Footings

Learning Objectives

  • Distinguish gross contact pressure, net foundation pressure, and gross or net allowable bearing values without changing geotechnical terminology.
  • Size footing plan dimensions with service-load bearing checks on one clearly stated pressure basis.
  • Evaluate full-contact pressure under concentric and uniaxially eccentric loading and recognize when a no-tension soil model leaves the linear full-contact range.
  • Locate and evaluate the critical sections for one-way shear, two-way punching shear, and flexure.
  • Detail footing reinforcement and column dowels with correct cover, effective depth, development, bearing, and interface-transfer requirements.

Gross Contact Pressure

Gross contact pressure is the total compressive pressure acting at the footing-soil interface from every service load included in the chosen foundation free body, such as the supported structure, footing self-weight, and overlying fill when those loads act on the soil.

Net Foundation Pressure

Net foundation pressure is the increase in vertical pressure at the founding level relative to the pre-existing overburden pressure at that level before excavation and foundation construction.

Allowable Bearing Pressure

Allowable bearing pressure is the service-level soil pressure limit established from the geotechnical basis for shear resistance and settlement. It must be identified as gross or net before it is used in structural footing sizing.

Gross and Net Bearing Must Use the Same Datum

A gross allowable pressure is compared with gross service contact pressure. A net allowable pressure is compared with net foundation pressure referenced to the same original overburden datum. Footing weight and backfill are loads in the foundation free body; subtracting them from a gross allowable value does not, by itself, redefine that value as a geotechnical net allowable pressure.

Gross-to-Net Pressure Conversion

Relates gross and net foundation pressure when the pre-existing overburden pressure at founding level is q_0.

qnet=qgross−q0q_{\mathrm{net}} = q_{\mathrm{gross}} - q_0

Variables

SymbolDescriptionUnit
qnetq_{\mathrm{net}}net foundation pressure relative to the original overburden datum-
qgrossq_{\mathrm{gross}}total contact pressure at the footing-soil interface-
q0q_0pre-existing vertical overburden pressure at founding level before excavation-

Bearing-Basis Consistency

If the geotechnical report gives qallow,grossq_{\mathrm{allow,gross}}, compare it with qgrossq_{\mathrm{gross}}. If it gives qallow,netq_{\mathrm{allow,net}}, compare it with qnetq_{\mathrm{net}}. Do not mix one datum with the other. Confirm groundwater, settlement criteria, load duration, and any geotechnical restrictions from the project report.

Footing Types and Structural Roles

  • Wall or strip footing: continuous footing supporting a wall and behaving primarily as a one-way cantilever transverse to the wall.
  • Isolated footing: spread footing supporting one column or pedestal.
  • Combined footing: one footing supporting two or more columns; its plan shape is proportioned so the resultant of service column loads is compatible with the contact-pressure objective.
  • Strap footing: separate pads connected by a strap beam that transfers eccentric effects between supports.
  • Mat foundation: large continuous foundation supporting many columns or walls when individual spread footings become impractical or settlement control governs.

Service Sizing versus Strength Design

Footing plan dimensions are checked against geotechnical allowable pressure using the service-load combination and the same gross/net basis as the geotechnical recommendation. After the plan size is selected, the reinforced-concrete footing is checked for strength using factored actions. For a concentric footing, the upward design pressure used for footing shear and flexure is commonly based on the factored column or wall action divided by the selected area when uniform footing self-weight and uniform fill effects cancel in the footing slab free body; this structural bookkeeping must not be called a new geotechnical net bearing capacity.

Uniform Service Contact Pressure

Gross contact pressure for a concentric footing when all included service vertical loads are represented explicitly.

qgross=Pservice+Wf+WsBLq_{\mathrm{gross}} = \frac{P_{\mathrm{service}} + W_f + W_s}{BL}

Variables

SymbolDescriptionUnit
PserviceP_{\mathrm{service}}unfactored supported structural vertical load-
WfW_ffooting self-weight included in the gross free body-
WsW_soverlying soil or surcharge included in the gross free body-
BBfooting dimension transverse to the eccentricity axis-
LLfooting dimension along the eccentricity axis-

Eccentricity

For a uniaxial service resultant PP with moment MM about the centroidal axis, the eccentricity is e=∣M∣/Pe=|M|/P measured along the footing dimension LL over which pressure varies.

