a)**.

Figure 2. Critical Shear Plane of Two-way shear

The **Two-way S****hear Demand **or **V _{u}** occurs at the Critical Shear Plane, located at a distance of “d/2” where the (red) hatched area, as indicated in Figure 2.

The **Two-way ****Shear Capacity **or** ϕV _{uo}** is defined as the Ultimate shear strength and calculated using Equation 5 based on

**AS3600 Clause 9.2.3**

\( \phi V_{uo} = \phi \times u \times f_{cv} \times d \rightarrow \) Equation 5 (**AS3600 Cl. 9.2.3(a)**)

f_{cv} = 0.17(1 + 2/β_{h}) √f’_{c} ≤ 0.34√f’_{c}

β_{h} = ratio of the length of the column at the Z-axis over the X-axis

d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement (mm)

u = length of the critical shear perimeter (mm)

Shear Demand and Shear Capacity must meet the following equation to meet the design requirements of AS 3600:

\(\text{V}_{\text{u}} \leq \phi\text{V}_{\text{uo}} \rightarrow \) Equation 6 (per **AS3600 Cl. 8.2.5**)

SkyCiv Foundation, in compliance with Equation 6, calculates the two-way shear utility ratio (Equation 7) by taking Shear Demand over Shear Capacity.

\( \text{Utility Ratio} = \frac{\text{Shear Demand}}{\text{Shear Capacity}} \rightarrow \) Equation 7

**Flexure**

In an isolated footing, the upward soil pressure causes two-way bending with tensile stresses at the bottom surface. Bending moments are calculated in each direction at section *0.7a _{sup}* distance from the center of the column, where

*a*is half the width of the column.

_{sup}

Figure 3. Critical Flexure Section

The **Flexural** limit state occurs at the Critical Flexure Section, located *0.7a _{sup}* from the center of the footing (Refer to Figure 3).

The **Flexural Demand **or **M _{u}** is located at the Critical Flexure Section indicated in Figure 3, and is calculated using Equation 8.

\( \text{M}^{*}= q_{u} \times D_{f} \times \left( \frac{ \frac{b_{f} – b_{c}}{2} }{2} \right)^{2} \rightarrow \) Equation 8

The **Flexural Capacity **or** ϕMn** is calculated using Equation 9.

\(M_{n} = A_{st} \times f_{sy} \times d \times \left(1- \frac{0.5}{\alpha_{s}} \times \frac{A_{st} \times f_{sy}}{b \times d \times f’_{c}} \right) \rightarrow \) Equation 9

ϕ = flexural design factor

b = footing dimension parallel x-axis, (mm)

d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, (mm)

A_{st} = reinforcement area, (mm^{2})

a = depth of equivalent rectangular stress block, (mm)

fsy = reinforcement strength, (MPa)

Moment Demand and Moment Capacity must meet the following equation to meet the design requirements of AS 3600:

\(\text{M}_{\text{u}} \leq \phi\text{M}_{\text{n}} \rightarrow \) Equation 10 (per **AS3600 Cl. 8.2.5**)

SkyCiv Foundation, in compliance with Equation 10, calculates the flexural utility ratio (Equation 11) by taking Flexural Demand over Flexural Capacity.

\( \text{Utility Ratio} = \frac{\text{Flexure Demand}}{\text{Flexure Capacity}} \rightarrow \) Equation 11

**Reinforcement**

The amount of reinforcement required is determined by flexural strength requirements, with minimum reinforcement specified in Cl. 21.3.1 (b)

\( \rho_{ \text{min} } = 0.19 \times \frac{D}{d}^{2} \times \frac{f’_{ct.f} }{ f_{sy} } \rightarrow \) Equation 12

The area of steel can be determined with the following equation:

\( \rho = \frac{ 2.7 \times M^{*} }{ d^{2} } \text{ or } \text{A}_{\text{st}} = \frac{ \text{M}^{*} }{ 370 \times \text{d} } \rightarrow \) Equation 13

As advised by AS 3600, a minimum concrete cover of *60 mm* for footing is recommended.

## Additional Verifications

Other verifications not mentioned by the code, including soil pressure checks, uplift, and other stability checks are also verified.

### Soil Pressure

The determination of base pressure or the interaction between the soil and footing primarily relies on the footing dimensions and the resulting eccentricity of the applied loads. Depending on the positioning of this resulting eccentricity, the base pressure can induce full or partial compression on the footing. This assessment enables us to confirm whether the underlying soil can sustain the entirety of the loads transmitted from the footing.

For a detailed guide for manually calculating the soil pressure, please refer to this link: Pressure Distribution Under a Rectangular Concrete Footing

The utility ratio is evaluated by comparing the maximum soil pressure (serviceability state) with the allowable gross bearing soil capacity:

\( \text{Utility Ratio} = \frac{\text{Max. Soil Pressure}}{\text{Gross Allowable Soil Bearing Capacity}} \rightarrow \) Equation 14

### Uplift

Checks the governing axial load acting on the footing. Sums all vertical loads including the user load and self-weights of the column, footing slab, soil, and buoyant force. If the column experiences an upward force, the self-weights specified must counterbalance the upward force; otherwise, the design risks failure due to instability.

### Overturning

Overturning of the footing is checked by summing up all moments about a point in the footing including all the forces acting on it. All serviceability load combinations must be considered to check the governing overturning moment. Usually, a safety factor of 1.5-2 is employed to evaluate whether the footing passes the overturning check.

### Sliding

To check for sliding, the sum of the horizontal resisting loads pointing to the right is divided by the sum of the loads pointing to the left.

- Resisting loads:
- Horizontal force due to friction between the footing base and the substructure soil
- Passive soil pressure (if included)

- Sliding loads:
- The horizontal component of the active soil pressure
- The horizontal component of the surcharge resultant pressure

Generally, a minimum factor of safety of 1.5 is used. If no horizontal force is acting on the footing, checking for sliding is not required.

## SkyCiv Foundation Design Module

The Foundation Design Module is a powerful tool integrated with Finite Element Analysis (FEA), capable of conducting thorough soil pressure and wood armer analyses for detailed flexural checks. It performs all structural checks specified by ACI 318 and other verifications mentioned above and presents them in a comprehensive report.

**Get Started with SkyCiv Foundation today!**

Launch the Foundation Design and try it today! It’s easy to get started but if you need more help, then be sure to visit our documentation or get in touch with us!

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**Jerome Carlo San Juan**

Product Developer

BSc (Civil), MSc (Civil)

**Albert Pamonag**

Structural Engineer, Product Development

B.S. Civil Engineering

## References

- Council of Standards Australia. (2009) Australian Standard AS3600-2009.
- SJ Foster, AE Kilpatrick & RF Warner. (2011) Reinforced Concrete Basics 2nd Edition.
- Taylor, Andrew, et al.
*The Reinforced Concrete Design Handbook: a Companion to ACI-318-14*. American Concrete Institute, 2015. - YC Loo & SH Chowdhury. (2013) Reinforced & Prestressed Concrete.