How To Calculate Steel Quantity For Staircase

In this post, you’ll learn how to calculate the required steel quantity for a staircase.

This is the easy method I have found so far.

And it’s a 5-step process.

Before discussing the process, let’s see…

What Is A Staircase?

A staircase is a set of stairs that gives people an easy way to move through the floors of a building. It looks like the image below:

This type of stair is called a dog-legged staircase.

And, the plan of this staircase looks like this:

Now, let’s see…

How To Calculate Steel Quantity For A Dog-legged Staircase?

Let’s say we have the following drawing of a staircase:

And the section of the staircase is:

Now you can easily calculate the required steel quantity.

For that, you just need to go through the following five steps:

• Step-1: Calculate steel quantity for Waist slab-1
• Step-2: Calculate steel quantity for Waist slab-2, and
• Step-3: Calculate steel quantity for Landing
• Step-4: Calculate steel quantity for steps, and
• Step-5: Summarise all the bars

Let’s see how to…

Step-1: Calculate The Steel Quantity For Waist Slab-1

The reinforcement details for the waist slab-1 is:

Here, 1-4 marked bars are main bars, and 5-7 marked bars are distribution bars.

If we see the main bars in a linear diagram it’ll look like the image below:

Let’s…

Calculate Steel Quantity For The Bar (1)

For that:

First, Get The Length Of A Bar

As you can see, the inclined length isn’t given in our drawing.

But we can calculate that from the plan and the section.

If we express that as linear, it’ll look like:

Now using the Pythagorean theorem:

The inclined length is,

= √{(5′)²+(7½′)²}

= 9 feet.

Now we can calculate the length of the bar.

And the formula is,

= Lapping + L + 9D

Here,

• Lapping is 40D
  = 40 × 10
  = 400 millimeter
  = 16″ or 1.33′

[NOTE: You should check your structural notes for the lap length. We assumed here as 40D where D is the diameter of the bar.]

• L (inclined length) = 9 feet.

• Hook length = 9D
  = 9 × 10
  = 90 millimeter
  = 3.6″
  = 0.3′

So the length is,

= 1.33′ + 9′ + 0.3′
= 10.63′
Say, 11 feet.

Next, Get The Required Number Of Bars

The formula is,

= (Width of waist slab ÷ spacing of bars) + 1

Here,

• Width of the waist slab = 4′
• Spacing of bar = 4” or 0.33′

So the required numbers are,

= (4′ ÷ 0.33) + 1
= 13.12
Say, 14 nos.

Finally, Calculate The Required Steel Quantity for the bar (1)

The formula is,

= Length of a bar × Number of bars

= 11′ × 14

= 154 feet.

Similarly,

Calculate The Steel Quantity For The Bar (2)

For that:

First, Get The Length Of A Bar

Here,

The length of the bar is,
= L/3 + 9D
= 9/3′ + 0.3′
[9D is the hook length which is 0.3′. We calculated this above.]
= 3.30′
Say, 4 feet.

Next, Get The Required Number Of Bars

The number of bars (2) is the same as the number of bars (1) as the width of the waist slab is the same.

That is 14.

Finally, Calculate The Required Steel Quantity for The bar (2)

The formula is,

= Length of a bar × Number of bars
= 4′ × 14
= 56 feet.

And then,

Calculate The Steel Quantity For Bar (3)

For that:

First, Get The Length Of A Bar

Here,

The length of the bar is,

= 9D + Width of landing + L/3

= 0.3′ + 4′ + 9/3′
= 7.3′
Say, 8 feet.

Next, Get The Required Number Of Bars

The required number of bars for bar no (3) is the same as bar no (1) as the width of the waist slab is the same.

That is 14.

Finally, Calculate The Required Steel Quantity For The Bar (3)

As you know, the formula is,

= Length of a bar × Number of bars
= 8′ × 14
= 112 feet.

Similarly,

Calculate the Steel Quantity For The Bar (4)

For that:

First, Get The Length Of A Bar

Here,

The length of the bar is,

= 9D + Landing’s width + Beam’s width + Lap length

= 0.3′ + 9/3′ + 10″ + 1.33′
= 5.46′
Say, 6 feet.

Next, Get The Required Number Of Bars

The required number of bars for Bar (4) is the same as for Bar (1) as the width of the waist slab is the same.

That is 14.

Finally, Calculate The Required Steel Quantity For The Bar (4)

And, the formula is,

= Length of a bar × Number of bars
= 6 × 14
= 84 feet.

So far, we have calculated all the main bars.

But we also have distribution bars in the waist slab-1.

And, they are marked as (5), (6), and (7).

