A staircase is a structural element that provides upward mobility in a building and similar structures. It provides access from one floor to another adjacent floor below or above.
This article provides guidance on analysis, structural design, and other aspects such as safety of staircases according to BS Codes and Eurocode 2.
Components of staircase
Tread: A tread is the horizontal part of a staircase step on which user place their feet.
Riser: A riser is a vertical distance between two adjacent treads. It is the vertical part of the step and it is always greater than tread by one in numbers in any staircase flight.
Going: Going is the horizontal distance of the tread in the direction of the flight
Rise: Rise is the vertical distance of the riser.
Nosing: Nosing is the horizontal projection from the tread over the staircase tread.
Pitch line/Line of nosing: The pitch line is an imaginary line running through the nosing of the steps.
Steps: Steps are each triangular shape part of a staircase that consist of a riser and a tread just after the riser.
Flight: A staircase flight is the part of staircase that consist of series of consecutive steps without being interrupted by a landing or floor. A Flight is always between two landings, or between two floors, or between a landing and a floor.
Landing: A Landing is the horizontal platform of the staircase before and after each flight.
Waist Slab: The waist slab is the inclined slab below the staircase steps. In non-waistless staircase, it is often the main structural member.
Handrail: A handrail is the horizontal member of the balustrade located on the baluster. It serves a guide and support to stair users
Baluster: The vertical member on which the handrail is supported
Balustrade: Balustrade is the guide that prevent users from falling over the stair. It consists of a vertical member called baluster and a horizontal member called handrail
Types of Stairs
Straight Flight Stair: A straight flight is a stair that rises from one floor to another with or without intermediate landing without a change in direction.
Half-turn stair: A half-turn stair has a flight that spans to an intermediate landing between floors and then turns through 180 degrees, then another flight spans parallel but in opposite direction to the first flight to reach the upper floor. It is also called scissors stair, and dog-legged stair.
Quarter-turn (L-shape) Stair: A quarter-turn stair looks like letter L in plan. The stair rises to an intermediate stair between floors, and then turn through 90 degrees then the second flight rises to reach the floor above.
Open-well Stair: Open well staircase is a staircase with three flights where the first and third flight are parallel but opposite in direction and the middle flight is oriented at right angle to both flights
Helical: A helical staircase is a stair describing a helix around a central void
Spiral: A helical staircase is a stair describing a helix around a central column
Click here to study a worked example on the design of half turn staircase to BS 8110-1-1997
Or, click here to study a worked example on the design of half turn staircase to Eurocode 2
Structural Category of staircase
Longitudinal Spanning Stair: Longitudinal spanning stairs are staircase that bends along the staircase flight. They are either supported on walls or landing beams at the ends of the staircase spanning perpendicular to the stair flight. Often times the wall or beam support are always at the end of the landing so that the flight and landing acts like one single slab. Other times there are trimmer beams between the flight and landing so that the landing is an overhang cantilever.
Transverse Spanning Stair: Transverse stairs are staircase that spans across the stair width. They are supported along the stair on stringer beams. The stringer beam is either on one side or both sides. When the stringer beam is only on one side then the staircase is a transverse cantilever stair.
Guide to staircase dimension and Safety Precaution (BS 5395)
The staircase rise ideally should be between 3 and 16 in number in a single flight except for exceptional cases. When the staircase rise is too shallow it causes user to trip, and when it is too high it causes discomfort to user when lifting their legs. The rise of a staircase should be between 100mm and 220mm.
Staircase tread width should be sufficient to allow comfortable usage by users. When ascending the stair, it should be able to support part of the heel for adequate balance of the stair user. It should not also necessitate the user to have to place his leg at an uncomfortable angle when descending the stair. The tread should never be less than the riser and should have a dimension between 200 to 300mm.
The primary purpose of adequate stair width is to enable seamless movements of occupants, furniture, or goods. A Private stair should have a clear width not less than 900 or 1000mm. Public stair should have width greater than 1000mm, however when the width is greater than 1.8m then it should be divided by a handrail. The width of the landing should not be less than the flight width.
According to BS 5395-1, the handrail of a staircase should be: a) Fixed at the vertical line above the pitch line of not less 900mm or more than 1000mm b) Rigid and strong enough to provide adequate support for the user c) Comfortable to grip without sharp arises and yet able to provide resistance to hand slippage d) a poor conductor of heat, if exposure to heat is likely.
Stair headroom should not be less than 2m. Additional headroom should be provided for stairs of short flight of three to four risers or steps because of the tendency of a young person to jump the stairs at once.
An open tread staircase is better avoided altogether if the stair will constantly serve children and elderly, if there is however a compelling reason to use it, the space between adjacent treads should not be large enough to allow a sphere 100mm diameter to pass through
Guide to computing staircase load.
