**Introduction**

One of the advantages of using spiral stairs in structures is to maximize space. Besides these, they also provide good aesthetic looks. The functional design of spiral staircases involves the determination of the type, shape, material, structure, location, and correct layout of staircases. Based on materials, spiral staircases can be made of wood, steel, or reinforced concrete. Based on structural configuration, spiral stairs can be categorized as:

1. Circular,

2. Square, and

3. Helical

The circular configuration (Figure 1) is usually the most popular as it occupies less area when compared to other configurations and also ensures savings on cost and installation time. Sometimes, it can be confined within 1.2 m diameter. The structure comprises a central support post that develops vertically where cantilevered steps are inserted. In this post, I will show how to carry out the functional and structural design of a spiral staircase.

**Functional Design**

The determination of ideal staircase dimensions considers four important factors viz

**1.** **Relationship between risers and treads**

The formula provided by Francis Blondel has been the most popular. It states thus; 2R + T = 620…640 mm, where R = riser height and T = thread length.

**2.** **The distance between floors of the staircase:** This may normally depend on the headroom of the structure. However, the minimum should be 2.15 m.

**3.** **The angle of rotation:** This depends on the origin and insertion of the stairs.

**4.** **The number of steps:** To determine the number of steps, it is important to know the length of the staircase and the diameter. The diameter depends on the radius. The minimum radius is 700 mm. However, 800 – 900 mm are preferred.

The length of the staircase can be determined by the expression;

(π x R x α)/180

Where,

R = radius of stair; α = angle of rotation.

The irregularity of the shape of the staircase, as it approaches the central post, affects the point of application of the calculation of the steps. The **Useful line** principle is normally used. The useful line principle assumes that the person climbing the stairs walks at usually 2/3 from the centre. This principle is normally applied to the length of the steps.

**Example**

If a spiral staircase would be built in 900 mm radius and 3200 mm height determine the other dimensions of the staircase.

If it is assumed that the staircase will stop (insertion) at the point where it would start (origin), the angle of rotation would be 360^{0}.

Length of staircase, L = (π x 900 x 360)/180 = 5655 mm

Using the **useful line** principle, (2/3) x 5655 = 3770 mm would be where people would step on the stairs.

Using an ideal riser of 170 mm, the number of steps = 3770/170 = 22.18 = 23 steps

Height of each riser = 3770/23 = 164 mm

Using Blondel formula, 2R + T = 630

2 (164) + T = 630

T = 630 – 328 = 302 mm, say 300 mm

**Structural Design**

According to Oyenuga (2011), a spiral staircase is the most commonly used staircase in dwelling places. They can go as far as four stories in height. They are usually pre-cast members and are arranged around the periphery of the central column or post. The column can be designed axially with some little eccentricities allowed. The steps are cantilever slabs and are designed as such. In most cases, the steps are narrower at the column end and increase in width towards the tip. Depending on the span, depth ranges between 100 and 175 mm. There is no need to check for deflection. For domestic buildings, the common span is 900 mm with thickness ranging from 100 mm or 125 mm at the column end and tapering to 75 mm at the free end.

**Example**

Design a spiral staircase for a domestic dwelling with the following dimensions:

Span, L = 900 mm

Length of thread, T = 300 mm

Height of riser, R = 164 mm

Diameter of the central column = 300 mm (See Figures 2 and 3)

Assume a variable action of 2.5 kN/m^{2}

**Use**

Characteristic strength of concrete, f_{ck} = 25N/mm^{2}

Characteristic strength of steel, f_{yk} = 460 N/mm^{2}

Bar diameter, Ø_{bar} = 12 mm

Concrete cover, C_{cover} = 25 mm

**Solution**

Average step width = (200 +300)/2 = 500/2 = 250 m

Area of step = area around column + area of the cantilever section (Figure 4)

Area of section around column = [π (D^{2} – d^{2}) h]/4 = [π (0.35^{2} – 0.2^{2}) 0.164]/4 = 0.011 m^{3}

Area of the cantilever section = 0.5 (0.1 + 0.075) x 0.725 x 0.25 = 0.016 m^{3}

Total area = 0.011 + 0.016 = 0.027m^{3}

**Loading**

Stair own weight = area x unit weight of concrete = 0.027 x 24 = 0.648 kN

Assume finishes weight = 0.5 kN

Total permanent action = 1.148 kN

Variable action (kN) = effective length of stair x average width x 2.5 = 0.9 x 0.25 x 2.5 = 0.563 kN

Design Action, n_{d} = 1.35g_{k} + 1.5q_{k} = 1.35 (1.148) + 1.5 (0.563) = 1.55 + 0.845 = 2.395 kN

The stairs would be designed as a cantilever.

Ultimate moment of resistance, M_{Ed} = 0.5 x n_{d} x l^{2 }= 0.5 x 2.395 x 0.9 = 1.1 kN

Breadth at column end (b) would be used; b = 200 mm

Effective cover = nominal cover + 0.5 x bar diameter = 25 + 0.5 (12) = 25 + 6 = 31 mm

The maximum depth (100 mm) of the stair would be used to estimate the effective depth

Effective depth = 100 – 31 = 69 mm

K = M_{ED} / (f_{ck}bd^{2}) = (1.1 x 10^{6})/ (25 x 200 x 69^{2}) = 0.046 < 0.167 Ok

Compression reinforcement is not required

Z = d (0.5 + √ (0.25 – 0.882k) = 0.96d ˃ 0.95d, use 0.95d

Z = 0.95 x 69 = 65.6 mm

A_{st} = M_{ED}/ (0.87f_{yk}Z) = (1.1 x 106)/(0.87 x 460 x 65.6) = 42 mm^{2}/m

Provide 2H12 mm bars Top. Also, provide H10@ 300mm bars c/c as distribution bars.

**Note:**

- According to Oyenuga (2011), the landing does not bear any load from the stairs. Thus, it can be designed as a normal slab with variable action not less than 2 kN/m
^{2}. The landing reinforcement could be the top if it cantilevers or the bottom if the landing is supported on both sides. - On the other hand, as stated earlier, the column may be designed as an axially loaded column with allowance for little eccentricities from the stair. Generally, the column does not have much critical load and minimum reinforcement for circular columns (6H12mm) can be provided for it.

**Reference**

Oyenuga (2011): Simplified Reinforced Concrete Design. 2^{nd} edition. Vasons Concept Engineering Series.

## 1 Comment

good one