Isolated, Spread and Combined Footings: Types and Design

An isolated footing, also called a pad or spread footing, is a square or rectangular slab of reinforced concrete under a single column. It spreads the column’s load over enough soil for the ground to carry it without failing in shear or settling too much. A combined footing does the same for two or more columns on one slab, and a strip footing does it along a wall. All of them are shallow foundations, the usual choice wherever the soil a metre or two down can take the load.

Designing a footing takes two passes: the soil sets its plan size, and ACI 318 sets its thickness and steel. The two worked examples below run both, one for an isolated footing under a column with a moment, checked with Rischio’s engine, and one for a combined footing that carries two columns at a property line.

The five types of footings

Isolated footing (pad or spread footing)

An isolated footing carries one column. It is square when the load is centred, and rectangular when the site limits one side or the column bends it mostly one way. Dowels anchored in it lap with the column’s bars, so the load and any moment pass into the slab. Isolated footings suit framed buildings with columns well apart, on soil that is competent near the surface. When neighbouring footings grow until they nearly touch, a combined footing or a mat takes over.

Strip footing (continuous or wall footing)

A strip footing runs under a load-bearing wall or a close row of columns, and it is designed per metre of its length. Take a wall bringing 150 kN/m onto the soil of the first example below, where the allowable pressure is 200 kPa and the footing with the soil over it takes about 30 kPa of that. It needs a width of 150/(200 − 30) = 0.88 m, so 0.90 m. The main steel runs across the width, where the overhangs bend, and bars along the strip control shrinkage and help it span a soft spot in the ground.

Combined footing

A combined footing carries two or more columns on one slab. It is used when the isolated footings of neighbouring columns would overlap, and when an exterior column stands on the property line, where a footing centred on it would cross into the next lot. Its centroid is placed under the resultant of the column loads, so the soil pressure under it is uniform. A rectangle works when the interior column is the heavier one. When the column at the line is heavier, the resultant moves toward the line and the footing becomes a trapezoid, wider at that end.

Strap footing (cantilever footing)

A strap footing joins two footings with a stiff beam. The exterior footing sits off-centre under its column at the property line, and the strap carries the moment of that eccentricity to the interior footing, so both bear with a nearly uniform pressure. The strap is built so it does not bear on the soil. When the columns are far apart, a strap footing usually takes less concrete than one long combined slab between them.

Mat or raft foundation

A mat, or raft, is a single slab under the whole building or a large part of it. It replaces footings when they would cover more than about half of the plan, when the soil is weak or variable, or when the differential settlement between columns has to stay small. Mats have their own guide, raft foundation design.

Spread, pad, isolated: what the names mean

In US practice, spread footing is the family name for any footing that spreads its load over the soil right under it, so isolated, strip and combined footings are all spread footings. Many engineers use the term for the isolated column footing alone, which also goes by pad footing, column footing and individual footing. A continuous footing is the strip under a wall.

An eccentric footing is one whose column sits off its centre, as at a property line, or whose column brings a moment. The pressure under it is no longer uniform, and how far off centre the load may go is one of the design checks below.

How deep a footing must go

The founding level comes from the geotechnical report, and it has to meet several conditions at once:

• Below the frost line where the ground freezes, since freezing soil grows ice lenses that heave whatever sits on it. The local building authority publishes the frost depth.
• On undisturbed, competent soil, below topsoil, organic soil and uncontrolled fill. Soil the excavation loosened is removed or recompacted before the concrete goes in.
• Below the depth where expansive clays swell and shrink with the seasons.
• At least 12 inches (305 mm) below the undisturbed ground surface, the minimum in Section 1809.4 of the International Building Code, with frost protection added where it applies (Section 1809.5).

Depth also adds capacity: the soil above the base is the overburden $q$ in the bearing capacity equation, so a deeper footing carries more. How to read a geotechnical report shows where a report gives the founding level and the allowable pressure at it.

Geotechnical design: sizing the footing

Footing design starts with the soil, which sets the plan size through four checks, all under service (unfactored) loads. They are the checks Rischio’s footing tool runs.

1. Area from the allowable bearing pressure

The report gives an allowable bearing pressure $q_a$. When it is a gross value, the pressure under the footing includes the footing itself and the soil over it, so a column load $P$ needs an area of

where $h$ is the footing’s thickness, $D_f$ its depth, and $\gamma_c$ and $\gamma$ the unit weights of the concrete and the backfill. A net allowable pressure is handled differently; gross vs net bearing pressure works through both.

