Design Guide: RC Staircase

IntroductionA staircase is a flight of steps between multiple levels. Simple, right? Well, as it turns out, there’s much more engineering behind choosing a standard size from a manufacturer. Most staircases are specially designed to meet required design standards. Some key design standards include AISC 360/16 or ASIC 318/19 - Specifications for structural steel or concrete buildings, respectively, Eurocode 2 or 3 - Design of Concrete and Steel Structures, respectively, or in Australian Standards- AS 1657. 
Safe to say, staircases need to be designed as structural components. Staircases are most commonly made from steel or concrete or both, and even then, the options are endless; however, regardless of the complexity, engineers should treat staircases as a system of beams and supports that carry the load. Below is a summary of some of the universal key terms and definitions ubiquitous in staircase design. What follows is a step-by-step guide to RC Staircase Design to Australian Standards. 
Technical Terms
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RC staircase technical terms
Putting it all together
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Figure 1: Typical staircase
Steps to staircase design according to AS1657 and the Building Code of Australia (BCA)Architects and designers are spoiled for choice when it comes to staircase design. From a feature and floating stairs to transparent stairs, staircases no longer only need to meet a purely functional purpose. They can be the centerpiece of building design. However, local regulations and standards often limit the use of innovative designs and materials. Australian Standards are quite complicated when it comes to leveraging unique staircase designs. So, we’ve provided a step-by-step guide to RC staircase design using Australian standards and regulations. 
Staircases used in habitable rooms or externally must comply with the Building Code of Australia (BCA) Part 3.9.1. All areas not specified in BCA should be referenced in the Australian Standard AS1657 Section 4.
Staircases in storage areas or un-habitable spaces such as attics can be constructed outside the scope of the BCA, but designs must comply with AS 1657.
Three key Australian standards outline requirements for the design, construction, and installation of stairways: 
AS 1428.1: Design For Access and Mobility, General Requirements for Access - New Buildings
AS 1657: Fixed Platforms, Walkways, Stairways, and Ladders - Design, Construction, Installation
AS/NZ 4586: Slip Resistance Classification of New Pedestrian Surface Materials
Before we go into a step-by-step guideline for staircase design, we’ll summarise some of the key design requirements and specifications for staircases according to the BCA and the design standards listed above:
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‍Risers and Stair Treads
A staircase's pitch angle shall be not less than 26.5 degrees and not greater than 45 degrees.
A staircase must have no more than 18 risers without a 750 mm2 landing or rest area.
The staircase should have no more than 36 rises without a change of direction.
Your staircase must have no less than two risers or no more than 18 risers without a 750 mm2 landing or rest area.
Each tread and riser must be the exact measurement within a single flight.
Tread depth must be greater than or equal to 185mm.
All treads and top nosing must have a slip-resistant finish or a non-slip strip system near the edge of each tread nosing.
If a door in your home opens onto a staircase, a landing is required unless the floor-to-floor dimension is less than 570 mm. If the floor-to-floor is less than 570 mm, all that is required is a zero tread.
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Handrails
Handrails are required on all exposed sides of a staircase unless there’s a fixed structure within 10cm of the stairway, and every staircase needs one handrail. A handrail is required on both sides of a stairway if it is wider than 1m.
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Flights
With floors or balconies which have the potential of people falling more than 4000mm to the surface below, all horizontal elements between 150mm and 760mm above the floor or balcony must not facilitate climbing.
All the steps on the same flight must be identical.
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Loadings
When it comes to loads, Australian standards specify that stairs need to have:
A minimum loading of 2.5kPa, or an equivalent linear load of 2.2kN/m.
A minimum point load of 1.5 kN is applied on a 10cm2 area on each step.
‍💡 Note: loading requirements differ for landings.
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Balustrades
The height of the balustrade on the pitch of the staircase must be not less than 865mm from the nosing line. This dimension is taken from the nosing line with the rail or balustrade running parallel up the pitch of the staircase.
The height of the balustrade on a finished floor, balcony, landing, or path must be above 1000mm.
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‍Platforms and Landings
Any stairway with more than 15 steps must incorporate a landing in between flights of stairs.
A step-by-step guide to RC Staircase Design to Australian Standards:A staircase must be designed so it fits properly in a proposed building plan; therefore, it is difficult to provide definite dimensions and guidelines without the exact type and orientation of the building. Nevertheless, we’ve provided some general steps and a cheatsheet for simply supported longitudinally spanning RC stairs:
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Figure 2: Straight stairs spanning longitudinally
In the case of longitudinally spanning stairs, the supports to the stair slab are parallel to the riser, commonly in two locations, causing the slab to bend longitudinally between the supports.
