**Calculation guide in designing an isolated footing based on CSA A23.3-14**

SkyCiv Foundation covers the design of isolated footing conforming to CSA A23.3-14¹ and NBCC 2010^{2}.

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**Design Parameters of an Isolated Footing**

Some calculations presented are similar with ACI 318, which is also one of the references of its CSA counterpart.

**Dimension Requirements**

To determine the dimensions of an isolated footing, service or unfactored loads, such as dead (**D**), Live (**L**), Wind (**W**), Seismic (**E**), etc will be applied using Load Combinations, as defined by NBCC 2010. Whichever Load Combination governs will be considered the design load, and will be divided to the allowable soil pressure as shown in Equation 1.

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

where:

q_{all} = allowable soil pressure

P_{n} = unfactored design load

A = Foundation area

**One-way Shear**

To check for **one-way shear,** the Critical Shear Plane (Refer to Figure 1)** **is located at a distance “d” from the face of a column.

Figure 1. Critical Plane Shear of One-way shear

The **One-way ****Shear** **Demand** or **V _{f}** is calculated assuming the footing is cantilevered away from the column where the area is (red) indicated in Figure 2, in accordance of

**CSA A23.3-14, Section 13.3.6**.

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

**CSA A23.3-14, Section 11.3.4**.

\(\text{V}_{\text{c}} = \phi _{\text{c}} \times \lambda \times \sqrt{\text{f’}_{\text{c}}} \times \text{b}_{\text{w}} \times \text{d} \rightarrow \) Equation 2 (**CSA A23.3-14 Eq. 11-6**)

where:

ϕ_{c} = resistance factor for concrete

λ = modification factor for concrete density

f’_{c} = specified concrete strength, MPa

b_{w} = width of the footing, mm

d = effective shear depth, mm

Shear Demand and Shear Capacity must meet the following equation to meet the design requirements of **CSA A23.3-14**:

\(\text{V}_{\text{f}} \leq \phi\text{V}_{\text{c}} \rightarrow \) Equation 3 (**CSA A23.3-14**** Eq. 11.3**)

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

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

**Two-way Shear**

The **Two-way Shear** limit state, also known as **punching shear,** extends it critical section to a distance “d/2” from the face of the column and around the perimeter of the column. The Critical Shear Plane is located at that section of the footing (Refer to Figure 2).

Figure 2. Critical Shear Plane of Two-way shear

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

**CSA A23.3-14, Section 13.3.3**.

The **Shear Capacity **or** V _{c}** is governed by the least value calculated using Equation 5, 6, and 7 per

**CSA A23.3-14, Section 13.3.4.1**

\(\text{V}_{\text{c}} = \left ( 1 + \frac{2}{\beta_{\text{c}}} \right ) \times 0.19 \times \lambda \times \phi _{\text{c}} \times \sqrt{f’_{c}} \rightarrow \) Equation 5 (**CSA A23.3-14**** Eq. 13.5**)

\(\text{V}_{\text{c}} = \left ( \frac{\alpha_{\text{s}} \times \text{d}}{\text{b}_{\text{o}}} + 0.19 \right ) \times \lambda \times \phi _{\text{c}} \times \sqrt{f’_{c}} \rightarrow \) Equation 6 (**CSA A23.3-14**** Eq. 13.6**)

\(\text{V}_{\text{c}} = 0.38 \times \lambda \times \phi _{\text{c}} \times \sqrt{f’_{c}} \rightarrow \) Equation 7 (**CSA A23.3-14**** Eq. 13.7**)

**Note:** β_{c} is the ratio of long side to short side of the column, concentrated load, or reaction area and α_{s} is given by 13.3.4.1

where:

λ = modification factor for concrete density

f’_{c} = specified compressive concrete strength, MPa

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

Shear Demand and Shear Capacity must meet the following equation to meet the design requirements of CSA A23.3-14:

\(\text{V}_{\text{f}} \leq \phi\text{V}_{\text{c}} \rightarrow \) Equation 8 (**CSA A23.3-14**** Eq. 11.3**)

SkyCiv Foundation, in compliance of Equation 8, calculates the two-way shear unity ratio (Equation 9) by taking Shear Demand over Shear Capacity.

\( \text{Unity Ratio} = \frac{\text{Shear Demand}}{\text{Shear Capacity}} \rightarrow \) Equation 9

**Flexure**

Figure 3. Critical Flexure Section

The **Flexural** limit state occurs at** **the Critical Flexure Section, located at the face of the column on top of the footing (Refer to Figure 3).

The **Moment Demand, **or **M _{f}** is located at the Critical Flexure Section (blue hatch area) indicated in Figure 3, and is calculated using Equation 10.

\( \text{M}_{u} = \text{q}_{u} \times \left ( \frac{l_{x}}{2} – \frac{c_{x}}{2} \right ) \times l_{z} \times \left ( \frac{\frac{l_{x}}{2} – \frac{c_{x}}{2} }{2} \right ) \rightarrow \) Equation 10

where:

q_{u} = factored soil pressure, kPa

l_{x} = footing dimension along the x-axis, mm

l_{z} = footing dimension along the z-axis, mm

c_{x} = column dimension along the x-axis, mm

The **Moment Resistance, **or** Mr** is calculated using Equation 11.

\( \text{M}_{r} = \phi_{\text{s}} \times A_{s} \times f_{y} \times \left( d – \frac{a}{2} \right) \rightarrow \) Equation 11

where:

ϕ_{s} = resistance factor for non-prestressed reinforcing bars

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

A_{s} = reinforcement area, mm^{2}

a = depth of equivalent rectangular stress block, mm

fy = reinforcement strength, MPa

Moment Demand and Moment Resistance must meet the following equation to meet the design requirements of CSA A23.3-14:

\(\text{M}_{\text{r}} \leq \phi\text{M}_{\text{f}} \rightarrow \) Equation 12

SkyCiv Foundation, in compliance of Equation 12, calculates the flexural unity ratio (Equation 13) by taking Flexural Demand over Flexural Capacity.

\( \text{Unity Ratio} = \frac{\text{Flexure Demand}}{\text{Flexure Capacity}} \rightarrow \) Equation 13

## NEW SkyCiv Foundation with FEA

As of March 2024, the Foundation Design Module has integrated the Finite Element Analysis (FEA) solver into its capabilities. This new feature allows users to conduct in-depth soil pressure and wood armer analyses while still performing all structural checks specified by CSA A23.3-14, including all verifications mentioned above. Summary of the FEA Results is included in the comprehensive report.

## Free Concrete Footing Calculator

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**References**

*A23.3-14: Design of concrete structures*. Canadian Standards Association, 2014.- Brzev and Pao. Reinforced Concrete Design: A Practical Approach, 2009.

**Wilross Papaya**

Product Developer

BSc (Civil)