2. Eccentricity: the middle third and B’

A column moment $M$, or a column off the footing’s centre, moves the resultant of the load $V$ a distance $e = M/V$ from the centre, and the contact pressure becomes linear across the base:

While $e \le B/6$, the resultant stays in the middle third of the base and all of the base presses on the soil. Beyond $B/6$, $q_{min}$ turns negative. The soil can’t pull, so that edge lifts off. For the bearing capacity, Meyerhof’s method keeps the part of the base centred on the resultant, of width $B' = B - 2e$.

3. Bearing capacity

The ultimate bearing capacity $q_u$ comes from the general bearing capacity equation, Terzaghi’s three terms with shape, depth and inclination factors:

The footing passes when $FS = q_u / q_{max} \ge 3$. Every factor is in the docs’ bearing capacity theory, and the free bearing capacity calculator works them out for any footing.

4. Settlement

A footing that passes the bearing check can still settle too much. Rischio computes the elastic settlement at the centre of the base and checks it against 25 mm, as its settlement theory explains. A footing on clay also needs its consolidation settlement, from oedometer tests (one-dimensional consolidation in the Academy), and neighbouring footings must not settle so differently that the frame cracks. Foundation settlement covers both.

Structural design to ACI 318

With the soil satisfied, the thickness and the steel come from ACI 318 strength design with factored loads: $1.2D + 1.6L$ for gravity, and $1.4D$. The footing’s weight and the soil on it press down as much as the soil pushes them back, so they cause no shear or bending. The slab is designed for the net factored pressure $q_{nu} = P_u/A$, plus the linear part a moment adds.

Punching shear (two-way)

The column tries to punch through the slab. ACI 318 checks a critical perimeter at $d/2$ from the faces of the column, $d$ being the effective depth; for a square column of side $c$, $b_0 = 4(c + d)$. The shear on that perimeter is the column load less the soil pressure inside it, $V_u = P_u - q_{nu}(c + d)^2$, and without shear reinforcement the concrete provides

with $\phi = 0.75$ and $\lambda = 1.0$ for normal-weight concrete. Two other limits take over when they are smaller: $0.17(1 + 2/\beta)$ for a column whose long side is $\beta$ times its short side, and $0.083(2 + \alpha_s d/b_0)$ for a perimeter that is long next to $d$, with $\alpha_s = 40$ for an interior column. ACI 318-19 also multiplies them by a size factor $\lambda_s = \sqrt{2/(1 + 0.004d)} \le 1$, which lowers the strength once $d$ passes 250 mm. A column that transfers a moment adds eccentric shear on the perimeter; the first example works it out.

One-way shear

Each overhang also works as a wide beam. The critical section is at $d$ from the face of the column, and $V_u$ is the soil pressure on the part of the footing beyond it. Footings have no stirrups, and for members without them ACI 318-19 makes the concrete’s strength depend on the steel ratio $\rho_w = A_s/(b_w d)$:

With the light steel of a typical footing, this check can set the thickness before punching does.

Flexure, minimum steel and cover

Bending is checked at the face of the column, with the moment of the soil pressure on the overhang. Then come the minimums: $0.0018\,bh$ of Grade 420 steel in each direction, 75 mm of cover to concrete cast against the ground, and at least 150 mm of depth above the bottom steel. In a rectangular footing, the steel in the short direction is concentrated under the column, in a band as wide as the short side. The bars need their development length past the face of the column, and the column’s force crosses into the footing by bearing and through dowels of at least 0.5 % of the column’s area.

Worked example 1: an isolated footing with a moment

A 400 × 400 mm column carries a dead load of 600 kN and a live load of 300 kN, with moments of 60 and 30 kN·m about the same axis. The geotechnical report recommends founding at 1.50 m in a medium-dense silty sand, below the frost depth, with a gross allowable bearing pressure of 200 kPa. The borings found no groundwater.

Step 1: size from the allowable pressure

The footing and the soil over it weigh $0.60 \times 24 + 0.90 \times 18 = 30.6$ kPa, which leaves $200 - 30.6 = 169.4$ kPa for the column:

For the axial load alone, a 2.35 m footing would do. The moment adds $6M/B^3$ at one edge, so the size has to be checked with it.

Step 2: the moment and the middle third

Try $B = 2.60$ m. The load on the soil is the column’s plus the footing and its backfill:

The resultant stays in the middle third, and the heavier edge, at 194.5 kPa, is within the 200 kPa allowed. At 2.40 m that edge would reach 225.9 kPa, and at 2.50 m 209.2 kPa, so the moment is what takes the footing from 2.35 m to 2.60 m.

