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  

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
  • 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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