Trapezoidal Footing Formula with Calculation

# Trapezoidal Footing Formula with Calculation 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

#### 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
• A3 =1/6 Truncated Pyramid Area

Truncated PyramidArea

= 1/6 A3

= 1/6 (a-b) 3

= 1/6 (a-b) (a2 + b2 +ab )

a-b = 2h

a2 = a x a = A1

b2 = b x b = A2

= 1/6 . 2h. (a2 + b2 +ab )

=1/3. h. (a2 + b2 +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 m3.

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 m3.

Volume of Trapezoidal Footing V = V1 + V2 = 0.675 + 0.695 = 1.37 m3

The formula can be used to get trapezoidal footing that’s either square or rectangle in dimension.

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