Footings

Footings

Learning Objectives

Differentiate between types of shallow and deep foundations.
Distinguish between gross allowable soil pressure and net allowable bearing capacity.
Analyze bearing pressure distributions under concentric and eccentric loading.
Identify the critical sections for one-way shear, two-way shear, and flexure in footing design.
Understand the purpose and code requirements for dowel reinforcement.

Footings are the substructure elements that interface directly with the ground. Their primary function is to safely distribute the concentrated loads from columns and walls over a large enough area of soil so that the bearing capacity of the soil is not exceeded and settlements are kept within acceptable limits.

Types of Foundations

Foundations are broadly classified into shallow and deep foundations. Footings are shallow foundations, typically located just below the frost line or ground surface where competent soil is found.

Common Shallow Footing Types

Wall Footings (Strip Footings): Continuous concrete strips supporting load-bearing walls. They are designed as one-way cantilevers extending from the wall face.
Isolated Footings (Spread Footings): The most common and economical type. Individual rectangular or square slabs supporting a single column.
Combined Footings: A single rectangular or trapezoidal footing supporting two or more columns. Used when columns are so close together that isolated footings would overlap, or when an exterior column is right on the property line and cannot have a concentric footing.
Cantilever (Strap) Footings: Two isolated footings connected by a rigid beam (strap). Used to transfer the eccentric moment from an exterior property-line column to an interior column.
Mat Foundations (Raft): A massive continuous slab supporting all columns and walls of a structure. Used when the soil bearing capacity is very low, requiring individual footings to cover more than 50% of the building area.

Plain vs. Reinforced Concrete Footings

Footings can be constructed with or without steel reinforcement, drastically changing their structural behavior and thickness.

Footing Construction

Plain Concrete Footings: Unreinforced footings rely entirely on the limited tensile strength of the concrete ( $f_r$ ) to resist bending. They are very thick (deep) to minimize flexural stresses and are typically only used for lightly loaded walls or pedestals on excellent soil or rock.
Reinforced Concrete Footings: Utilize a mat of steel reinforcement near the bottom face to resist the tensile stresses caused by the upward soil pressure bending the footing like a cantilever. They are significantly thinner and more economical for typical building loads because the steel reinforcement efficiently handles the tensile stresses, allowing for a much smaller required depth.

Gross Allowable Soil Pressure ( $q_a$ )

The maximum gross pressure the soil can safely carry, established by geotechnical testing based on shear failure and settlement criteria. Provided in the geotechnical report.

Net Allowable Bearing Capacity ( $q_{\text{net}}$ )

The additional, new pressure the soil can safely carry from the structure beyond the original, pre-existing overburden pressure. It subtracts the weight of the new concrete footing and any backfill soil from the gross allowable soil pressure.

Soil Bearing Capacity

The interaction between the footing and the soil dictates the footing's plan dimensions (Area). Geotechnical engineers provide an allowable soil pressure ( $q_a$ ) based on the soil's shear strength and acceptable settlement criteria.

Gross vs. Net Bearing Capacity

The footing is placed at a depth $D_f$ below the surface. Before excavation, the soil at that depth was already supporting the weight of the soil above it ( $\gamma_{\text{soil}} \times D_f$ ). When we excavate and pour a concrete footing, we change the stress state.

Net Allowable Bearing Capacity

Calculates the net pressure available to support the column load by deducting the weights of the footing and soil surcharge.

q_{\text{net}} = q_a - \frac{W_f}{A} - \frac{W_s}{A}

Variables

Symbol	Description	Unit
$q_{\text{net}}$	net allowable bearing capacity	-
$q_a$	gross allowable soil pressure provided by geotechnical report	-
$W_f$	weight of the concrete footing	-
$W_s$	weight of soil surcharge above the footing	-
$A$	footing plan area	-
$P$	total unfactored vertical column load ( $P = D + L$ )	-

Footing Area Sizing

The net allowable bearing capacity ( $q_{\text{net}}$ ) is the additional pressure the soil can safely carry beyond the original overburden pressure.

Footing plan Area ( $A_{\text{req}}$ ) is determined exclusively using Unfactored Service Loads ( $P$ ) divided by $q_{\text{net}}$ : $A_{\text{req}} = P / q_{\text{net}}$ . Ultimate Strength Design (load factors) is NEVER used to size the footing area against soil failure.

Bearing Pressure Distribution

The actual distribution of soil pressure beneath a footing depends on the rigidity of the footing itself and the soil type (e.g., cohesive clay vs. cohesionless sand). However, to drastically simplify structural design, footings are modeled as perfectly rigid bodies, assuming a linear or planar pressure distribution.

If a footing supports only a concentric axial load, the upward soil pressure is assumed to be uniform ( $q = P/A$ ). However, if the column also transfers a bending moment ( $M$ ), the pressure distribution becomes trapezoidal or triangular due to eccentricity ( $e = M/P$ ).