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Figure 3: Alternate support arrangements
The Cheat-sheet (Stairs to BCA/NCC-3.91 & AS1657)
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staircase design guide
Determine the height of each flight.
The height of each flight is determined by dividing the total story height by the number of flights. Remember that according to Australian standards, the minimum number of flights is two, equivalent to two risers or a minimum height of 230mm. The maximum number of risers in a flight before a landing is required is 18. 
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Determine flight width.
The designer chooses the width of each flight. In residential settings, the minimum codified width of a flight is 600mm; this is generally very narrow for most circumstances, as often furniture or fixtures need to be taken up the stairs. So, ideally, a width of 1000mm is desirable. Note that stair width is measured from the inside of a handrail to the inside of the other handrail. However, this staircase configuration is more common in commercial settings than residential ones, so care must be taken when measuring flight width.  
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Calculate the number of Risers and Treads.
The number of risers required is simply the total height of each flight divided by the height of each riser:
The number of treads is calculated as the number of risers minus 1:
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Number of risers =Total height of each flight (mm)Height of individual riser (mm)Number\ of\ risers\ = \frac{Total\ height\ of\ each\ flight\ (mm)} {Height\ of\ individual\ riser\ (mm)}Number of risers =Height of individual riser (mm)Total height of each flight (mm)​
The number of treads is calculated as the number of risers minus 1:
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Number of treads =Number of risers −1
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Calculate the Effective Span (L).In a longitudinally spanning staircase and a simply supported arrangement, the effective span (L) can be taken as the distance between the centrelines of support:
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L=Going(G) +Landing width2(x)+Landing width2(y)wherex=X but<1.8m (whichever is less)y=Y but<1.8m (whichever is less)L = Going (G)\ + {\frac{Landing\ width} {2}}(x) + {\frac{Landing\ width} {2}}(y) \\ \text{where} \\ x = X \ but < 1.8 m \text{ (whichever is less)} \\ y = Y \ but < 1.8 m \text{ (whichever is less)}L=Going(G) +2Landing width​(x)+2Landing width​(y)wherex=X but<1.8m (whichever is less)y=Y but<1.8m (whichever is less)
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Figure 4: Effective width in longitudinal spanning stairs
Assume waist slab thickness.
The thickness of a waist slab can be assumed to be between L/20 and L/25 where L is the effective span calculated in Step 4 or between 40mm to 50mm per metre run of horizontal span.
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Calculate the total load on the staircase.
As per the standards, stairs should have a loading capacity of 2.5 kPa and 2.2 kN per linear meter whilst also withstanding a point load of 1.5 kN/10cm2 on each step. Total loads (w) on stairs include the dead load + live load + floor finishes where:
Dead Load: self-weight of steps + self-weight of waist slab (common in RC stairs) + self-weight of tread finish
Live Load: generally taken between 2 kPa to 4 kPa (refer to Table 3.1 of AS 1170.1 structural design actions for reference values for imposed loads). Where a stair tread or landing is structurally independent of the adjoining elements, it should withstand a line load of 2.2 kN/m of the span of the tread or landing.
Floor finishes: generally taken between 0.8 kPa to 1 kPa. 
❗Note that the total load (w) obtained above will be inclined, so it must be converted into an equivalent horizontal load by multiplying it with a factor that factors in the length of the tread (T) and height of the riser (R) and then finally multiplied by the appropriate factor of safety obtained in AS1170.1:
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Factor=R2+T2TFactor = \frac{\sqrt{R2+T2}}{T}Factor=TR2+T2​​
❗Note on the landing area, the weight of steps is not included.
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Calculate the maximum bending moment.
With the maximum loading (w) obtained in Step 4, the reactions at each end support can be calculated using equilibrium equations. Given reactions and load values, the maximum bending moment can be calculated where it will occur at a point of zero shears. Suppose the system is treated as a simply supported beam with a UDl. In that case, the max bending moment can be found as:
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Mmax=WL28M_{max} = \frac{WL^2} {8}Mmax​=8WL2​
Where W is the factored total uniformly distributed load from Step 5, L is the effective length of the staircase calculated in Step 4.
