How to calculate the volume of concrete in a trapezoidal footing

In this exclusive construction video tutorial, you will learn how to work out the quantity of concrete in trapezoidal footing.

Sloped footings belong to trapezoidal footings. Here, the top slope of 45 degree is retained from all sides. In the trapezoidal footing, less concrete is used. So, the cost of footing along with reinforcement is decreased significantly.

The trapezoidal footing is mainly applied where loads are asymmetrical. When the area of footing is fixed and the soil at the construction site is loose, the trapezoidal footing is ideal.

A trapezoid is a mixture of a cuboid and a truncated pyramid.

Trapezoidal footing = Cuboid + trancated pyramid.

In order to work out the volume of trapezoidal footing, it is required to measure the volume of a cuboid and a truncated pyramid.

If the size is in cuboid shape, the calculation can be done by multiplying length, breadth and height. The calculation for trapezoidal shape can be done with a special formula.

For lower base, the length of the cuboid is 1800 mm and breadth is 1800 mm. For upper base, the length of the cuboid is 900 mm and breadth is 900 mm. The height of the cuboid shape is taken as 200 mm and the height of the trapezoidal shape is taken as 400 mm.

Initially, you have to find out the volume of cuboid1 = Length x Breadth x Height

After putting all the values, we get 1.8 x 1.8 x 0.2 (after converting from mm to meter) = 0.648 m³

Now, the volume of trapezoidal shape will be calculated with the following formula :- h/3 {(A₁ + A₂ + √(A₁ x A₂)}

First, determine the value of A1 = 1.8 x 1.8 = 3.24 m² (lower base area)

Then, determine the value of A2 = 0.9 x 0.9 = 0.81 m² (upper base area)

After putting these values in the above formula, we get the following output :-
Volume = 0.4/3 {(3.24 + 0.81 + √(3.24 x 0.81)} = 0.756 m³
Now, add the volume of cuboid shape and the volume of trapezoidal shape.
So, total volume = 0.756 + 0.648 = 1.404 m³
So, the volume of trapezoidal footing = 1.404 m³

To get more clear information, go through the following video tutorial.

Video Source: ENGINEERING TACTICS