We will be learning the materials estimation for domes / sloped slab in this lecture. We will also do the calculation for a spherical dome like half spherical domes and segmental domes. Bear in mind that spherical dome is basically a half sphere. The calculation for a half sphere is pretty simple; but the calculation for a segmented sphere is quite complicated.
Volume of hollow sphere = 4π (R3 – r3)/3
Where R represents external surface radius and r represents interior surface radius.
Now lets us calculate the cement, sand, crushed stone, external surface paint and steel for half spherical dome. Concrete is 1:2:4 and steel is 1.5% as #4 bar.
R = 7.5 feet and thickness ‘T’ = 6 inches,
r = 7 feet and height ‘h’ = 7 feet
Then, volume of half spherical dome = 4π (R3 – r3)/3(2) = 4π ((7.5)3 – (7)3)/6 = 165.195 cft
Steel = 1.5/100 x 165.195 = 2.478 ft3
Multiply it with unit weight of mild steel which provides, 2.478 ft3 x 222.323 kg/cft = 55 kg # 4 bar
Total net RCC = 165.195 ft3 – 2.478 ft3 = 162.717 ft3
External surface paint = 4πR2/2 (as the sphere is half) = 4π (7.5)2/2 = 353.43 ft2
Therefore, total PCC work (1:2:4) = 162.717 ft3
We know that material = ratio of material/sum of ratio x Dry volume
Then, cement = 1/7 x 162.717 x 1.54 = 35.8 ft3
Furthermore, cement (in bags) = 35.8/1.25 = 29 bags
Sand = 35.8 x 2 = 71.6 feet3
Crushed stone = 35.8 x 4 = 143.2 ft3
Let’s us take another example. There is a segmental dome with thickness ‘T’ = 6 inches, the height ‘h2 = 4.5 feet, radius of full sphere ‘R1’ = 10 feet, interior radius ‘R2’ = 9.5 feet and the external height h1 = 5 feet.
Therefore, dome volume = πh12 (3R1 – h1) / 3 – πh22 (3R2 – h2) /3
Dome volume = π (5)2 (3 x 10 – 5) / 3 – π (4.5)2 (3 x 9.5 – 4.5) / 3 = 145.56 ft3
Video Source: SL Khan