Full-Contact Uniaxial Pressure

Linear rigid-footing contact pressure while the entire rectangular base remains in compression.

qmax⁡,min⁡=PBL(1±6eL),e≤L6q_{\max,\min}=\frac{P}{BL}\left(1\pm\frac{6e}{L}\right), \qquad e\le\frac{L}{6}

Variables

SymbolDescriptionUnit
PPvertical resultant used for the pressure check-
eeabsolute load eccentricity along L-
BBfooting dimension perpendicular to the pressure-gradient direction-
LLfooting dimension parallel to the pressure-gradient direction-

Partial Contact Is a Different Model State

When e>L/6e>L/6, the linear full-contact equation predicts tension at one edge, but soil is normally idealized as carrying no tension. The contact area must then be recomputed under a no-tension equilibrium model. If a teaching tool does not implement that model, it must flag the state rather than display a negative qmin⁡q_{\min} as physical soil tension. When e≥L/2e\ge L/2, the resultant is at or beyond the base edge and the simple gravity-contact footing model is not valid.

Interactive Pressure Check

Use the footing-pressure visualizer to vary PP, MM, BB, and LL. It reports the full-contact pressure only within its stated range and explicitly flags partial-contact or edge-resultant states.

Footing Pressure: Full-Contact Check

Concept and model scope

Rigid rectangular footing under one vertical resultant and one moment. Pressure varies along LL; BB is perpendicular to that gradient.

Full contact is valid only while the eccentricity e=∣M∣/Pe=|M|/P remains within the middle third, e≤L/6e\le L/6. In that domain, qmax,min=P/(BL)(1±6e/L)q_{max,min}=P/(BL)(1\pm6e/L).

Partial contact is detected but intentionally not solved because a no-tension contact formulation is then required. The allowable pressure must use the same gross/net service basis as the entered load.

Controls

Vertical load PP1200 kN
Moment MM150 kN·m
Width BB2.0 m
Length LL3.0 m
Allowable service pressure250 kPa
PMallowableL = 3.0 m

Results and validity

Area
6.00 m²
e=∣M∣/Pe=|M|/P
0.125 m
L/6L/6
0.500 m
P/(BL)P/(BL)
200.0 kPa
qmax⁡q_{\max}
250.0 kPa
qmin⁡q_{\min}
150.0 kPa
Full contact: maximum service pressure is within the entered allowable pressure.

For full contact only: qmax⁡,min⁡=P/(BL)(1±6e/L)q_{\max,\min}=P/(BL)(1\pm6e/L). The entered allowable pressure must itself be on the same gross or net service basis as the load used here.

Effective Depth

The effective depth dd is measured from the extreme compression face used in the footing flexural model to the centroid of the tension reinforcement. For bottom bars in a footing of thickness hh, dd depends on bottom cover, bar diameter, and bar layering.

One-Way Shear

For an isolated footing supporting a concrete column, the one-way critical section is located a distance dd from the column face. The factored shear is the net upward design reaction on the cantilevered area outside that section. For the ordinary nonprestressed teaching cases in this topic, the concrete strength check uses the applicable ACI/NSCP one-way shear provision and the correct strength-reduction factor.

Two-Way Punching Shear

For a concentrated column reaction, the basic punching critical perimeter is located d/2d/2 from the column faces. The factored punching shear is the column action minus the upward reaction acting inside that critical perimeter, equivalently the upward reaction on the area outside the perimeter for the symmetric concentric case. The nominal concrete strength is the least of the applicable ACI/NSCP two-way shear expressions; column aspect ratio, perimeter geometry, and interior/edge/corner location matter.

