How To Design a Cantilevered Staircase

Staircases are a lot of fun. That is, even though the design process is strictly regulated by the building code, it can be the perfect opportunity to flex your creative muscles. But how exactly do you design a cantilevered staircase? How do the stairs stay in place? And what do you need to take into consideration during the design phase?

We’ll tackle these questions by first having a look at the relevant building regulations, and then moving onto understanding the basic physics behind the cantilevered structure. This is where it gets a bit more technical – but don’t worry – we won’t get carried away with complex equations. We’ll only look at deflection and the basic stresses under expected loading conditions, i.e. under every day use.

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Figure 1 – Cantilevered Staircase

Drawings for the staircase assembly are available to download in DWG format from the link below.


BUILDING REGULATIONS

To set the scene, let’s imagine a typical London townhouse that is undergoing a substantial refurbishment, and you’ve been given the task to design a cantilevered staircase for it. Now, where would you start?

Well, before we get carried away with the detailed design work, the first thing to do is to familiarise ourselves with the relevant building regulations. Below is a table taken from The Building Regulations 2010 K showing the maximum and minimum dimensions for rise and going. As we are working on a residential project, we only need to concern ourselves with the regulations related to private stairs.

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Table 1 – Building Regulations (SOURCE: Building Regulations 2010 K)
1. RISE

Rise is the vertical distance between each step. With the above regulations in mind, we can determine how many steps are required to complete our staircase. The critical dimension that we need to know first is the difference between finished floor levels, also known as floor-to-floor dimension. These are marked as FFL (finished floor level) on the drawings. Figure 2 below shows the difference as 2850 mm.

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Figure 2 – Setting Out

To work out the number of risers, you need to pick a number that falls within the specified range (150 – 220 mm) and divide the floor-to-floor dimension with that number. Remember that we need a whole number here, so round it up to the nearest number if you end up with decimals. You can’t have half risers on your staircase. So, in this case, 2850 mm was divided by 190 mm, resulting in 15. This means that our staircase will have 15 steps, each with a rise of 190 mm.

2. GOING

Going is the horizontal distance between two stair nosings. Again, looking at the values specified by the building code, I’ve chosen to go with 280 mm. Usually you would end up trying different values, and then checking what pitch it gives you until you’re happy with the result. If the space at landings is limited, then you may need to have a shorter going – i.e. a steeper pitch. Landings are the floor areas where the stairs end at the top and bottom that, again, are specified in the building code. In this case, we have plenty of space at both landings, so we can stick with 280 mm going to give us the preferred pitch.

3. PITCH

Pitch is probably the most important planning parameter in staircase design. It determines how comfortable it is to walk up and down the stairs. As a rule of thumb, we can use something called the normal ratio to check our dimensions. This ratio states that twice the rise plus going should be between 550 mm and 700 mm. We can check this by using the values that we just worked out;

Normal Ratio: 2R + G = between 550 mm and 700 mm, so 2(190) + 280 = 660

To calculate the pitch, we will take the total rise (number of risers x rise) and divide it by total going (number of stairs x going). In other words, we’re calculating the tangent (tan = opposite/adjacent). The equation gives us the following;

(15 x 190) / (15 * 280) = 0.68

inverse tangent of 0.68 = 34 degrees.

The preferred pitch for comfort and safety is given as 30.58 – 35.26 degrees, so 34 degrees satisfies this criteria.

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Figure 3 – General Arrangement

DESIGN PRINCIPLES

Now that we know the basic dimensions, we are finally ready to start designing. Figure 3 shows a general arrangement drawing of the staircase design, based on the values we worked out earlier. If you look at the front elevation you’ll notice that we are using 900 mm as the width for the staircase. This dimension is as per the building code. The main principle here is to design one detailed stair assembly, and then repeat it 14 times to make up the whole staircase assembly. Simple enough, right?

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Figure 4 – Stair Detail Assembly

In the drawing above and the visual below you can see the detail for a single stair assembly. Couple of things you’ll notice right away; the steel frame inside the stair, and the fixing detail. When looking at the staircase, you’d think the steps are all made of timber. When in fact, there is a steel frame which is covered by 20 mm thick oak cladding panels. The steel frame is made from 3 lengths of 60 x 40 x 3 mm rectangular hollow section (or RHS) welded to a 8 mm fixing plate. The fixing plate is then bolted onto 3 pieces of M16 studding, which is what keeps the stairs fixed in place.

You could, of course, use different size sections or custom designed profiles if you wanted to. Another common method is to use an upside-down steel channel profile under the timber cladding. It all comes down to what available sizes and materials you want to use, and the budget of course. To help you keep the costs down just remember that the more common the material, the cheaper is it.

