BIZOMAT MAKEOS · Engineering
Tapered Pad Footing Check (Prismoidal Volume, Self-Weight, Bearing Pressure, Concrete Order)
For a column pad footing with a tapered top, how much concrete does it take, what does it weigh, and is the bearing pressure under it within the ground’s allowable pressure?
Check of a square or rectangular pad footing with a straight base block and a tapered (frustum) top: the volume of the taper by the prismoidal formula (as the prismoidal volume tool) plus the base block, the self-weight, the bearing pressure under the base from the column load and self-weight against your allowable ground pressure, the base area needed, and the concrete to order with a waste allowance.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Base length | mm | Length of the footing base. |
| Base width | mm | Width of the footing base. |
| Depth of the straight base block | mm | Depth of the vertical-sided block at the bottom. |
| Top length (at the column) | mm | Length of the flat top where the column or plinth sits. |
| Top width (at the column) | mm | Width of the flat top. |
| Height of the tapered part | mm | Height of the sloping part above the base block. |
| Loads and ground | ||
| Column load on the footing | kN | Load the column brings down onto the footing. |
| Concrete density | kg/m³ | Density of the concrete (about 2400 for reinforced concrete). |
| Allowable bearing pressure of the ground | kPa | Allowable bearing pressure of the ground, from site investigation. |
| Waste allowance on the order | % | Extra concrete to order for spillage and over-excavation. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Base length
- What it is
- The plan length of the footing at its base, the bottom of the straight-sided block that bears on the ground.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer base adds bearing area and lowers the bearing pressure.
- Get it right
- Use the size of the concrete base, not the excavation.
What this means: Base width
- What it is
- The plan width of the footing at its base, at right angles to the base length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider base adds bearing area and lowers the bearing pressure.
- Get it right
- Use the size of the concrete base, not the excavation.
What this means: Depth of the straight base block
- What it is
- The depth of the vertical-sided block at the bottom of the footing, below where the taper starts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A deeper block adds volume, self-weight and concrete to order.
- Get it right
- Use 0 when the taper starts right at the base with no straight block.
What this means: Top length (at the column)
- What it is
- The length of the flat top of the tapered part where the column or plinth sits.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The top must not be larger than the base, or the tool rejects the inputs.
What this means: Top width (at the column)
- What it is
- The width of the flat top of the tapered part, at right angles to the top length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The top must not be larger than the base, or the tool rejects the inputs.
What this means: Height of the tapered part
- What it is
- The vertical height of the sloping part, from the top of the straight block to the flat top under the column.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A taller taper adds volume, self-weight and concrete to order.
- Get it right
- Use 0 for a plain block footing with no taper.
Loads and ground
What this means: Column load on the footing
- What it is
- The vertical load the column brings down onto the top of the footing, from the structural design. The footing’s own weight is added to it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 10000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The bearing pressure rises in direct proportion to the total of load and self-weight.
- Get it right
- Enter it in kN and use the load case your engineer specifies for bearing checks.
What this means: Concrete density
- What it is
- The density of the concrete, from the concrete supplier or your design data. It turns the footing volume into self-weight.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 5000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2400 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in kg/m³; the tool converts it to weight with standard gravity.
What this means: Allowable bearing pressure of the ground
- What it is
- The ground pressure under the footing that the site can safely carry, from the geotechnical report or site investigation. The bearing pressure is compared with it.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0.000001 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower allowable raises the base area needed.
- Get it right
- Use the allowable value from the geotechnical engineer, not an ultimate value; kPa equals kN/m².
What this means: Waste allowance on the order
- What it is
- The extra concrete to order above the calculated volume to cover spillage, over-excavation and pump losses.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The order volume rises in proportion to one plus this share.
- Get it right
- Type the percentage itself. It affects the order volume only, not the bearing check.
Method and formulas
- Taper volume V = h (A₁ + 4A_m + A₂) ÷ 6 with the middle section from the averaged sides (as the prismoidal volume tool).
- Block volume = a₁ b₁ h_b; self-weight = volume × density × g.
- Bearing pressure = (P + self-weight) ÷ (a₁ b₁); base area needed = (P + self-weight) ÷ allowable pressure.
- Example: 0.63733 m³ of concrete weighing 15 kN; the ground carries 218.75 kPa.
Limitations
- Concentric vertical load; moments or horizontal loads make the pressure uneven.
- Reinforcement, punching shear and settlement need a structural design.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a pad for a column or machine leg
- Order concrete for tapered footings
- Check a footing for a heavier load
Who it is for
- Site engineers
- Plant engineers
- Builders
What you get
- Taper, block and total volume
- Self-weight and bearing pressure
- Base area needed and concrete to order
Interpreting the result
- Tapering the top saves concrete with little effect on the bearing pressure, which depends on the base area.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 66. Topic reference; no source tables or recommended settings are reproduced.
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