Step 3: bearing capacity

For the bearing capacity, the effective width is $B' = 2.60 - 2 \times 0.0813 = 2.437$ m and $L' = 2.60$ m, so $B'/L' = 0.937$. With $c' = 0$ only two terms remain, and with no horizontal load the inclination factors are 1. For $\phi' = 30°$, $N_q = 18.40$ and $N_\gamma = 22.40$, and the overburden is $q = 18 \times 1.50 = 27.0$ kPa. The shape factors are $F_{qs} = 1 + 0.937 \tan 30° = 1.541$ and $F_{\gamma s} = 1 - 0.4 \times 0.937 = 0.625$, and the depth factor, with $D_f/B = 0.577$, is $F_{qd} = 1 + 2 \tan 30° \,(1 - \sin 30°)^2 \times 0.577 = 1.167$. Carrying full precision to the end:

The margin is wide because in sand the allowable pressure a report gives for a footing of this size is usually set by settlement, the next check.

Step 4: settlement

Rischio computes the elastic settlement at the centre of the base, with the load spread over the whole base, $q_0 = V/A = 163.7$ kPa:

Here $I_s = 0.512$ is Steinbrenner’s shape factor, for the 14.5 m from the surface down to $5B$ below the base, and $I_f = 0.745$ is Fox’s depth factor for $D_f/B = 0.577$. The 19.7 mm are within the 25 mm limit.

Rischio’s engine gives the same. For the model with $B = L = 2.60$ m, $D_f = 1.50$ m, $V = 1{,}106.9$ kN, $M_B = 90$ kN·m and the silty sand, it returns $e = 0.081$ m and $B' = 2.437$ m, $q_{max} = 194.5$ and $q_{min} = 133.0$ kPa, $q_u = 1{,}200.4$ kPa with $FS = 6.17$, and a settlement of 19.7 mm, the check closest to its limit. It also warns that the settlement leaves out consolidation. A sand drains as it is loaded, so its settlement is the immediate one computed here.

The calculator below runs the bearing check on the same engine. Choose a square footing 2.60 m wide at 1.50 m, a vertical load of 1,106.9 kN with a moment of 90 kN·m, and the sand (18 kN/m³, $c' = 0$, $\phi' = 30°$, no water table), and it returns the same $q_u$ and $FS$.

To keep the footing, try other sizes or get the calculation report with every step, model it in Rischio’s footing tool.

Step 5: punching shear, by hand

The concrete is checked with factored loads, $P_u = 1.2 \times 600 + 1.6 \times 300 = 1{,}200$ kN and $M_u = 1.2 \times 60 + 1.6 \times 30 = 120$ kN·m. The average net factored pressure is $q_{nu} = 1{,}200/6.76 = 177.5$ kPa. With 75 mm of cover and two layers of 16 mm bars, $d \approx 600 - 75 - 16 = 510$ mm, measured to the middle of the two layers.

$V_u/\phi V_c = 0.43$. For a square column the other two limits are larger, $0.17 \times 3 = 0.51$ and $0.083\,(2 + 40 \times 510/3{,}640) = 0.63$, so the 0.33 governs.

The column’s moment adds stress on the side it bends toward. ACI 318 transfers a share $\gamma_v = 1 - 1/(1 + \tfrac{2}{3}\sqrt{b_1/b_2})$ of it by eccentric shear on the perimeter, 0.40 for a square column, so the largest stress is

with $b_1 = b_2 = 0.91$ m and $J_c = d\,b_1^3/6 + b_1 d^3/6 + d\,b_2 b_1^2/2 = 0.276$ m⁴. That is about half of $\phi v_c = 0.75 \times 0.33 \times \sqrt{28} = 1.31$ MPa, and still under the 1.06 MPa left once ACI 318-19’s size factor applies ($\lambda_s = 0.81$ at $d = 510$ mm).

Step 6: one-way shear, bending and steel

With the moment, the net factored pressure runs from 136.5 kPa at one edge to 218.5 kPa at the other, and the overhang on the heavier side governs. The one-way section, at $d$ from the face of the column and 0.59 m from the edge, carries $V_u = 321$ kN. At the face, the 1.10 m overhang bends with $M_u = 325$ kN·m, which needs about 1,710 mm² of steel. The minimum, $0.0018 \times 2{,}600 \times 600 = 2{,}808$ mm², governs: 14 bars of 16 mm in each direction (2,815 mm²), about 190 mm apart.

