Trapezoidal footing is a type of footing that holds unequal loads from 2 columns when the heaviest load outside the column distance is restricted.
It is utilized when the area of footing is fixed and the soils at the site are loose soil.
1. Formula for Calculating Trapezoidal Footing Volume
As we know, Trapezoidal footing is made by the superimposing of a rectangular cuboid and truncated pyramid as shown in the figure below.
Now,
The volume of trapezoidal footing=Volume of Rectangular cuboid (V_{1}) + Volume of a truncated pyramid (V_{2})
= V1 + V2 …………….(Eq.1)
I. Volume of rectangular cuboid (V_{1});
= A * B * hc …………….(Eq.2 )
where,
A= length of the cuboid
B= Breadth of cuboid
hc= Height of cuboid
II. Volume of a truncated pyramid ( V_{2} );
= ht/3 * ( A_{1} + A_{2} + √(A_{1} +A_{2}) ) ……..(eq.3)
Where,
A_{1}= area of the bottom surface of the truncated pyramid
A_{2}= area of the upper surface of the pyramid
ht= height of the pyramid
From equations 1,2 and 3, we can write the final formula for calculating the volume of trapezoidal footing as shown below;
= V_{1} + V_{2}
= ( A*B*hc) + ht/ 3 ( A_{1} + A_{2} + (√ (A_{1}+A_{2})) )
Now, We are going to find out the volume of trapezoidal footing shown in Figure 3 above;
i. ht= 300mm = 0.3m
ii. hc= 300mm=0.3m (let us assume)
iii. Area of cuboid (A *B)= (2000 mm * 1600 mm) = 3.2 m²
iv. Area of the bottom surface of the pyramid(A_{1}) =3.2m²
v. Area of the top surface of the pyramid (A_{2})= (800*800) mm^{2 }=0.64m²
Now,
Total Volume= V_{1} + V_{2}
=( A*B*hc) + ht/ 3 ( A_{1} + A_{2} + (√ (A1+A2)) )
=(3.2 * 0.3) + 0.3/3 (3.2+0.64 +(√(3.2+0.64)))
=0.96 +0.57995
= 1.539959 m^{3}
The total volume of the trapezoidal footing in figure 3 = 1.5399m^{3}
3. Uses
Trapezoidal footing’s uses are as follows:
I. For residential houses and buildings.
II. When the load applied is uneven or unequal.
III. The soil at the site is loose.
4. Advantages
The advantages of trapezoidal footing are as follows:
a. Concrete uses are less.
b. Cheap to construct.
c. Less reinforcement is needed.
5. Disadvantages
The disadvantages of trapezoidal footing are as follows:
a. Good for small buildings only.
b. Chance of settlement.
c. Foundation subjected to pull out, torsion, moment.
6. References1. Content Filter & Authenticity Checking Team, The Civil Engineering (Our team checks every content & detail to maintain quality.) |
Read More: Continuous Footing
Read More: Shallow Foundation