Staircase calculations are the most crucial step for the correct dimensioning of the vertical circulation of your project, which usually makes many professionals anxious. To make your life easier, read on and learn all the necessary steps to safely and efficiently scale your staircase, as well as some essential tips!

TYPES OF STAIRS

Even though it is a fixed element of circulation, the staircase can play a prominent role in the design proposal of the building, where we can explore its format and its interface with the project.

Staircases usually occupy a significant space, so working with different formats can be a solution that, besides being efficient, provides greater harmony with the proposed use of the areas planned in the project.

Let's get to know the most common formats and which one will best meet the needs of your work.

• Straight Staircase is the most straightforward format, connecting one level to another, where the height and intermediate level may be necessary.
• L-shaped Staircase – also widely used, starting with a flight of steps and changing its path by 90 °, a shape that resembles an L, which is the reason for its name.
• U-shaped Staircase – also widely used, starting with a flight of steps and changing its path by 180 °, with a shape similar to a U, which gives it its name.
• Circular / spiral staircase – one of the formats that occupies less space since its steps are distributed around a central axis.

Another essential characteristic is that in formats where we have a change of direction, it is common to use fan-shaped steps, also known as winding or turned staircase, which usually reduces the space occupied by the stairs.

They are steps, the so-called winders, that have different widths between the right and the left side - very common in circular or spiral stairs, but they can also be applied to L or U stairs.

Winding staircases must follow NBR 9077 – Emergency exits in buildings, where the smallest side of the fan in the step must be equal to or greater than 15 cm.

Even with this variety of formats, it is essential to note that the calculation for the correct dimensioning of a staircase is the same.

After all, on every staircase, regardless of the shape, we have the same essential elements.

But what elements are these? Let's explore them below!

STAIR CALCULATION: WHAT ARE THE MAIN ELEMENTS?

A STAIR CALCULATION of vertical circulation for different levels, allowing access between them.

The following components give the basic structure of a staircase:

• Tread – the horizontal surface where we step up or down the stairs;
• Riser – vertical component that separates one step (tread/step) from the other;
• Nosing – protruding edge of the step;
• Flight – set of steps between two levels or levels, not exceeding 16 steps and not exceeding 2.90 m in height;
• Landing – horizontal resting surface, interspersed between two flights of stairs and must be at least three steps deep;
• Handrail – element for hand support when going up or down the staircase;
• Railing – vertical component installed along the stairway, serving as protection to prevent accidental falls.

For the staircase to be used safely, we need to take some precautions - especially in the dimensioning of the steps - in this case, the tread and the riser-to perform the correct calculation of the staircase.

HOW TO DO THE STAIR CALCULATION?

The calculation of a staircase is not carried out arbitrarily. It is necessary to follow technical criteria for its development, ensuring that the staircase is safe and comfortable.

We must consider some important information for the correct dimensioning of a stair:

• The height of the steps (risers) must be constant throughout the stairway;
• The minimum width of a private-use staircase is 90 cm;
• The stairs-to must guarantee a free height of 2.00 m or more;
• Each flight of stairs must have a maximum of 16 steps or 2.90 m in height;
• A landing must be at least three treads wide, never less than the width of the stairs.

To calculate the height of the risers and the depth of the treads, we need to use Blondel's formula.

BLONDEL’S FORMULA

Seeking to design a safe and efficient staircase, Frenchman Nicolas François Blondel developed an efficient calculation for the ideal dimensioning of a staircase.

Blondel observed between 63 cm and 64 cm. However, an efficient, every 1 cm of step height, the step decreases by 2 cm when he comes across a step.

Following this criterion, Blondel stipulated that the sum of the height of two steps (risers) plus one tread is equal to the variation of one step, where the ideal dimension is from 16 cm to 18 cm for the height of the riser and a minimum of 25 cm to the tread.

However, we must take into account the issue of accessibility, which is governed by NBR 9050.

STAIR CALCULATION ACCORDING TO NBR 9050

The NBR 9050, a brazilian norm, establishes criteria and parameters for accessibility to buildings by the most significant possible number of people, regardless of age, stature, or mobility limitation.

