Volume of trapezoidal footing calculation with easy formula step-by-step

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The footing is the most important part of the structure. The footing is the section of the structure through which the overall load is transmitted to the soil.
 
In any structure to be stable, there must be a strong design of footing enough to carry the load of the superstructure. The superstructure is part of construction above the ground level. The construction below the ground level is known as the foundation.
 
There are different types of footing like step footing, pile footing, trapezoidal footing, etc. You can calculate the volume of a step up footing easily as it is a combination of the cuboid, You can calculate the volume of pile easily as it is cylindrical in shape.
 
So, in above footing volume can be calculated directly by using a simple formula and their structure are easy to understand.
 
But in the case of trapezoidal, it becomes somewhat hard to understand its structure and calculate its volume. Here i have given some simple step by step calculation of the volume of trapezoidal footing. Read it carefully for a better understanding of calculation. Let’s start.
 
How to calculate the volume of trapezoidal footing easily?
Fig:- Volume of trapezoidal footing
Tihe trapezoidal footing is a combination of cuboid at the upper part and truncated pyramid at the lower part of footing as shown in the figure above in part (1) and part (2) respectively.
 
So, to calculate the total volume of trapezoidal footing you have to calculate the volume of the cuboid and truncated pyramid and then add them together.
 
Let us assume the dimension of any trapezoidal footing as below
 
 For part one (Cuboid)
 
 Length (L) = 2 meter
 Breadth(B)= 1.5 meter
 Height (H)=  0.3 meter
 
For part two (Truncated pyramid)
 
:-Lower base
Length(L)= 2 meter
{Lower length of the pyramid will be equal to the length of cuboid)
Breadth(B)= 1.5 meter
{Lower breadth of the pyramid will be equal to the breadth of cuboid}
 
:-Upper base
Length(L’)= 0.5 meter
Breadth(B’)= 0.4 meter
 
And let the (H’) height of truncated pyramid (ie. Distance between upper base and lower base of the pyramid) be = 0.3 meters.
 
Don’t be confused in height of cuboid and pyramid. It may be different according to structure and design. Here i have kept the same value (as 0.3 meters) for easy calculation.
 
Now, let us move further stepwise as shown in the figure above
 
Also Read,
 
 

Calculation of volume of trapezoidal footing.

Step1:- Calculate the volume of Cuboid.
 
The volume of a cuboid is given as
,        ( V’) = (L X B X H) {see above for denotation of symbol}
                 = 2 X 1.5 X 0.3
                 = 0.9 cubic meter
 
Step2:- Calculate the volume of the Truncated pyramid.
 
The volume of the truncated pyramid is given as
,       (V”) =(1/3)[A’+A”+√(A’+A”)] X H’
Where A’ = Area of upper base of the truncated pyramid.
             A” = Area of the lower base of the truncated pyramid.
        H’ = Height of the truncated pyramid.
             So, A’ = (L’ X B’)
                       = 0.5 X 0.4
                       = 0.2 m^2
 
                   A” = (L X B)
                        = 2 X 1.5
                        = 3 m^2
 
Hence, putting the value of (A’), (A”) and (H’) in the above formula we get,
           (V”)= 0.397 cubic meter.
 
Step3:- Add (step1) and (Step2).
 
 The total volume of trapezoidal footing,
         V = V’ + V”
             = 0.9 + 0.397
             = 1.297 cubic meters.
 
Hence, In this way, you can easily calculate the total volume of trapezoidal footing in three steps.
 
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