The trapezoidal footing formula is used to determine the volume of a trapezoidal footing from the respective drawing specifications. Here, the trapezoidal footing formula is explained and clarified with the help of an example.
Trapezoidal Footing Formula
As shown in figure-1 below, the trapezoidal footing is a combination two components:
Truncated Pyramid
Rectangular Cuboid
Fig.1. Trapezoidal Footing- Combination of the Rectangular cuboid and Truncated Pyramid
So,
The volume of trapezoidal footing = Sum of (Volume of truncated pyramid + Volume of Rectangular Cuboid)
Fig.2. Plan and Elevation of Trapezoidal Footing
1. The volume of the Truncated Pyramid is given by,
From figure-2,
ht = height of the pyramid
A1 = Area of the bottom surface of the pyramid
A2 = Area of the top surface of the pyramid
A1 = A x B
A2 = a x b
2. The volume of a cuboid is given by,
From figure-2,
A = Length of the cuboid
B = Breadth of the cuboid
hc = Height of the cuboid
Example - Calculation Using Trapezoidal Footing Formula
The trapezoidal footing formula can be explained with an example. Consider a trapezoidal footing arrangement as shown in figure-3 below.
Fig.2. Example of Plan and Elevation of Trapezoidal Footing
Here, a square trapezoidal footing is taken into consideration. Let a= 0.8 m and b = 0.8m.
From, the figure-2, A = 1.5m and B = 1.5m
Hence,
A1= A x B = 1.5 x 1.5 = 2.25m2
A2 = a x b = 0.8 x 0.8m = .64m2
ht = 0.3m
Therefore, from Eq.2 and substituting the respective values,
Vt = (0.3/2)( 2.25 + 0.64 + square root of ( 2.25 x 0.64))
= 0.15(2.89 + 1.2)
= 0.614m3
From Eq.3 and substituting the respective values
Vc = 1.5 x 1.5 x 0.2
= 0.45m3
From Eq.1,
Volume of Trapezoidal Footing V = Vt + Vc = 0.614 + 0.45 = 1.064m3
The formula can be used for trapezoidal footing which is either rectangle or square in dimension.