Punching Capacity Is Not Always One Formula

The familiar 0.33λfc′bod0.33\lambda\sqrt{f'_c}b_od metric expression is one limit used in common square interior-column teaching cases. A complete design must evaluate the applicable two-way shear expressions and geometry rather than assume that single expression always governs.

Flexure and Reinforcement

For a concrete column or pedestal, footing flexure is evaluated at the face of the support. The soil reaction on the cantilever projection produces tension near the footing bottom for the usual isolated footing. Required reinforcement is obtained from factored moment strength and then checked against the applicable minimum reinforcement and spacing provisions. Reinforcement distribution in rectangular footings must follow the code provisions for the long and short directions.

Cover and Effective-Depth Detailing

Reinforcement cast against and permanently exposed to earth requires the applicable large concrete cover, commonly 75 mm75\text{ mm} for the reinforcement sizes normally encountered in spread footings under the adopted ACI/NSCP provisions. Cover is measured to the outside of the bar, while effective depth is measured to its centroid. Layering one direction above the other therefore gives slightly different effective depths.

Column-to-Footing Bearing and Dowels

Concrete bearing at the column-footing interface must satisfy the applicable bearing-strength provision, including the permitted supporting-area enhancement where its geometric conditions are met. Reinforcement crossing the interface is also checked for the required minimum area and for the force that must be transferred after concrete bearing is considered.

Minimum Interface Reinforcement

Minimum reinforcement crossing the interface for a reinforced-concrete column supported by a footing under the adopted ACI/NSCP provision.

As,min⁡=0.005AgA_{s,\min}=0.005A_g

Variables

SymbolDescriptionUnit
As,min⁡A_{s,\min}minimum dowel or extended-column reinforcement crossing the interface-
AgA_ggross area of the supported reinforced-concrete column-

Compression Development and Hooks

A column dowel that must develop compression into the footing must satisfy the straight-bar compression development provision for the required force and detailing conditions. A standard 90-degree or 180-degree hook is a tension-anchorage device and must not be credited as a generic substitute for missing compression development length. If the available straight embedment is insufficient, revise the footing depth, dowel size/layout, force-transfer mechanism, or another code-permitted connection detail. A bend may still be present for construction or another force case, but that does not make it compression development length.

Coordinated Footing Design Sequence

  1. Read the geotechnical recommendation and identify whether its allowable bearing value is gross or net and what service combinations and settlement limits apply.
  2. Establish the footing service-load free body, compute contact pressure on the same datum, and select practical BB and LL dimensions.
  3. Check eccentricity and contact validity before using a linear pressure distribution; enlarge or otherwise redesign the footing when pressure or contact is unacceptable.
  4. Establish factored structural actions and the corresponding upward design reaction used for reinforced-concrete strength checks.
  5. Select a trial thickness and compute the actual effective depths from cover, bar size, and layer position.
  6. Check one-way shear at dd from the support face and two-way punching shear on the applicable d/2d/2 critical perimeter.
  7. Design flexural reinforcement at the support face and satisfy minimum steel, spacing, distribution, and cover requirements.
  8. Check concrete bearing and column-to-footing force transfer, then detail dowels or extended column bars with the correct tension, compression, splice, or mechanical-development provisions for the actual force state.
  9. Recheck the selected geometry and all development lengths after reinforcement sizes and layers are finalized.
Key Takeaways
  • Gross and net bearing pressures are geotechnical terms tied to different stress datums; structural load bookkeeping must not redefine them.
  • Service bearing checks and factored reinforced-concrete strength checks serve different limit states and must use internally consistent free bodies.
  • The full-contact equation q=P/A±M/Sq=P/A\pm M/S is valid only while the entire base remains in compression; partial contact requires a no-tension contact model.
  • One-way shear is checked at dd from the support face, punching shear on the applicable perimeter at d/2d/2, and flexure at the support face for a concrete column.
  • Effective depth, cover, bar layering, and selected bar size must be recomputed together before shear, flexure, and development checks are accepted.
  • Standard hooks provide tension anchorage; they are not a substitute for insufficient straight compression development of footing dowels.