# Calculation of Concrete Quantity for Staircase

We will discuss about the calculation of concrete quantity for staircase and also find out the volume of waist slab along with the number of risers and the number of tread in staircase. We will also try to look into what are incline length, horizontal length, flight height and landing in staircase.

### What are the different parts of a Staircase?

The different parts of a staircase include riser, tread, landing, horizontal length, step, flight and inclined length.

Staircase: A staircase is essential in a building if one has to go from a lower floor to a higher floor. The staircase consists of components such as the riser, tread, flight, landing, etc.

Tread: The tread is the horizontal portion of a staircase. It is the area where one places their foot to climb the next step.

Riser: Vertical part of a stair.

Step: Step is the series of vertical risers and horizontal tread.

Flight: A series of steps excluding the platform makes a flight. A building staircase generally consists of two flights and a landing.

Waist slab: Inclined length of staircase.

### Calculation of Concrete Quantity of a Staircase

First we have to calculate the volume of all steps

Dimension given

Height of building: 10 ft

If each flight have equal height

Height of landing: 10/2’=5’

Height of one flight: 5’

Riser: 6’’=6’’/12= 0.5 ft

Tread: 10’’=10’’/12= 0.833’

No of riser= height of flight/ 1 riser height

Number of riser: 5’/0.5=10

Number of tread= (riser-1)=10-1=9

Since number of tread is equal to the number of steps

No of steps= 9

One step length= 4 ft

Volume of all steps in a flight= ½*riser*tread*length of step* no of steps

½*0.5’’*0.833*4*9= 7.497cft

Volume of step in one flight is therefore 7.497cft

### Calculate Volume of Waist Slab in Staircase

To find the volume of waist slab in staircase we must find the horizontal length of the waist slab and also the inclined length of it.

Horizontal length= tread* no of steps

Horizontal length= 0.833*9=7.497’

Therefore, inclined length of waist slab= √(5*2+7.497*2)

= 9.012 feet

Volume of waist slab= incline length of each slab* length of step* thickness of waist slab

Thickness of slab= 6’’= 6’’/12= 0.5’

Volume= 9.012’* 4’* 0.5’= 18.024 ft

Volume of waist slab= 18.024ft

### Calculate Volume of One Flight in Staircase

Volume of one flight is equal to sum of volume of all steps in one flight and volume of waist slab

Volume of one flight= volume of step+ volume of waist slab

= 7.497+ 18.024

=25.521 cft

Therefore, Volume of two flights= 25.521*2 = 51.042 cft

### Calculation of Volume of Landing

Length= 8.5 ft

Thickness= 6’= 0.5’

Breadth= 4 feet

Volume of landing- L*B*T

Volume of landing= 8.5’*4’*0.5’= 17cft

### Calculation of Total Volume of Staircase

Total volume= volume of two flights + volume of one landing

Total volume= 51.042+ 17= 68. 042 cft

Therefore, total concrete volume of staircase is 68.042 cft.

### Calculation of Wet Volume and Dry Volume of Concrete

Wet volume= 68.042 cft

Dry volume is increased by 54% in concrete reinforcement. Therefore, a cofactor of 1.54 is added in wet volume to calculate dry volume

Dry volume= 68.042*1.54=104.78 cft

The mix ratio of concrete reinforcement is 1:1.5:3 in which one part is cement, 1.5 part is sand and 3 part is aggregate

Total ratio= 1+1.5+3= 5.5

### Cement Required for Construction of Stairways

In mix ratio cement is 1 part of 5.5

Volume of cement= 1/5.5* dry volume

Volume of cement= 1/5.5* 104.78 cft

Volume of cement= 19.05 cft

Volume of 1 bag cement = 1.226cft

No of bags of cement= 19.05/ 1.226

No of bags of cement= 15. 538 bags

### Calculation of Sand Quantity for Staircase

Mix ratio quantity of sand is 1.5 and total ratio is 5.5

Volume of sand= 1.5/5.5* 104.78

Volume of sand= 28.57 cft

### Calculation of Aggregate Quantity of Staircase

Mix ratio quantity of aggregate was 3 and total ratio is 5.5

Volume of aggregate= 3/5.5*104.78

Volume of aggregate= 57.15 cft

### Quantity of Steel Required for Staircase Construction

0.5% to 0.1 percent of steel reinforcement used in slabs from which we have taken about 0.75 % of steel reinforcement of dry volume of concrete

Density of steel= 7850 kg/m3

1m3= 31.315cft

Weight of steel= volume* density

Steel quantity= (0.75*140.78*7850)/ (100*35.315)

Weight of steel= 174.68 kg