So, Let’s…

Calculate The Steel Quantity For Distribution Bars.

For that:

First, Get The Length Of A Distribution Bar

Look, The length of a distribution bar for (5), (6), and (7) is the same.

That is the width of the waist slab-1 which is 4 feet.

Next, Get The Required Number Of Bars

And the formula is,

= (Length ÷ spacing) + 1

So,

For bar (5):

Here,

• The length = L/3 = 3 feet
• Spacing = 6″ or 0.5′

So, the number of bars,

= (3′ ÷ 0.5′) + 1
= 7 nos

For bar (6):

Here,

• The length = L = 9 feet
• Spacing = 6″ or 0.5′

So, the number of bars,

= (9′ ÷ 0.5′) + 1
= 19 nos

For bar (7):

Here,

• The length = L/3 = 3 feet
• Spacing = 6″ or 0.5′

So, the number of bars,

= (3′ ÷ 0.5′) + 1
= 7 nos

So, the total required number of distribution bars in the waist slab-1,

= 7 + 19 + 7
= 33 nos.

Finally, Calculate The Required Steel Quantity For Distribution Bars

The formula is,

= Length of a bar × Number of bars
= 4′ × 33
= 132 feet

So, the required steel quantity for waist slab-1 is,

= 154+56+112+84+132
= 538 feet.

With this, we have just calculated the steel quantity for waist slab-1.

Now, Let’s…

Step-2: Calculate The Steel Quantity For Waist Slab-2

The reinforcement details for the waist slab-2:

As you can see, all the bars in waist slab-2 are the same as waist slab-1. So, the required steel quantity will be the same.

That is,

= 538 feet.

Step-3: Calculate The Steel Quantity For Landing

Look, all the main bars of the landing have been calculated with waist slab-1 and waist slab-2.

We just need to…

Calculate The Distribution Bar Of The Landing

For that:

First, Get The Length Of A Bar

As the length of the landing is 8′-5″. So the length of a bar is 8′-5″ or 8.42′.

Next, Calculate The Number Of Bars

The formula is,

= (width ÷ spacing) + 1
= (4′ ÷ 6″) + 1
= 9 nos. [6″ = 0.5′]

Finally, Calculate The Required Steel Quantity

The formula is,

= Length of a bar × Number of bars
= 8.42′ × 9
= 75.78
Say, 76 feet.

Step-4: Calculate The Steel Quantity For Steps

Keep in mind that reinforcement in steps sometimes isn’t used.

If used, it’ll look like this:

So,

Calculate The Steel Quantity For Steps

For that:

First, Calculate The Number Of L-shape Bars For A Step

The formula is,

= (Width of the step ÷ Spacing of bars) + 1
= (4′ ÷ 6″) + 1
= 9 nos. [6″ = 0.5′]

Next, Calculate The Length Of A L-shape Bar

The length of an L-shape bar is,

= Tread + Riser
= 10″ + 6″
= 16″ or 1.33′

After That, Calculate The Required Steel For One Step

The formula is,

= (Number of L-shape bar × Length of an L-shape bar) + Length of the nose bar
= (9 × 1.33) + 4′
[Length of nose bar is same as the width of waist slab]
= 15.97′
Say, 16 feet.

Next, Get The Number Of Steps

The formula is,

= Height of the floor ÷ Height of riser

= 10′ ÷ 6″
= 20 nos. [6″ = 0.5′]

Finally, Calculate The Steel Quantity For All Steps

The formula is,

= Number of steps × Steel quantity for a step
= 20 × 16′
= 320 feet.

Now,…

Step-5: Summarize All The Steel Quantity

As we’ve calculated above, the required steel quantity for:

• Waist slab-1: 538 feet
• Waist slab-2: 538 feet
• Landing: 76 feet
• Steps: 320 feet

So total steel quantity is,

= 538+ 538 + 76 + 320
= 1472 feet.

If you want to convert this steel quantity into kilograms, use this formula:

= Length of bars × Unit weight of the bar
= 1472 × 0.19
[Here, all the bar size is 10mm. And we know 10mmØ is 0.19 kilo/ft]
= 279.68 kilograms.
Say, 280 kilograms.

Read More: How To Calculate The Unit Weight Of Steel Bars

Conclusion

As you can see, I didn’t consider the concrete clear cover during the steel calculation. You actually don’t need to consider that to find the required steel quantity.

Moreover, you need to add some extra steel. So that you don’t run short of steel quantity during construction.

Editor’s Note: This post was originally published in Feb 2021 and has been updated for accuracy and comprehensiveness.

Your Turn:

How much extra steel do you add to the calculated steel quantity for purchasing?
Please share your experience in the comments below…