With that steel, $\rho_w = 2{,}815/(2{,}600 \times 510) = 0.0021$, and ACI 318-19’s one-way check with $\lambda_s = 0.81$ gives $\phi V_c = 362$ kN against $V_u = 321$ kN. This is the check that holds the footing at 0.60 m. At 0.50 m, with its minimum steel, one-way shear would fail while punching still passed.

Worked example 2: a combined footing at a property line

Column A, 400 × 400 mm, has its outer face on the property line and carries 600 kN (400 dead, 200 live). Column B, of the same size, stands 4.50 m away, centre to centre, with 900 kN (600 dead, 300 live). The soil, the founding depth and the allowable pressure are those of the first example.

A footing centred on column A would cross the line. An isolated footing with column A at its edge would put the load far outside its middle third: on a footing 2.00 m wide, 0.80 m off centre against a limit of 0.33 m, so both columns go on one footing.

Step 1: place the resultant

Measured from the property line, the centre of column A is at 0.20 m and that of column B at 4.70 m:

Step 2: length for a uniform pressure

The footing starts at the line and its centroid goes under the resultant, so it is twice as long as $\bar{x}$:

It runs 1.10 m past the centre of column B.

Step 3: width

The thickness isn’t designed yet, so the footing and the soil over it are taken at an average of 20 kN/m³ over the 1.50 m, which is 30 kPa. That weight gets updated once the structural design sets the thickness.

With $B = 1.55$ m, the pressure is uniform at $1{,}500/(5.80 \times 1.55) + 30 = 196.9$ kPa, under the 200 kPa allowed.

Step 4: the structural design

Along its length the footing works as an upside-down beam, pushed up by the soil and held down by the columns. The factored loads are 800 and 1,200 kN. Both columns have the same ratio of dead to live load, so their resultant stays at 2.90 m and the soil pushes up $2{,}000/5.80 = 344.8$ kN per metre. The shear changes sign 2.32 m from the line, where the moment peaks at about 768 kN·m with tension at the top, so the main steel between the columns goes at the top. Past column B, the 1.10 m overhang bends the other way, with tension at the bottom. Across its width, the footing is designed like an isolated footing in a band under each column, and punching is checked around each column, on three sides for column A at the edge.

Common mistakes

• Sizing the footing with factored loads, or the concrete with service loads. Allowable pressures go with service loads, and the ACI 318 checks with factored ones.
• Leaving the moment out of the sizing. In the first example it takes the footing from 2.35 m to 2.60 m a side.
• Mixing a net allowable pressure with a gross load, which counts the soil over the footing twice or leaves it out.
• Founding on fill, topsoil or soil loosened by the excavation, which settles more than the report assumed.
• Checking punching and stopping there. ACI 318-19 made one-way shear stricter for members with little steel, and footings are such members.

Frequently asked questions

What is the difference between an isolated and a combined footing?

An isolated footing carries one column. A combined footing carries two or more on one slab, with its centroid under the resultant of their loads, and it is used where isolated footings would overlap or would cross a property line.

What are the five types of footings?

Isolated (pad or spread), strip (continuous or wall), combined, strap (cantilever), and mat or raft. The first four each carry a wall or a few columns, while a mat carries the whole building.

What is another name for an isolated footing?

Pad footing, spread footing, column footing or individual footing. In US practice, spread footing also covers strip and combined footings.

What is the difference between a spread footing and a continuous footing?

A continuous footing is a kind of spread footing: a strip under a wall, designed per metre (or foot) of its length. Used on its own, spread footing usually means the isolated footing under a column, designed for that column’s load.

What is the difference between a strap footing and a spread footing?

A strap footing is two spread footings tied by a beam that balances the eccentric one at a property line. A spread footing works alone, with its column at or near its centre.

Is a spread footing a deep foundation?

No. It is a shallow foundation: it bears on the soil just under its base, usually at a depth no greater than its width. Piles and drilled shafts are deep foundations, which carry the load down to stronger ground through their shaft and tip; pile foundation design covers them.

How far down do footings need to be?

As deep as the geotechnical report says: below the frost line, on undisturbed soil under any topsoil and fill, and below the seasonal movement of expansive clays. The IBC sets a floor of 12 inches (305 mm) below the undisturbed ground surface.

What are the disadvantages of spread footings?

They need competent soil near the surface. On soft or compressible ground they settle too much, or grow until a mat or piles make more sense. Separate footings can settle by different amounts, they resist uplift only with their own weight and the soil on them, and at a property line they turn eccentric.