As per below method how to find Trapezoidal footing volume
In this method drive formula of trapezoidal footing as per drawing specification
As shown in Fig of trapezoidal footing. In this footing, two different parts show in fig.
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
Rectangle Cubic Area
Truncated Pyramid Area (V2)
One Cubicl = Six part of Truncated Pyramid
Truncated PyramidArea
= 1/6 A^{3}
= 1/6 (a-b) ^{3}
= 1/6 (a-b) (a^{2} + b^{2} +ab )
a-b = 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))
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.
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