Eccentric Loading Cases

$e \leq L/6$ (Resultant inside the middle third): The entire footing remains in compression against the soil. The pressure distribution is trapezoidal: $q_{\text{max},\text{min}} = \frac{P}{A} \left(1 \pm \frac{6e}{L}\right)$ .
$e > L/6$ (Resultant outside the middle third): The heel of the footing lifts off the ground, causing zero pressure over a portion of the base (soil cannot take tension). The pressure distribution is triangular over an effective length of $3(L/2 - e)$ : $q_{\text{max}} = \frac{2P}{3B(L/2 - e)}$ . This condition should generally be avoided by increasing the footing size.
Biaxial Eccentricity: If the column transfers moments about both axes ( $M_x$ and $M_y$ ), the pressure distribution is skewed in 3D. The general equation is $q = \frac{P}{A} \pm \frac{M_x y}{I_x} \pm \frac{M_y x}{I_y}$ , provided the entire footing remains in compression.

Pile Caps (Deep Foundations)

When shallow soil is too weak, loads are transferred deeper using piles. The thick concrete slab that connects a group of piles to a single column is called a pile cap.

Pile Cap Behavior

Load Transfer: The pile cap acts as a massive, extremely rigid block that distributes the column load to the individual piles as concentrated point loads.
Shear Critical: Because they are heavily loaded and relatively short, punching shear (two-way) around the column, punching shear around individual piles, and deep-beam one-way shear usually govern the immense thickness of the cap.
Strut-and-Tie: For deep pile caps, traditional flexural theory is inaccurate. The loads are transferred from the column to the piles via direct concrete compression struts, tied together at the bottom by the main tension steel grid.

Two-Way Shear (Punching Shear)

A failure mechanism where the heavily loaded column punches directly through the footing slab along a defined failure perimeter, typically located at $d/2$ from the column face. This critical check almost always dictates the minimum required depth ( $h$ ) of the footing.

Structural Design Checks (LRFD)

Once the plan dimensions ( $L \times B$ ) are established using service loads, the footing thickness ( $h$ ) and reinforcement ( $A_s$ ) are designed as concrete members using Factored Loads ( $P_u = 1.2D + 1.6L$ ) and the resulting factored ultimate soil pressure ( $q_u = P_u / A$ ).

Design Sequence

STEP-BY-STEP

Calculate Factored Soil Pressure ( $q_u$ ): Use the actual chosen dimensions ( $L \times B$ ) and the factored column loads.
Two-Way Shear (Punching Shear): Often dictates the thickness ( $h$ ) of isolated footings. The column tends to punch through the slab along a perimeter $b_o$ located at a distance $d/2$ from the face of the column. The factored shear force $V_{u2}$ (total upward pressure outside the perimeter $b_o$ ) must not exceed $\phi V_c$ ( $\phi=0.75$ ), where $V_c$ represents the nominal shear strength provided by the concrete. For footings, $V_c$ is the smallest of three specific ACI equations evaluating the aspect ratio of the column, the location of the column (interior, edge, corner via $\alpha_s$ ), and the $b_o/d$ ratio.
One-Way Shear (Beam Shear): The footing acts as a wide beam cantilevering from the column. The critical section is a line across the entire width of the footing, located at a distance $d$ from the face of the column. The factored shear $V_{u1}$ (total upward pressure from the critical section to the edge) must not exceed $\phi V_c$ ( $\phi=0.75$ ), where $V_c$ is the one-way shear strength of the concrete.
Flexure (Bending Moment): The critical section for maximum bending moment ( $M_u$ ) is exactly at the face of the column (or halfway between the face and the edge for steel base plates). Calculate the required reinforcement ( $A_s$ ) to resist this moment. The steel is placed at the bottom of the footing.
Load Transfer at Column Base (Bearing): The massive compressive force in the column must transfer safely into the footing without crushing the concrete at the interface. The bearing stress $f_b = P_u / A_{\text{col}}$ must not exceed $\phi(0.85 f'_c) \sqrt{A_2/A_1}$ ( $\phi=0.65$ ), where $\sqrt{A_2/A_1}$ is a confinement factor (max 2.0) accounting for the surrounding unloaded concrete area $A_2$ .
Dowels: Even if the concrete bearing capacity is sufficient, the code mandates a minimum area of dowel reinforcement across the interface equal to $0.005 A_g$ (0.5% of the column gross area). These dowels must extend up into the column a full lap splice length ( $l_{\text{sc}}$ ) and down into the footing a full compression development length ( $l_{\text{dc}}$ ). If $l_{\text{dc}}$ is greater than the footing depth, standard 90-degree hooks must be added, resting on the main footing steel mat.

Key Takeaways

Footing plan dimensions (Area) are strictly sized based on Service Loads (unfactored) to ensure the allowable soil bearing capacity ( $q_a$ or $q_{\text{net}}$ ) is not exceeded.
Footing thickness ( $h$ ) and reinforcement ( $A_s$ ) are designed using Factored Loads ( $q_u$ ) per LRFD methodology.
If the column applies a moment creating an eccentricity $e > L/6$ , the footing lifts off the soil, resulting in a severe triangular pressure distribution that drastically increases $q_{\text{max}}$ .
The critical section for two-way (punching) shear is located at $d/2$ from the column face, while one-way (beam) shear is checked at distance $d$ . Punching shear usually governs the depth of isolated footings.
The critical section for flexure is exactly at the face of the column.
Dowels ( $A_{s,\text{min}} = 0.005 A_g$ ) must cross the column-footing interface to safely transfer bearing loads, moments, and shear forces between the members.