Footings

• Wall or strip footing: continuous support under a wall; typically behaves as a one-way cantilever transverse to the wall.
• Isolated square footing: one column on a square spread footing; useful when geometry and loading are approximately symmetric.
• Isolated rectangular footing: one column on a rectangular spread footing; projections, one-way shear, effective depth, and reinforcement can govern differently by direction.
• Combined footing: one slab supports two or more columns. Its plan geometry is proportioned so the footing-area resultant is compatible with the service-load resultant and intended soil-pressure distribution.
• Strap footing: separate pads are linked by a strap beam that transfers eccentric effects between supports; the strap is not treated as ordinary soil-supported footing area unless the analysis explicitly models that contact.
• Continuous footing: one footing supports a line of columns or wall-like support sequence; longitudinal analysis may require a beam-on-foundation model beyond simple rigid-contact assumptions.
• Mat or raft: a large foundation supporting many columns and/or walls; global rigidity, differential settlement, punching, flexure, and soil-structure interaction can require more advanced analysis.
• Pile cap: a related reinforced-concrete foundation transfer element, but the load is transferred primarily to piles rather than directly through a shallow footing-soil contact pressure. It is therefore a distinct foundation problem.

The interactive solver in this lesson fully analyzes a rigid rectangular isolated footing with a centered interior rectangular column and uniaxial eccentricity. It solves full compression contact and triangular no-tension partial contact, then evaluates directional one-way shear, interior-column punching, flexure, reinforcement provision, and compression bearing using the same factored state. Combined-footing equilibrium is treated deterministically at first-order level. Strap, continuous, mat, and pile-cap behavior are taught conceptually and through transparent equilibrium/detailing visuals rather than being mislabeled as complete solvers.

Service and geotechnical checks include compatible service reactions, gross or net contact pressure, allowable bearing pressure, settlement, differential settlement, sliding or global stability when applicable, groundwater effects, and validity of the assumed soil-contact state.

Structural strength checks use factored actions and the corresponding factored upward soil reaction to evaluate one-way shear, two-way punching shear, flexure, concrete bearing, reinforcement, development, and force transfer.

An allowable service pressure is not inserted directly into factored shear or flexural strength equations. Likewise, a factored structural reaction must not be compared directly with an allowable service bearing pressure. The free body, load basis, and pressure datum must stay internally consistent.

Structural footing reinforcement design does not establish that the supporting ground has adequate ultimate bearing resistance or acceptable settlement. A geotechnical recommendation normally considers both shear failure and settlement, and the acceptable pressure may also depend on footing size, embedment, groundwater, layering, compressibility, adjacent foundations, construction sequence, and tolerable movement. The reinforced-concrete design starts only after that geotechnical basis is defined.

For a rigid rectangular footing with uniaxial eccentricity, $|e|\le L/6$ keeps $q_{\min}\ge0$, so the entire base can remain in compression. At $|e|=L/6$, pressure reaches zero at one edge. If $L/6<|e|<L/2$, the linear full-contact formula would predict tension over part of the base. Ordinary soil contact is instead idealized as no-tension, so only a compression zone remains. If $|e|\ge L/2$, the vertical resultant is at or beyond the footing edge and the simple gravity-contact footing state is not a stable supported solution.

Use the simulator below to change service and factored actions independently, adjust footing and column geometry, and inspect the contact region, directional shear sections, punching perimeter, reinforcement demand/provision, concrete bearing, governing utilization, and invalid geometry states. The pressure drawing changes to a triangular compression block after contact loss; it never continues to display a fictitious full-contact trapezoid with negative soil pressure.

For an isolated footing supporting a concrete column, the ordinary one-way shear critical section is located a distance $d$ from the column face. The factored demand is the upward factored soil reaction on the footing area outside that section. Rectangular footings must be checked directionally because the cantilever projection, section width, pressure distribution, and effective depth can differ.

For the normal-weight, nonprestressed teaching case on the adopted basis, the familiar nominal concrete expression is $V_c=0.17\lambda\sqrt{f'_c}b_wd$ in SI units, with the applicable shear strength-reduction factor applied to obtain design strength. A project design must confirm all governing code conditions and exceptions.

For an interior rectangular column without a special drop or pedestal, the basic punching perimeter is located $d/2$ from the column faces, giving an overall critical rectangle approximately $(c_L+d)\times(c_B+d)$. Punching demand is the factored column reaction minus the upward factored soil reaction acting inside that perimeter.

The punching capacity is not represented by one universal $0.33\lambda\sqrt{f'_c}$ stress. On the adopted ACI/NSCP teaching basis, the applicable nominal concrete stress is the least of the expressions that account for column aspect ratio $\beta$, critical-perimeter geometry through $b_o$, and column location through $\alpha_s$. The interior-column teaching model uses $\alpha_s=40$; edge and corner conditions require different geometry and coefficients and are outside the interactive solver's centered-interior-column scope.

