## Doglegged Staircase:

The staircase provides access to the various floors of the building. It consists of a series of steps(flight) with the landing at appropriate intervals. Each step consists of a tread and riser. Tread is a flat part that you step on and riser is a vertical part between each tread in the staircase.

Fig1

## Components of the Staircase:-

*Waist slab:*Waist slab refers to a slab of the stair that is inclining from the floor slab to the landing slab.

*Flight*

*:*The series of steps between floor and landing.

*Landing:*The level of floor between flight.

*Step:*The step consists of Riser and tread.

*Tread:*

*The tread is the flat part that you step on.*

*Riser:*The riser is the vertical(up and down) part between each tread in the stairway.

## Finding the volume of concrete required for construction of the staircase:

### Important basics in the calculation:

Different shapes have different formulas for area:

The Area of rectangle = Length x BreadthArea of Triangle = 1/2 x Base x Height

For clear understanding, we are considering the below example of the doglegged staircase. Have a look at it. All the below-mentioned values in the calculation are considered from this image.

### Steps in the calculation of the volume of concrete required for the staircase:

Each component of the staircase is individually calculated.

- Waist slab concrete volume
- Steps Concrete volume
- Landing area concrete volume
- Handrail concrete volume

### 1. Waist slab concrete volume:

The waist slab is an inclined slab. The length of the waist slab is determined by using the Pythagorean formula.

(Hypotenuse)2 = (Opposite)2 + (Adjacent)2

Hypotenuse = √[(Opposite)2 + (Adjacent)2]

Hypotenuse = √[(1.5)2 + (3.0)2]

From the above fig, The length of waist slab (x) = 3.35m

The Volume of concrete required for waist slab=

From the figure, Waist slab is in the shape of a rectangle.

The volume of concrete required for waist slab = Area of rectangle x Depth

= Length x Breadth x Depth

The Concrete volume required for waist slab = 3.35 x 1.20 x 0.15 = 0.603m3

No. of Waist slabs = 2

Total concrete volume of waist slab in staircase = 2 x 0.603 = 1.206m3

### 2. Steps concrete volume:

From fig: width of tread = 0.30m, height of riser = 0.15m , Length of tread = 1.20m, No. of steps = 20

Steps are in the shape of triangle, therefore

The Volume concrete required for each step = Area of triangle x Depth

Volume of each step = 1/2 x Base x Height x Depth

Volume of concrete for steps = 1/2 x b x h x d = 0.5 x 0.15 x 0.3 = 0.0225

No. of steps = 20

Total volume of concrete required for steps = 20 x 0.0225 = 0.54m3

### 3. Landing concrete volume:

Landing is in the shape of the rectangle

The volume of concrete required for Landing = Area of rectangle x depth

= Length x Breadth x Depth

= 2.50 x 1.20 x 0.15 = 0.45m3

### 4. Handrail concrete volume:

Hand rail is in the shape of a rectangle, therefore

The volume of concrete required for handrail = Area of rectangle x depth

= Length x Breadth x Depth

= 3.35 x 0.10x 0.8 = 0.268m3

No. of Hand Rail = 4

Total concrete volume required for hand rail = 4 x 0.268 = 1.07m3

Total concrete volume required for construction of above staircase = waist slab concrete volume + Steps concrete volume + Landing concrete volume + Handrail concrete volume

Total volume of concrete required for staircase = 1.206 + 0.54 + 0.45 + 1.07= 3.26m3

If you wanted to find amount of cement, sand and aggregate required for above concrete volume. Refer : Concrete Mix design