Flights with significant end restraint, such as those that are continuous with their supporting beams or slabs, may be designed for a mid-span design moment of:
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Mmax=WL210M_{max} = \frac{WL^2} {10}Mmax​=10WL2​
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Using the maximum bending moment, you can calculate the minimum waist slab depth required using this equation and solving for d:
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Mu=Astfsy0.925dM_u = A_{st}f_{sy}0.925dMu​=Ast​fsy​0.925d
Where, 
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fsy=yield strength (MPa)Ast=cross-sectional area of longitudinal tensile reinforcementd=depth of waist slab (mm)f_{sy}=\text {yield strength (MPa)}\\ A_{st}= \text {cross-sectional area of longitudinal tensile reinforcement}\\ d = \text{depth of waist slab (mm)}\\fsy​=yield strength (MPa)Ast​=cross-sectional area of longitudinal tensile reinforcementd=depth of waist slab (mm)
If the calculated depth is less than the assumed thickness of the slab then the design is safe. Otherwise, a greater waist slab depth needs to be assumed and steps repeated. 
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Reinforcements 
The main reinforcement for stairs is calculated as:
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Papprox=2.54M∗d2                              P_{approx} = \frac{2.54M^*} {d^2}Papprox​=d22.54M∗​
P (approx) is the reinforcement for the slab per metre width of the slab and it provides a moderate degree of crack control for flexural strength at first interior support.
The minimum reinforcement for the waist slab to not fail upon cracking is given by:
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Pmin=0.2(Dsd)2(fct.f′fsy′)P_{min} = 0.2 (\frac{D_s} {d})^2 (\frac{f'_{ct.f}} {f'_{sy}})Pmin​=0.2(dDs​​)2(fsy′​fct.f′​​)
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Where, 
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Ds=overall depth (mm)fct.f′=0.6f′c(MPa)fsy′=characteristic yield strength of reinforcement (MPa)D_s   = \text {overall depth (mm)}\\ f'_{ct.f} = 0.6 f'c (MPa) \\ f'_{sy}   = \text{characteristic yield strength of reinforcement (MPa)}\\Ds​=overall depth (mm)fct.f′​=0.6f′c(MPa)fsy′​=characteristic yield strength of reinforcement (MPa)
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The minimum reinforcement for crack control: temp and shrinkage
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Pmin=0.75∗0.0035∗(Dsd)P_{min} = 0.75 * 0.0035 * (\frac{D_s} {d})Pmin​=0.75∗0.0035∗(dDs​​)
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Finally, the area of steel reinforcement required is:
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As(required)=ρ∗b∗d(mm2)A_{s(required)} = \rho * b * d (mm^2)As(required)​=ρ∗b∗d(mm2)
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Where, 
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ρ=required reinforcementb= width of the slab (taken as 1000mm)d=depth of slab (mm)\rho= \text{required reinforcement}\\ b =\text{ width of the slab (taken as 1000mm)}\\d= \text{depth of slab (mm)}\\ρ=required reinforcementb= width of the slab (taken as 1000mm)d=depth of slab (mm)
In the simply supported case, a positive moment will be induced by the uniform loading, causing tension on the underside of the beam, and requiring reinforcement to be placed on the bottom side of the beam.
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Check for Shear.
The slab's design shear strength shall be calculated per Clause 8.2 of AS3600: 2018. Flexural shear is unlikely to be a critical condition; however, your design must satisfy the following condition:
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ϕVuc≥V∗{\phi}V_{uc}\geq V^*ϕVuc​≥V∗
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Where, 
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Vuc=ultimate shear strength=kvbvdvf′cV_{uc} = ultimate\ shear\ strength= k_vb_vd_v\sqrt{f'c}Vuc​=ultimate shear strength=kv​bv​dv​f′c​
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kv=[0.41+1500ϵx]k_v = [\frac{0.4} {1 + 1500\epsilon_x}]kv​=[1+1500ϵx​0.4​]
where x is the longitudinal strain factor for concrete, and the formula for this factor is a bit of a doozy, so AS3600-2018 gives allowance for a simplified approach and the process can be found in Clause 8.2.4.3 in AS 3600-2018. 
Note that this simplified approach only applies to non-post tensioned sections. If you are confident that your post-tensioning effects are increasing beam shear capacity (most of the time they will), the simplified approach would be safe to use.  
bv = effective width of a web for shear
dv = effective shear depth (see clause 8.2.1.9)
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Check for Deflection
Strength requirements are not always critical for stair slabs. It is, therefore, essential that the other limit states are checked, particularly deflection. For concrete longitudinal straight stairs, as before, it is treated as a one-way spanning slab and deflection requirements can be addressed per Clause 9.3.2 or Clause 9.3.3 in AS3600, making appropriate allowances as per the standard. 
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📚 References[1] Standards Australia, AS 3600:2018 Concrete Structures. Sydney, Australia, 2010
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