There are numerous loads that acts on a staircase. These include the dead load of staircase which comprises of the self-weight of the steps and landing slab, and also the self- weight of the waist slab for a staircase with a waist slab. There are also super dead loads from finishes and other components such as handrail and balusters. There are also live loads from users.
The first concept the esteemed reader must first appreciate is that staircases are designed like a typical horizontal slab. This means the staircase is designed as a beam with a constant width, for example 1m. Consequently, all load computations are to evaluate the load acting on a 1m-width beam per metre run.
We can derive from the foregoing paragraph that the loads are computed in KN/m2 and also applied vertically on the stairs. This is quite easy when it comes to live loads as codes such as BS 6399-1 (Table 1) and Eurocode 1 (Table 6.2) already make provisions for minimum live loads that could be considered to be acting on stairs. These loads from the codes are meant to be applied vertically on the stair on a horizontal plane. However, there is always a bit of awkwardness when it comes to estimating the dead loads, especially the self-weight of the inclined waist slab which is also assumed to be acting on a horizontal plane of the stair. This is because the components of the stair that make up the dead weight are obviously not horizontal but in an inclined plane. The following sections elucidate on principle behind how these loads are calculated.
Computation of waist slab self-weight.
Since loads on staircase are applied on a horizontal plane in contrast to the inclination of the waist slab, this always leave the length of the slab to be underestimated. The fig below shows that a 1000mm (1m) length of the slab in horizontal plane is actually 1250mm (1.250m) when measured in an inclined plane between the same points along the waist slab. This shows the length of the waist slab has been underestimated and would in turn affect the self-weight estimated.
Inclination/Slope factor
The inclination factor is used to correct the underestimation arising from considering the stair waist slab in horizontal plane rather than in inclined plane. In the figure above, the 1m length parallel to the inclined plane is longer than that parallel to the horizontal span between the same points. We shall derive a slope factor to modify the self-weight of the waist slab so that there is always allowance for increment due to inclination of the slab.
The diagram below shows a staircase where the inclined length is denoted by “a” and the horizontal length which is obviously 1m denoted by “c”. Another triangle is formed by joining the tip of a tread to the tip of a riser.
Using similar triangles
b/R = c/T
b = c/T x R
since c = 1
b = R/T
a² = b² + c²
a² = b² + 1
Sub b = R/T
a² = (R/T)² + 1
a = √(R² + T²)/ T
√(R² + T²)/T is the slope factor.
Application of slope factor
This slope factor shall always be multiplied by the self-weight of the waist slab for increased load on plan due to the inclination of waist slab.
By implication, if a stair waist slab is 200mm thick, then the self-weight of the waist slab becomes:
24 x 0.2 x 1m (breadth) x = 4.8KN/m
To modify the load so as to factor the inclination of the stair slab, we have:
4.8 x √(R² + T²)/ T
Computation of Steps self-weight.
The steps are always shaped in a triangle; hence their area is ½ x R x T. The steps self-weight is also to be computed in KN/m2 so that consecutive steps stretching a length of 1m with breadths of 1m are assumed. However, the treads are always in the direction of the stair span and are always shorter than 1m, so to compute the steps weight per metre run, the number of steps in 1m length along the stair span = 1m/T
The self-weight of steps = unit weight of concrete x volume of stair = 24 x ½ x R x T x 1m (breadth)
The self-weight of step considering 1m length along the stair flight becomes = 24 x ½ x R x T x 1m (breadth) x 1m/T = 24 x ½ x R
Hence, to get the self-weight of the steps per metre run, the unit weight of concrete is multiplied by ½R
Computation of live load
The live load of a staircase should be lifted from codes such as BS 6399 or Eurocode 1 or can be assumed based on the engineering judgement of the designer. The loads are assumed to be acting vertically on a horizontal plan so it requires no modification.
Effective Span of Staircase
According to clause 3.10.1.4 of BS 8110-1, the effective span of simply-supported staircases without stringer beams is the horizontal distance between the centre-lines of the supports or the clear distance between the faces of supports plus the effective depth, whichever is the lesser. However, if the staircase is constructed monolithically with supporting structural members spanning perpendicularly to the stair span the effective span can be calculated using:
la + 0.5(lb,1 + lb,2)
Where:
la is the clear horizontal distance between the supporting members.
lb,1 is the breadth of the supporting member at one end or 1.8 m, whichever is the lesser.
lb,2 is the breadth of the supporting member at the other or end 1.8 m, whichever is the lesser.
