Calculating Volume of Trapezoidal Footing: A Step-by-Step Guide with Formulas and Example

As per below method how to find Trapezoidal footing volume (Isolated Footing Formula) In this method drive formula of trapezoidal footing as per drawing specification

Trapezoidal Footing Formula (Trapezoidal Footing Volume Formula)

As shown in Fig of trapezoidal footing. In this footing, two different parts show in fig.

• • 1. Rectangle/ Square Cubic Area
    2. Truncated Pyramid Area

Trapezoidal Footing =

Rectangle/ Squared Cubic Area (V1) 

Truncated Pyramid Area (V2)

 

The volume of trapezoidal footing  (Footing Calculation)

= Rectangle/ Square cubic area (V1) + Truncated Pyramid Area (V2)

V = V1 +V2  

V = Volume of Trapzodial Footing.(Area of Trapezoidal Footing / Trapezoidal VolumeFormula)

V1 = Rectangle/ Square Cubic Area (V1) 

Rectangle Cubic Area

V1 = L x B x H

• 1. L =  Length of the cuboid = m. / mm.
  2. B = Breadth of the cuboid = m. / mm.
  3. H = Hight of the cuboid = m. / mm.

V2 = Truncated Pyramid Area (V2)

Truncated Pyramid Area (V2)

V2 = (h/3) (A1 + A2 +√(A1 . A2))

1. 1. A1 = L1 x B1 = Sq.m /Sq. mm
   2. A1 = Truncated Pyramid Bottom Area
   3. A1 = L2 x B2 = Sq.m /Sq. mm
   4. A2 = Truncated Pyramid Top Area
   5. h = Height of Truncated Pyramid = M. / MM.

Derive Trapezoidal Pyramid Formula.(Trapezoidal Formula)

V2 = (h/3) (A1 + A2 +√(A1 + A2))

One Cubicl  =  Six part of Truncated Pyramid

V2 =Truncated Pyramid Area

• 1. Cubic = 1/6 Truncated Pyramid area
  2. 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.

FAQ: Volume Calculation for Trapezoidal Footings

What is a trapezoidal footing?

A trapezoidal footing is a type of foundation structure that has a trapezoidal shape when viewed from the top. It is commonly used to support columns or walls in construction projects.

How do you calculate the volume of a trapezoidal footing?

The volume of a trapezoidal footing can be calculated using the formula: V = V1 + V2, where V1 represents the volume of the rectangular or square portion and V2 represents the volume of the truncated pyramid portion.

What are the formulas involved in calculating V1 and V2?

1. V1 (Volume of Rectangle/Square Cubic Area): V1 = L x B x H, where L is the length, B is the breadth, and H is the height of the rectangular or square portion.
2. V2 (Volume of Truncated Pyramid Area): V2 = (h/3) (A1 + A2 + √(A1 x A2)), where h is the height of the truncated pyramid, A1 and A2 are the bottom and top areas of the pyramid, respectively.

Can you provide an example calculation?

Sure! Let’s consider a trapezoidal footing with dimensions provided in the article: L1 = 1.5m, B1 = 1.5m, H = 0.3m, L2 = 0.72m, B2 = 0.7m, and h = 0.5m. Plugging these values into the formulas will yield the volume of the footing.

Are there any specific units to be used in these calculations?

The units used in the calculations should be consistent. Typically, measurements are provided in meters (m) or millimeters (mm) for length, breadth, and height.

What if my trapezoidal footing has different dimensions?

The formulas provided can be applied to trapezoidal footings of various dimensions. Simply substitute the given lengths, breadths, and heights into the formulas to calculate the volume accordingly.

Is there any practical application for this calculation?

Yes, calculating the volume of trapezoidal footings is essential for estimating the amount of concrete needed for construction projects accurately. It helps in budgeting and planning materials effectively.

Can the same method be applied to other types of footings?

While the specific formulas may vary, similar principles can be applied to calculate the volumes of other types of footings, such as rectangular, square, or circular footings. Adjustments to the formulas may be necessary based on the geometry of the footing.