Combined footing design per ACI 318-19

Q: Why is the transverse band width = column + 2d?

Section 13.3.3.3 defines this as the effective zone for moment transfer perpendicular to the footing length. The band is the column width plus d on each side; reinforcement placed outside the band may not engage at the critical section, so the transverse steel is concentrated inside it.

A combined footing carries two columns on a single slab. It is designed as a beam spanning between and beyond the columns, loaded upward by soil pressure and downward by the column loads. This page covers sizing the plan so the soil pressure is uniform, the bearing pressure model, the shear and moment diagrams V(x) and M(x), longitudinal and transverse reinforcement, and the punching shear check at each column.

Applicable clauses

Clause	Requirement
§13.3.3.2	Minimum footing depth.
§13.3.2.1	Base area from unfactored (service) loads and allowable bearing pressure.
§13.2.7.1	Factored moment in the footing at the critical section.
§13.2.6.2	One-way shear, with the critical section at d from the column face.
§22.6.5	Punching shear at each column.
§13.3.3.3	Transverse band width and reinforcement.

When to use a combined footing

Two columns close together, or one column on a property line, often leave no room for two separate isolated footings: the pads would overlap, or the property-line footing would be loaded eccentrically. A single combined footing under both columns solves both problems and lets the soil pressure be made uniform by placing the footing centroid under the load resultant. When the column spacing is large or the loads are very unequal, a strap footing is usually more economical.

Sizing for resultant alignment

Locate the centroid of the combined vertical loads, measured from column 1:

x_R = \frac{P_2\,s}{P_1 + P_2}

where P₁ and P₂ are the column loads and s is the center-to-center spacing. Choose the footing length so that its geometric centroid coincides with x_R. If column 1 sits a distance a from the end of the footing:

L = 2\,(x_R + a)

The width follows from the allowable bearing pressure applied to the total service load (§13.3.2.1):

B \ge \frac{P_{1,s} + P_{2,s}}{q_{allow}\,L}

Illustration. Service loads P₁ = 150 kips and P₂ = 250 kips, spacing 18 ft, column 1 at 1 ft from the end, q_allow = 4 ksf:

x_R = 250 × 18 / 400 = 11.25 ft from column 1
L = 2 × (11.25 + 1.0) = 24.5 ft, so the footing projects 24.5 − 1.0 − 18 = 5.5 ft past column 2
B ≥ 400 / (4 × 24.5) = 4.08 ft (round up to a practical width)

The resultant lies closer to the heavier column, so the end of the footing beyond the heavier column projects farther than the end beyond the lighter one. A rectangular plan gives uniform pressure only when the resultant is centered; a trapezoidal plan is used when the width must vary.

Beam-on-soil pressure model

With the resultant aligned, the factored soil pressure is uniform:

q_u = \frac{P_{u,1} + P_{u,2}}{B\,L}

If the factored resultant is offset from the footing centroid by e, the pressure is trapezoidal (valid while e ≤ L/6):

q_{max,min} = \frac{P_{u,1} + P_{u,2}}{B\,L}\left(1 \pm \frac{6e}{L}\right)

The footing is then treated as a beam of width B carrying the line load w_u = q_u × B (upward) with the two column loads acting downward. The footing is assumed rigid, so the pressure follows the straight-line distributions above.

V(x) and M(x) diagrams

Measuring x from the left end of the footing, the shear and moment at any section are:

V(x) = w_u\,x - \sum_{x_i \le x} P_{u,i}

M(x) = \frac{w_u\,x^2}{2} - \sum_{x_i \le x} P_{u,i}\,(x - x_i)

where x_i is the position of column i. The diagrams give the design values:

Maximum negative (hogging) moment occurs where V(x) = 0, between the columns, and puts tension on the top face.
Positive (sagging) moment at the face of each column (§13.2.7.1) puts tension on the bottom face, which governs the cantilevered overhangs.
One-way shear is checked at d from the face of each column (§13.2.6.2) against φV_c using the V(x) value at that location.

Longitudinal reinforcement

Longitudinal bars are designed for the extreme values from the moment diagram: bottom steel for the positive moment at the column faces and top steel for the maximum negative moment between the columns. Each is sized with the same flexural design used for isolated footings, with the minimum depth of §13.3.3.2 and the minimum steel and bar development rules applied at every section.

Transverse band design (§13.3.3.3)

Each column also bends the footing in the transverse direction. The load concentrates in a band under the column whose width is:

b_{band} = c_{col} + 2d

The transverse moment is a cantilever from the face of the column to the footing edge, carried by the band. With the column dimension c_t measured across the footing width:

M_{u,t} = \frac{q_u\,b_{band}\,\ell^2}{2}, \qquad \ell = \frac{B - c_t}{2}

The reinforcement for M_u,t is placed inside the band at each column. Steel outside the band may not engage at the critical section, so it is not counted toward the transverse requirement.

Punching shear at each column (§22.6.5)

Each column is checked as an isolated footing column. The net shear is the column load minus the soil pressure acting within that column’s critical perimeter:

V_{u,i} = P_{u,i} - q_u\,A_{crit,i}

The capacity v_c is the smallest of the three Table 22.6.5.2 equations. Interior columns use α_s = 40; a column near the end of the footing is an edge or corner column with a truncated perimeter and a lower α_s. See the footing punching shear page for the equations and a worked example, and the eccentric punching shear page for edge and corner moment transfer.

What calcnote computes

Auto-sizing: footing length and width from the load resultant and allowable bearing pressure.
Diagrams: V(x) and M(x) along the full length, with the governing sections marked.
Reinforcement: longitudinal top and bottom steel, plus transverse band steel at each column.
Shear checks: one-way shear and punching shear at each column, with the governing case and demand-capacity ratio.

Frequently asked questions

How do I size a combined footing to avoid eccentricity?

Align the geometric centroid of the footing with the resultant of the column loads so the soil pressure is uniform. The resultant lies closer to the heavier column, so for two columns with different loads the footing extends farther past the heavier column than past the lighter one when the lighter column is held at a property line or minimum overhang. The plan area then follows from the total service load divided by the allowable bearing pressure.

Why is the transverse band width = column + 2d?

§13.3.3.3 defines this as the effective zone for moment transfer perpendicular to the footing length. The band is the column width plus d on each side; reinforcement placed outside the band may not engage at the critical section, so the transverse steel is concentrated inside it.

Does calcnote check punching shear at both columns?

Yes. Each column is checked independently using the net shear, which is the column reaction minus the soil pressure within the punching critical perimeter, against the Table 22.6.5.2 capacity for that column position.

Sources

ACI 318-19: §13.3.3.2 (minimum footing depth), §13.3.2.1 (base area from service loads), §13.2.7.1 (factored moment in footings), §13.2.6.2 (one-way shear critical section), §22.6.5 and Table 22.6.5.2 (punching shear capacity), §13.3.3.3 (transverse band).