A combined footing supports two or more columns when individual footings would overlap or when columns are close to a property line. It transfers column loads to soil while controlling pressure, eccentricity and bending.
This article explains practical calculation steps, common checks and an example to help size a rectangular combined footing. The emphasis is on clarity and calculations you can follow with simple inputs.
When combined footings are appropriate
Combined footings are used when two columns are so close that their individual footings would intersect, or when a column sits near a boundary so its footing must share load with a neighboring column.
They are also chosen to balance unequal column loads and keep soil pressure within allowable limits. The shape can be rectangular, trapezoidal or inverted-T depending on loads and space.
Key steps to perform the calculation
Start with clear knowns: column axial loads, footing depth constraints, soil allowable bearing pressure, and column spacing. These inputs drive area, dimensions and internal force checks.
Follow a sequence: compute required area, choose preliminary dimensions, check eccentricity and soil pressure distribution, then verify bending and shear. Reinforcement details come after structural checks.
Step 1 — Required plan area using bearing pressure
Calculate the total vertical load from the columns (sum of factored loads if applying safety factors). Divide this total by allowable soil bearing pressure to get the required plan area.
Required area = (P1 + P2) / q_allow. Choose a width or length that fits site constraints and solve for the other dimension.
Step 2 — Locate resultant and check eccentricity
Find the centroid of the loaded area measured from a reference edge. If the resultant is not at the geometric center, eccentricity creates a non-uniform pressure under the footing.
For a rectangular footing of width B and length L, compute eccentricity e_x and e_y relative to centerlines. If eccentricity causes compressive stress to become tensile at an edge, adjust layout or use a cantilevered detail.
Step 3 — Soil pressure distribution
Under axial and bending actions, pressure varies. Use linear distribution: p = p0 +/- Δ depending on eccentricity. Maximum pressure must not exceed q_allow and minimum must be non-negative for contact.
For one-directional eccentricity, p_max = (P/A) (1 + 6e/B) where e is eccentricity about the axis and B is the relevant dimension. Keep p_min ≥ 0 or redesign.
Step 4 — Bending moment and shear checks
Model the footing strip spanning between column reactions and check for bending about both axes. Compute factored moments from column loads and soil pressure couple.
Use reinforced concrete flexural formulas to find required area of steel. Check punching shear around columns if column loads create high shear near supports.
Step 5 — Iteration and detailing
Adjust dimensions if pressure or structural checks fail. Increase footing depth, spread the plan area or change reinforcement layout until all conditions are satisfied.
Provide development length and anchorage for bars, and consider spacing limits to control cracking and serviceability.
Design checks and common calculations
Several checks ensure safety and serviceability: bearing capacity, eccentricity limits, bending, shear and punching shear. Each has straightforward formulas tied to geometry and loads.
Keep the checks simple and sequential so changes in one parameter propagate correctly into others.
Bearing capacity and allowable pressure
Use the chosen allowable soil pressure q_allow. The first check is area: A_required = (P1 + P2)/q_allow. If A_required is larger than site limits, consider ground improvement or deeper foundations.
Also compute the distribution: if eccentricity e_x about the y-axis exists, the maximum pressure along x becomes p_max = (P_total/A)(1 + 6e_x/B). Ensure p_max ≤ q_allow.
Bending moment estimates
For a rectangular footing, bending in one direction can be estimated treating the footing as a beam strip of width ‘1 m’ spanning between column reactions or supported by soil pressure.
Compute the moment due to eccentric load: M = P * eccentricity about the section. Add moment due to soil pressure couple if pressure is non-uniform. Use factored loads per design codes before reinforcement sizing.
Shear and punching shear
Check one-way shear around critical sections at distance d from column face. V_u = shear from reaction less soil pressure within that strip. Compare with V_c and provide shear reinforcement if needed.
Punching shear is critical near column faces. Evaluate perimeter at d/2 or relevant distance and check v_u against v_c. Increase depth or add shear reinforcement if capacity is exceeded.
Serviceability and settlement considerations
Even when pressures are within allowable limits, check differential settlement between columns. Unequal loads or eccentricity can cause tilting and cracking if settlement varies significantly.
For soft soils, consider increasing area to lower stress or use piles if total settlement must be limited.
Worked example: rectangular combined footing
This example walks through numbers so you can see each step clearly. Values are simplified and rounded to show the workflow.