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Figure 5 – Stair Detail
RESIN ANCHORS

If you look at Detail B in Figure 4, you’ll see that the end of the stair is anchored into the masonry wall. This is what the word cantilever means – fixed at one end only. You may have heard the term floating stairs thrown around, which is what some people call cantilevered stairs. The ‘floating’ effect is achieved by hiding the fixings from sight. Here the fixings are hidden behind a plasterboard that is offset from the masonry wall.

In this case, we’ve used  lengths of M16 studding that are resin anchored into the masonry wall. Basically, this means drilling a hole into the masonry wall, filling it with resin, and then inserting the piece of studding into the hole. The stair assembly is then bolted onto these pieces of studding. To better demonstrate this point, I’ve included a link to an instruction video from a resin manufacturer below (outside content).

STRUCTURAL ANALYSIS

As the stairs are fixed only at one end, the weight of a person walking on the stairs will introduce significant asymmetrical loading to the wall and the fixings. It is absolutely crucial that these forces are taken into account. Usually, this is where a structural engineer would come in and perform calculations to check the integrity of the design before manufacture. If not, then you run the risk of making a staircase that feels bouncy when you walk on it, or even worse, something that ends up crumbling down under your feet!

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Figure 6 – Typical Loading Condition

Let’s take a moment and look at the above visual of a lady walking up the stairs to demonstrate a typical loading condition. It shouldn’t come as a surprise to anyone, that every time you walk on the stairs you are applying a load to the structure. To validate the integrity of our design, we need to check if our structure is sound enough to take that user load. To keep things simple, let’s focus only on the steel frame. Because, well, if the steel frame isn’t strong enough, then the rest won’t even matter.

So for now, let’s focus on the lady. When she walks up the stairs, she places one foot on each stair. We will simulate this load from the foot by introducing a point load at the end of the stair tread. So the user load will be the weight of our lady. We’ll use 85 kg for her weight – which may sound a bit high, but it’s a standard value often used in engineering problems so let’s just stick with that. To convert this weight into force, we simply apply Newton’s second law of motion (Force = mass x acceleration). We’ll round the answer up to 850 N. This force, labelled as Force-1, is then applied to the tip of the stair as shown in the table below.

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RESULTS

After running the simulation, we’re presented with a magical rainbow-coloured visual of the steel structure. Now, I should probably point out that the visual results are exaggerated – the steel doesn’t actually bend that much under the given load (Force-1). The colours demonstrate the area of deflection in the structure. Naturally, the area of least deflection (blue) occurs near the fixed end, while the maximum deflection (red) can be found at the end of the cantilever.

The maximum deflection worked out to be 0.9 mm. This means that when a person weighing 85 kg or less walks on the stair, the deflection is less than a millimetre. This is a result we can be happy with. Remember that the timber cladding will add to the stiffness, as will the glass balustrade that is fixed to the end of each stair assembly.

If we were to do an in-depth analysis, we’d also include strain & stress results to understand just where the vulnerable areas are in the design. Mainly, this would include looking at the Von Mises stress. Also, a vibration simulation is worth including in your analysis. Although, ideally, a prototype stair assembly would also be fabricated and tested in real life before installation.

CONCLUSION

So to sum up, it all starts with understanding the relevant building regulations then working out your rise, going and pitch before designing your stair assembly. Once the design is complete, you need to perform a structural analysis to make sure the structure is sound. Then all that is left is to build the staircase.

When it comes to construction of the staircase, the first task at hand would be to drill holes to the masonry wall for the resin anchors. But measuring the hole distances by hand would be a lengthy, painstaking task, not to mention prone to dimensional errors.

To make life easier, you’d be better off using a CNC cut plywood template (or similar) that gives you the exact hole locations to drill. By fixing the template to the wall, all you have to do is drill through the template holes. Once all holes are drilled, simply remove the template and start resin anchoring the studding. Once all studding is in place, you can start fixing the stair assemblies to place. Also you could have slotted holes on the fixing plate to give you a bit of tolerance. Alternatively, you could fix a stringer to the wall that the stairs locate to. As always, there are more than one way to go about it.

Another area where you can shine with creativity is the balustrade design. For instance, it’s fairly inexpensive to fabricate custom design steel balustrades from flat or round bar. You can find plenty of inspiration on the internet if you just do a quick search. In this project I chose to use a glass balustrade, with an oak handrail fixed to it. This is fairly standard design, and not the most creative way to go. So it’s definitely worth exploring other options. You can check out more handrail and stair designs on my staircase board.

If you are looking for any design help with your cantilevered staircase project, we’d be happy to offer our services. Feel free to drop us an e-mail at info@homedesigntutorials.com or use the form in our contact page. The drawings used in this post can be downloaded in DWG-format from the PayPal link below. The cost of drawings is £4.90.

REFERENCES & FURTHER READING

   

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