Design of staircase to BS 8110
The staircase is designed like a typical slab. After analysis and evaluation of bending stress and shear stress, the following steps are followed in designing the staircase
- Initial Sizing of the staircase:
The staircase span and width are most times derived from the architectural layout. The same goes for risers and treads. If the structural engineer is to determine the riser and tread dimensions then it is a good practice that the dimensions assumed are such that:
2 x Riser + Tread <= 600 or 580
For typical staircase what the engineer is to size is the structural element such as the waist slab. The thickness of the waist slab can be conveniently determined from span-effective depth ratio using table 3.9 of BS 8110-1 as appropriate.
2. Flexural Design
a. Calculate the effective depth (d): use the equation: d = h – c – ø
b. Check whether the section is singly or doubly reinforced: We check whether K (M/bd²fcu) is less than K’ (0.156). For staircase, as in for typical slab, the section is always design as singly reinforced, so it does not require compression steel.
c. Calculate the lever arm: Use Z = $
Z\,\,=\,\,d\left( \text{0.5}+\sqrt{\text{0.25}-\,\,\frac{K}{0.9}} \right) \,\,\,\,\leqslant \,\,0.95d
$
d. Calculate the area of steel: use $A_{s\,\,=\,\,\frac{M}{0.87f_yZ}}
$
3. Shear design
For shear stress in staircase, the shear stress induce in the structural member is always less than half of the concrete shear strength (0.5Vc), hence no shear links is required.
4. Deflection Check
The deflection check is carried by checking the actual span-effective depth ratio against the basic span-effective depth ratio in table 3.9. If necessary, the basic span-effective depth ratio should be multiplied by the appropriate modification factor for tension reinforcement in table 3.10. Clause 3.10.2.2 also stipulates that if the stair flight occupies at least 60 % of the span, the basic span-effective depth ratio may be increased by 15 %.
Design of staircase to Eurocode 2
- Initial Sizing of the staircase:
The span and breath of staircase are often derived from architectural layout, the thickness of structural element for preliminary sizing can roughly be estimated using basic span-effective depth ratio given in table 7.4N of Eurocode 2. Alternatively, the span-effective depth ratios published in “manual for the design of reinforced concrete building structures to eurocode 2” in table 5.30 can be adopted. This is even more appealing as the ratios in the table are specifically made for staircase of different support configuration. And also, if the designer is required to determine the risers and treads dimension, it is a good practice that the dimensions are assumed to satisfy the expression below:
2 x Riser + Tread <= 600 or 580
2. Flexural Design
a. Calculate the effective depth (d): use the equation: d = h – c – ø
b. Check whether the section is singly or doubly reinforced: We check whether K (M/bd²fcu) is less than K’ (0.168). For staircase, as in for typical slab, the section is always design as singly reinforced, so it does not require compression steel.
c. Calculate the lever arm: Use Z = $
Z\,\,=\,\,d\left( 0.5+\sqrt{\text{0.25}-\,\,\frac{K}{1.134}} \right)
$
d. Calculate the area of steel: use $A_{st\,\,=\,\,\frac{M_{Ed}}{0.87f_{ck}Z}}
$
3. Shear design
Since staircase are often subjected to light uniformly distributed load, the shear capacity of the concrete section without shear reinforcement (VRdc) is often sufficient to resist the maximum design shear force (VEd )
4. Deflection Check
The deflection check is carried by checking the actual span-effective depth ratio against the limit span-effective depth ratio. The formula for the limit span-effective depth ratio is given in the code as:
l/d = K[11 + 1.5√fck ρ0/ρ + 3.2√fck (ρo/ρ – 1)3/2] if ρ ≤ ρo
l/d = K[11 + 1.5√fck ρo/ρ + 3.2√fck √ρo/ρ ] if ρ > ρo
Arrangement of bars in staircase
The flashpoint of reinforcement detailing in staircase is the placement of bars between the junction of the stair flight and landing slab. The bottom reinforcement from the waist slab shall be placed such that it becomes the top reinforcement at the landing while the bottom reinforcement from the landing slab becomes the top reinforcement in the waist slab. This is to provide:
- Adequate anchorage length for the bars.
- Prevent the reinforcement from straightening up to cause crushing of concrete within the waist-landing junction.
When the bottom reinforcement from the waist slab is taken to the top of landing slab, adequate quantity of concrete is present below it which holds the reinforcement in place. If the reinforcement had continued as bottom reinforcement in the landing, there will be to little amount of concrete within the junction to resist the reinforcement bars from straightening up under tensile stress.
References:
BS 5395-1-2000: Stair, ladder and walkways – Code of practice for the design, construction, and maintenance of straight stairs and winders
BS 8110-1-1997, Structural Use of concrete – Part 1: Code of practice for design and construction
BS EN 1992: Design of concrete structures – Part 1-1 : General rules and rules for buildings
Staircases Structural Analysis and Design by M.Y.H Bangash & T. Bangash
Manual for the design of reinforced concrete building structures to Eurocode 2 by IStructE