For a concrete column or pedestal, footing flexure is evaluated at the support face. The factored soil reaction on the cantilever projection produces bottom tension under the ordinary downward column-load case. Reinforcement is therefore normally concentrated at the bottom, but top reinforcement may be required where moment reversal, uplift, strap action, local transfer, construction stages, or another analyzed load case produces top tension.

Square footings commonly have similar directional behavior when geometry and loading are symmetric. Rectangular footings require separate moments, effective depths, and bar quantities by direction. Bar distribution must follow the adopted footing/slab provisions, and the selected bars must extend and develop beyond the flexural critical section. A bar may not be cut off merely because the theoretical bending moment falls.

The column reaction is not automatically "pure compression." A footing connection can be required to transfer axial compression, axial tension or uplift, moment, and interface shear depending on the structural system and load combinations.

For compression, concrete bearing acts over the loaded area $A_1$ and may receive the code-permitted supporting-area enhancement based on the geometrically similar supporting area $A_2$, subject to its cap. Reinforcement crossing the interface must also satisfy the minimum interface requirement and must be sufficient for force not transferred by concrete bearing. Dowels or extended column bars require the appropriate development and splice provisions for their actual tension or compression state.

For two or more column loads, first locate the service-load resultant. If uniform contact pressure is the proportioning objective for a rigid combined footing under vertical service loads, the centroid of the selected footing area should align with that resultant. A rectangular footing is convenient when the required centroid can be achieved with constant width; a trapezoidal plan can shift the area centroid when property limits or unequal loads make a rectangular plan inefficient.

After equilibrium and contact pressure are established, the footing is not designed as one simple cantilever. Longitudinal soil loading and column reactions create a beam-like shear and moment diagram, while transverse strips project from the column/longitudinal load path. Detailed combined-footing design therefore requires compatible longitudinal and transverse analysis rather than reusing an isolated-footing formula indiscriminately.

A strap footing is useful when an exterior column lies close to a property line and its pad cannot be centered beneath the column. A stiff strap beam connects the exterior and interior pads so the system can redistribute moment and bring the combined resultant into a compatible relationship with soil reactions. In the classical idealization, the strap itself is not relied on for soil bearing; each pad carries soil reaction and the strap transmits internal shear and moment.

This topic treats strap behavior as a transparent first-order equilibrium and detailing problem. It does not claim a complete soil-structure interaction analysis, nor does it assume the strap has no self-weight, no flexibility, or no construction effects in real work.

Continuous footings and mats may require elastic foundation, plate, finite-element, or staged soil-structure interaction models when rigidity, differential settlement, column spacing, or nonuniform soil response is important. Pile caps require pile-reaction distribution, deep-beam/strut-and-tie or flexural behavior as applicable, punching/shear transfer, anchorage, and pile-head detailing. Those analyses are related to reinforced-concrete foundation design but are intentionally not hidden inside the isolated-footing solver.

• Bottom reinforcement: normally resists the upward-soil-reaction flexure under gravity column loading.
• Top reinforcement: provide where analysis shows top tension from uplift, moment reversal, strap action, local effects, or construction states.
• Earth-contact cover: reinforcement cast against and permanently exposed to earth commonly requires $75\text{ mm}$ cover under the adopted basis for the sizes normally used in spread footings; verify the actual project bar size/exposure provision.
• Spacing and congestion: selected spacing must permit concrete placement and vibration around orthogonal bars, dowels, and column starters.
• Dowel and starter layout: coordinate column bars, footing bars, hooks or mechanical devices, splice zones, and concrete placement access.
• Pedestals: may improve load transfer, development room, punching geometry, and constructability but change the critical geometry and must be included explicitly in analysis.
• Construction joints: locate and detail them so shear transfer, reinforcement continuity, durability, and placement sequence remain deliberate.
• Excavation tolerance and blinding: actual founding elevation and subgrade condition affect thickness, cover, cleanliness, and bearing contact. Lean concrete/blinding can provide a clean working surface but is not structural footing thickness unless explicitly designed as such.
• Load path: column actions pass through the column-footing interface, reinforced-concrete footing, contact pressure, and supporting ground; every interface must be represented by the same compatible equilibrium model.

• Association of Structural Engineers of the Philippines (ASEP), publisher of the National Structural Code of the Philippines
• ACI Committee 318, Building Code Requirements for Structural Concrete and Commentary (ACI 318-14), official ACI record
• Federal Highway Administration, Geotechnical Engineering Circular No. 6: Shallow Foundations