According to the norm, we must use Blondel's formula, but we must use values within a result range, where we have a slight adjustment of the formula.

We understand then that the result should be between 0.63 m and 0.65 m.

But the result must meet the following range:

• The step going (G) must be between 28 cm and 32 cm.
• The step height (H) must be between 16 cm and 18 cm.

Maybe  with a practical application this concept could be more easily understood. Check out the following topic below.

CALCULATION EXAMPLE - 2.85 m DIFFERENCE

Assuming that we must overcome a difference of 2.85 m, we need to find out the number of steps and the dimensions of the treads and risers. 

According to NBR 9050, the maximum step height (riser) is 18 cm. Taking the amount of the gap to overcome and dividing by the maximum height of the riser we have:

It is very common to obtain a decimal number, which implies rounding the result to 16 risers.

However, this impacts the total height. After all, 16 risers of 18cm give us a total of 2.88m in height. To solve this, we will preserve the 16 steps and recalculate the height of the risers.

The process is simple, just take the height value (2.85m) and divide it by the result obtained (16 steps).

With the new result for the riser value, we have the information needed for Blondel's formula and obtain the tread dimension.

With the new result for the riser value, we have the information needed for Blondel's formula and obtain the tread dimension.

In addition to a properly sized staircase, we need to work with quality models in our project, but there is no need to make configurations or even enter formulas. You can count on Blocks Revit, which offers access to a high-quality library and updates regularly.

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HOW DO I CALCULATE A STAIRCASE IN REVIT?

In Revit, staircases are system families. That is, they cannot be saved to external files, but you can copy from one file to another or duplicate an existing stair family and customize.

Stair calculation in Revit is a straightforward process since the adjustments are effortless.

In the upper toolbar Architecture, we have the Circulation panel. Inside it, we have access to the Stair tool. 

Clicking on the Stair tool, we will go to the Properties panel to click on Edit type.

Here, you can select the Family and the Stair Type you want to set the stair calculation. I'm going to use the mounted stair family and Duplicate the family.

I will name it NBR 9050 and click OK.

In the Type properties window, we will make the necessary adjustments to correct our staircase within the Calculation rules field. In the Calculation rules field, click Edit.

In the Stair Calculator window, we can make the necessary adjustments, but we need to activate the Use stair calculator for the slope calculation field.

In this window, we can make the necessary adjustments for the stair to calculate according to Blondel's formula. Still, as we saw earlier, we must also consider the information present in NBR 9050.

The process is quite simple. Let's start with Blondel's formula, which according to NBR 9050, is:

We know then that we must multiply two steps (in Revit, as Elevation) and add to the tread value (in Revit, as Depth). With that, we have a value of 0.65 m.

Then we must adjust the value range for a valid calculation result, which is the interval between 0.63 and 0.65 m, and which we must fill in as follows:

• Maximum result for stair calculation: 0.65;
• Accurate result for staircase calculation: automatic;
• Minimum impact for stair calculation: 0.63;

Once the adjustments are complete, we can click OK.

The window will close, and we will return to the Type Properties window. Here we can finalize the adjustments in the Calculation rules field.

According to NBR 9050, the result range for the riser and the tread must be:

• The tread (G) must be between 28cm and 32cm.
• The riser (H) must be between 16cm and 18cm.

So let's fill in the fields as follows:

• Maximum riser height: 0.18;
• Minimum tread depth: 0.28.
• Minimum throw width: controls the width of the stairs, can be changed later.

All done! We have a family of stairs configured to meet Blondel's formula and NBR 9050.

You can still customize the staircase, changing all its characteristics according to your need, and it will still be dimensioned correctly!

CONCLUSION

A properly sized staircase offers the customer practicality, comfort, and safety, which can play a significant role in the building's design even though it is a fixed element of circulation.

Every professional must know the main types of stairs and their elements, dimensioning them correctly and safely, in addition to following the current technical standards.

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