Let us now calculate the volume of concrete in a staircase flight & landing as shown in the below drawings.

Let us calculate the concrete volume of the landing slab, steps, & waist slab separately for easy understanding.

**1. Landing slab:**

__Given data :__

Landing thickness = 200mm.= 0.2m.

Landing width = 0.9m.

Landing length = 1.0m.

**The concrete volume of the landing slab**

= [2nos.× length × width × thickness]

= [2nos. × 1m. × 0.9m. × 0.2m.]

= **0.36 cum.**

#### 2. Steps:

__Given data:__

No. of steps = 8 nos.

Width of the step = 1m. {length ( l ) }

Riser = 166.66mm. = 0.1667m. { height ( h ) }

Tread = 250mm. = 0.25m. { base ( b ) }

The individual step forms a triangular prism as shown in the above drawing.

The formula to calculate the volume of a triangular prism is [1/2 × b × h × l]

**The concrete volume of the total staircase steps**

= 8nos.× [ 1/2 × base × height × length ]

= 8nos. × [ 1/2 × 0.25m. × 0.1667m. × 1m.]

= 8nos. × 0.0208

= **0.1667 cum.**

#### 2. The waist slab:

__Given data:__

The thickness of the waist slab = 150mm = 0.15m.

Width of the waist slab = 1m.

Let us draw a triangle ABC, joining the two ends of the waist slab as shown above.

By Pythagoras theorem,

AC2=AB2 + BC2

From the staircase drawing,

The horizontal distance AB = 2m, &

The vertical distance BC

= [landing height + bottom landing thickness.]

= [1.3m + 0.2m.] = **1.5m.**

AC2 = 22 + 1.52

AC = √22 + 1.52

AC = √6.25

**Length AC = 2.5m.**** **

Now, **the concrete volume of the waist slab**

= [length × width × thickness.]

= [2.5m × 1m. × 0.15m.]

= **0.375cum**.

**The concrete volume of the staircase**

= [The volume of landing + the volume of steps + the volume of waist slab.]

= [0.36 cum. + 0.1667 cum + 0.375 cum.]

= **0.902 cum.**

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