Concrete quantity calculation is easy if it is for a rectangular or square shape. When it is complex geometric shapes, then it seems like a daunting task.
Every Complex Geometric shape can be disintegrated into simple shapes. Here in the staircase concrete calculation, we are going to dismantle the staircase into simple elements and going to find the volume.
In case the brickwork is planned for tread and risers means, the calculation becomes easy, or else have to follow the below method to calculate the quantity accurately.
We need to calculate the concrete quantity for each component separately and have to sum it all to find the total volume of concrete.
From the drawing
Assumption – Riser as 6″ and Tread as 10″
Number of riser = Height of the flight / riser = 4′ 6″/ 6″ = 4.5/0.5 = 9 Risers
Number of Treads = Number of Risers – 1 = 9-1 = 8 Treads
If you are confused here, we have a separate post for Riser and Treads Calculation. Please check that.
The volume of Concrete (for one-step) = Area of one step x Length
If you look closely, the riser and tread form a right angle triangle. We know the formula for that (right angle triangle)
Area of One-step = 1/2 x riser x tread
The volume of Concrete (for one-step) = 1/2 x riser x tread x length
= 1/2 x 6″ x 10 ” x 4′ = 1/2 x 0.5 x 0.833 x 4 = 0.833 cubic feet.
Therefore, the total concrete volume required for steps on first flight = Volume x number of steps
= 0.833 x 8 = 6.66 Cubic Feet
The above calculation is only for one flight. We know the 2 flights are having the same measurements.
So Total Concrete = First Flight Concrete Volume x 2 = 6.66 x 2 = 13.32 Cubic Feet
Volume of Landing = Length X Breadth X Thickness = 8′ 6″ x 3′ x 6″ = 8.5 X 3 X 0.5 = 12.75 Cubic feet
From the pic, since it is the right angle triangle in order to find the inclined length we use the Pythagorean theorem.
Where, Inclined Length = √ (Horizontal Length)2 + (Height)2
Horizontal Length = Tread Size X Number of Treads = 10″ x 8 = 6.4 Feet
Inclined Length = √ (Horizontal Length)2 + (Height)2
= √ (6.4)2 + (4′ 6″)2 = √ (6.4)2 + (4.5)2 = √ 61.21 = 7.82 Feet
Volume of Waist Slab = Area of the slab x Thickness of the slab
Area of the slab = 4′ X 6.4 = 25.6 Sq.ft
Volume of Waist Slab = 25.6 x 6″ = 12.8 Cubic Feet
Staircase Concrete Volume = Steps Volume + Landing Space Volume + Waist slab volume
= 13.32 + 12.75 + 12.8 = 38.87 Cubic Feet
Staircase Concrete Volume = 38.87 Cubic Feet
Happy Learning 🙂
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View Comments
the height of the flight is given as 4 feet but while calculating no of risers you used flight height as 4'6". so based on the first given the no of riser would be 8 instead of 9 . so can u elaborate on which value actually should be used as the height of the flight, 4 feet or 4 feet and 6 inches?
Zion, Hope you all doing well. Just read this article today and interested to comment on the point you raised. I think the way used for counting the raiser is... Total hight from the base to the platform is correct. since there isn't mentioned it as flight height the rest is all ok.
Please correct me if i made it wrong
Adding a point on calculating the volume of waist slab i have observed that it has been used the value of horizontal length instead inclined length. May be a typo
Please correct me of i understood wrong