In estimating the amount of concrete in a given piece of work and the
quantities of materials required, the unit of measurement is usually the
cubic yard (27 cubic feet). The following examples will explain best the
method of determining the quantities required:
=Example 1.=--A wall 9 inches thick, 12 feet high, and 30 feet long
has a door opening 3 feet wide and 6 feet high, also a footing 18
inches wide and 9 inches deep. The concrete is to be mixed in the
proportions of 1:2:4.
The volume of the footing is found by multiplying together the
dimensions expressed in feet, thus, 1-1/2 × 3/4 × 30 = 33-3/4 cubic
feet. Similarly, the volume in the wall is 3/4 × 12 × 30, less the
door opening 3/4 × 3 × 6 = 256-1/2 cubic feet.
The total volume in footing and wall is 290-1/4 cubic feet = 10-3/4
cubic yards.
To find the quantity of cement, sand, and gravel, multiply the
amounts for 1 cubic yard, indicated in line 7 of Table 1, by
10-3/4, and it will be found that 65 sacks of cement, 4.83 cubic
yards of sand, and 9.56 cubic yards of gravel are necessary to
build the wall.
=Example 2.=--A pavement 27 feet long, 4 feet wide, and 6 inches
thick has a 5-inch base mixed in the proportions of 1:3:5 and a
1-inch surface mixed in the proportions of 1:2.
The volume in the base is 27 × 4 × 5/12 = 45 cubic feet = 1-2/3
cubic yards.
The volume in the top is 27 × 4 × 1/12 = 9 cubic feet = 1/3 cubic
yard.
Multiplying the quantities in line 9 of Table 1 by 1-2/3 and those
in line 2 by it is found that the base requires 7.74 sacks cement;
0.86 cubic yard sand; 1.43 cubic yards gravel; and the top requires
4.49 sacks cement; 0.33 cubic yard sand.
=Example 3.=[1]--A tank 9 feet inside diameter has walls 6 inches
thick and 4 feet high (above the floor). The floor is 6 inches
thick, the concrete is to be 1:2:4.
The volume in the floor is 10/2 × 10/2 × 22/7 × 1/2 = 39-2/7 Cubic
feet.
The area of the larger circle is 5 × 5 × 22/7 = 78-4/7 cubic feet.
The area of the smaller circle is 4-1/2 × 4-1/2 × 22/7 = 63-4/7
cubic feet.
The area of the wall, therefore, is 15 cubic feet and the volume is
15 × 4 = 60 cubic feet.
The total volume in the structure is 99-2/7 cubic feet or 3-2/3
cubic yards. Multiplying the quantities in line 7 of Table 1 by
3-2/3, it is found that the following material is needed: 22.14
sacks of cement; 1.65 cubic yards of sand; 3.27 cubic yards of
gravel.
[1] A practical rule in finding the area of a circle is to multiply
one-half the diameter (radius) by itself and the product by 22/7. In
finding the volume in the wall of a circular structure, such as a silo
or tank, the area of the circle formed by the inside circumference
is deducted from the area of the circle formed by the outside
circumference and the remainder is multiplied by the height.