As per below method how to find Trapezoidal footing volume
In this method drive formula of trapezoidal footing as per drawing specification
Trapezoidal Footing Formula
As shown in Fig of trapezoidal footing. In this footing, two different parts show in fig.


 Rectangle/ Square Cubic Area
 Truncated Pyramid Area

Trapezoidal Footing =
Rectangle/ Squared Cubic Area (V1)
Truncated Pyramid Area (V2)
The volume of trapezoidal footing
= Rectangle/ Square cubic area (V1) + Truncated Pyramid Area (V2)
V = V1 +V2
V = Volume of Trapzodial Footing .
V1 = Rectangle/ Square Cubic Area (V1)
Rectangle Cubic Area
 V1 = L x B x H
 L = Length of the cuboid = m. / mm.
 B = Breadth of the cuboid = m. / mm.
 H = Hight of the cuboid = m. / mm.
V2 = Truncated Pyramid Area (V2)
Truncated Pyramid Area (V2)
 V2 = (h/3) (A1 + A2 +√(A1 . A2))
 A1 = L1 x B1 = Sq.m /Sq. mm
 A1 = Truncated Pyramid Bottom Area
 A1 = L2 x B2 = Sq.m /Sq. mm
 A2 = Truncated Pyramid Top Area
 h = Height of Truncated Pyramid = M. / MM.
Derive Trapezoidal Pyramid Formula.
 V2 = (h/3) (A1 + A2 +√(A1 + A2))
One Cubicl = Six part of Truncated Pyramid
 V2 =Truncated Pyramid Area
 Cubic = 1/6 Truncated Pyramid area
 A^{3} =1/6 Truncated Pyramid Area
Truncated PyramidArea
= 1/6 A^{3}
= 1/6 (ab) ^{3}
= 1/6 (ab) (a^{2} + b^{2} +ab )
ab = 2h
a^{2} = a x a = A1
b^{2} = b x b = A2
= 1/6 . 2h. (a^{2} + b^{2} +ab )
=1/3. h. (a^{2} + b^{2} +ab )
=1/3 . h. (a + b + √(a.b))
=1/3. h. (A1 + A2 +√(A1.A2))
Example : Calculation Using Trapezoidal Footing Formula
The trapezoidal footing formula could be explained with an example. Consider a trapezoidal footing arrangement as shown in as per below fig.
Elevation of Trapezoidal Footing
Plan of Trapezoidal Footing
Here, a square trapezoidal footing is taken into consideration
Volume of Trapezoidal Footing (V) = V1 +V2
V1 = Squared Cubic Area
V2 =Truncated Pyramid Area
Let’s Find V2 ,
Top Square area = A2 = L2 x B2
= 0.720m x 0.70 m
=0.49 sq.mm
Bottom Square area = A1 = L1 x B1
= 1.6 m x 1.6 m
=2.56 sq.mm
V2 = (h/3) (A1 + A2 +√(A1 . A2))
= (0.5 / 3) x ( 0.49 + 2.56 + square root of ( 0.49 x 2.56))
= (0.1667) x (0.49 + 2.56 + 1.12)
= (0.1667) x ( 4.17 )
= 0.695 Cubic meter.
V2 = 0.695 m^{3}.
Let’s Find V1,
Square Cubic Area
V1 = L1 x B1 x H
= 1.5m x 1.5 m x 0.3 m
= 0.675 m^{3}.
Volume of Trapezoidal Footing V = V1 + V2 = 0.675 + 0.695 = 1.37 m^{3}
The formula can be used to get trapezoidal footing that’s either square or rectangle in dimension.
Like this post? Share it with your friends!
Suggested Read –
Add Comment