Given: Column A load = 600 kN, Column B load = 300 kN, spacing between columns = 3.5 m, allowable soil pressure q_allow = 150 kN/m2. Assume footing width B = 1.2 m in the short direction (across columns) and unknown length L along columns.
Step A — Required area
Total load P_total = 600 + 300 = 900 kN. Required area A_req = P_total / q_allow = 900 / 150 = 6.0 m2.
With chosen width B = 1.2 m, length L = A_req / B = 6.0 / 1.2 = 5.0 m. So preliminary footing plan is 1.2 m × 5.0 m.
Step B — Locate resultant and eccentricity
Place origin at one end of the footing length. Let Column A be at x = 1.0 m from origin and Column B at x = 4.5 m (spacing 3.5 m). Compute centroid x_r = (P_A*x_A + P_B*x_B) / P_total.
x_r = (600*1.0 + 300*4.5) / 900 = (600 + 1350) / 900 = 1950 / 900 ≈ 2.167 m from origin. Geometric center is at L/2 = 2.5 m, so eccentricity e = 2.167 – 2.5 = -0.333 m (about 0.333 m toward column A).
Step C — Check pressure distribution
Average pressure p_avg = P_total/A = 900 / 6.0 = 150 kN/m2 (equals q_allow in this simplified case). For eccentricity about the length, p_max = p_avg (1 + 6e/L). Using L = 5.0 m and |e| = 0.333 m:
p_max = 150 * (1 + 6*(0.333)/5.0) = 150 * (1 + 1.998/5) = 150 * (1 + 0.3996) ≈ 150 * 1.3996 ≈ 210 kN/m2.
This exceeds q_allow = 150 kN/m2, so increase plan area or shift shape. One option is to increase width B to reduce L or reduce eccentricity by extending the footing toward the side with higher load.
Step D — Adjust dimensions
Try increasing width to B = 1.6 m. New L = A_req / B = 6.0 / 1.6 = 3.75 m. New center is 1.875 m. Recompute x_r with same column positions scaled to fit inside the new length; relocate columns to maintain their spacing and edge distances if needed.
With columns repositioned at x = 0.875 m and x = 4.375 m relative to original scale, recompute x_r and e, then recalc p_max. Iteration continues until p_max ≤ q_allow and p_min ≥ 0.
Step E — Structural checks
Once plan works for soil pressure, compute bending moments. For example, moment at midspan due to eccentricity M = P_total * e. With reduced eccentricity this moment will be smaller and easier to handle with reasonable reinforcement and slab depth.
Check shear near columns and punching shear. If any check fails, increase slab thickness or adjust reinforcing layout and retest.
Conclusion
Calculating a combined footing is an iterative process that balances soil capacity, geometry and structural capacity. Start with area based on bearing pressure, then refine positions to control eccentricity and pressure distribution.
Always perform bending, shear and punching checks after getting a feasible plan. Simple examples like the one above show how changes in width or column location affect pressures and internal forces.
Frequently Asked Questions
Below are common questions that arise when working through combined footing calculations. Each question includes a concise answer to clarify typical concerns.
What inputs are essential to start calculations?
Required inputs are column axial loads, column spacing, allowable soil pressure, initial estimate of footing width or length, and the design depth or concrete strength. These determine plan area and initial layout.
How to handle unequal column loads?
Place the resultant based on load magnitudes and positions. Unequal loads often cause eccentricity; adjust footing plan to bring maximum soil pressure within allowable limits or use an asymmetric shape to spread the heavier load.
When does eccentricity cause uplift?
Uplift occurs if eccentricity is large enough that p_min becomes negative at an edge. To avoid uplift, increase plan area, shift the footing toward the heavy load, or add a cantilever if structural detailing permits.
Is punching shear critical in combined footings?
Yes, especially when column loads are concentrated and slab depth is small. Evaluate punching perimeter at distance d around the column and compare shear stresses with allowable values. Strengthen if necessary.
What if soil pressure alone is not acceptable?
If required area is impractical, consider options like ground improvement, deeper foundations such as piles, or redistributing loads to reduce bearing pressure. These alternatives change the foundation system rather than the slab.
Can a trapezoidal footing perform better than a rectangle?
Trapezoidal or stepped plan forms can balance pressure for unequal loads and reduce eccentricity. They are useful when site constraints or load patterns make a rectangular plan inefficient.
