Chapter 16.12 - Design example of a Transverse stair

In the previous section we completed the discussion on 'load calculation on a transverse stair'. Link to a solved example which illustrates the analysis and design is given below:

Solved example 16.3

The reinforcement details according to the above solved example is shown in the figs.16.64 and 16.65 given below:

Fig.16.64
Sectional elevation of transverse stair

Fig.16.65
Section XX

We will now discuss the various features of the above two figs:
The main bars are given as the bottom most layer. The distributor bars are given as the second layer from the bottom. This arrangement will give maximum possible effective depth ‘d’ for the section. From the section XX, we can see that the main bars are given two 90^o bends at both the ends. This will give a 'hook' like arrangement at both ends. The top portion of these 'hooks' will act as the steel required for resisting any possible hogging moment at the supports. The length required for this top steel is 0.15l, where l is the effective span of the waist slab. But the area required for this top steel is only half of that at the mid span. So, as shown in the inset, only alternate bars are given these hooks.
The distributor bars are of mild steel. So the symbol Φ is given to denote them.
In the above example, only a part plan (shown in the fig. below) of the stair was given along with the problem data.

Problem data of solved example 16.3:

This is because, this small portion is sufficient for defining the problem of this type of a transverse stair. But some times, this stair may have a landing also as shown below.

Fig.16.66
Landing in a transverse stair

In this case also the sloping portion can be analysed and designed by the same procedure, and the landing can be analysed and designed as a simply supported one-way slab.

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Stairs cantilevering from the side of a beam

The following fig.16.67 shows the part view of a stair.

Fig.16.67
View of a cantilever stair

It is projecting from the side of a wall. The wall is shown in a finished state. So we cannot see more details. The fig. below shows the view before the plastering is applied to the wall.

Fig.16.68
View of a stair cantilevering from a stringer beam

We can see that the stair is projecting from the side of a beam, which is concealed inside the wall. In actual construction, the beam (which frames into columns) and the waist slab will be casted first, and after curing and removal of form works, the masonry wall will be constructed above and below the beam. The elevation and section are shown in the figs. below:

Fig.16.69
Part elevation view of cantilever stairs

Fig.16.70
Section XX

The waist slab bends in a direction perpendicular to the direction of travel of the pedestrians, and so it is a transverse stair. The load calculation procedure is the same as that for the transverse stair supported on two stringer beams. So we can use the same Eq.16.25 for the loads. The line diagram for the analysis will be as shown below:

Fig.16.80
Line diagram for cantilever stairs

The effective span l of the cantilever (cl.22.2.c) is the length of the cantilever up to the face of the support plus half the effective depth. For initial proportioning, we can assume the thickness of waist slab to be clear length of cantilever/10 . However, this should be finalized only after the complete design and doing the various checks.

In the next section, we will see a solved example of the above type of stairs.

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Chapter 16.4 - Bars for landings in stairs

In the previous section we designed a stair and saw it's reinforcement details. In this section we will discuss more details about the arrangement of bars.

In the fig.16.22 which shows flight AB, the bottom layer bar (bar type 'a') in the sloping portion becomes the top layer in the landing portion. For the bottom layer of landing, extra bars are given. Similar arrangement can be seen in flight CD (fig.16.23) also. We will now discuss the reason for giving such an arrangement. Consider fig. 16.24 below:

Fig.16.24
Stair bars without embedment

In the fig.16.24, the bottom bar from the sloping portion continues into the landing in such a way that it is the bottom bar in the landing also. When the loads are applied on the slab, the bar will be in tension, and it will try to straighten up. Only the concrete cover is present there to resist this tendency of the bar to straighten up. This concrete cover does not have enough thickness to adequately resist this tendency, and cracks may develop. So we must extend this bar to embed it into a 'mass of concrete'. To achieve this embedment, the bar is taken up to near the top surface of the landing, and then a bend is given to make it horizontal. The measurements required for this embedment is shown in the fig.16.25 below:

Fig.16.25
Length of embedment required by the bars

We can see that, when the type 'a' bars become the top bars of the landing, the bottom portion of the landing is left with out any bars. So some extra bars (denoted as bar type 'b') are given at the bottom layer of the landing. These bars should have the same diameter and spacing as 'a' type bars. The 'b' bars also should have sufficient embedment. So they are taken upto near the top surface of the sloping slab, and then given a bend, to make them parallel to the slope. 

The point of intersection of 'a' and 'b' is taken as the 'critical' point. The specified embedment should be measured from this point. In the fig., the length required is specified as 'Ld(min)'. Why is it specially mentioned as 'min'? The explanation is as follows: The bars we are considering are 'top bars'. Their main purpose is to resist the hogging moment (that can possibly arise even at a simple support due to partial fixity). So they must have the specified length which is more than the length over which the hogging moment can possibly act. Thus we have two lengths to consider:
• The length required for resisting the hogging moment. Which is taken as 0.25l for general cases
• The length required for the embedment to prevent straightening up. Which is Ld
The largest of the above two lengths should be used. This will satisfy both the requirements. So the mention of 'min' tells us to take both criteria into consideration. It may be noted that in Limit state design, Ld is the unique value that we saw in a previous chapter. Also, Ld  should be provided on both sides of the critical point.

Now we consider the landing portion at ‘C’ (the intermediate landing) for the flight CD in fig.16.23. Here the bar type ‘a’ will not try to straighten up. So it does not require any extra embedment. So these bars continue as bottom bars into the landing. But at the support at this intermediate landing, hogging moments can occur if a wall is constructed above the landing (causing partial fixity), as shown in the fig. below:

Fig.16.25 (a)
Hogging moment at support

We can give top bars in the landing which will continue as top bar in the sloping portion also. But when the hogging moment occurs, these bars will be in tension, and will try to straighten up. So we must give two sets of bars (types ‘c’ and ‘d’) as shown in fig.16.25(a) above.
It must be noted that in fig.16.23, the different sets of bars are shown in separate layers only for clarity. In the actual structure, they will be in same layer as shown in the fig. below:

Fig.16.25(b)
Types of bars in same layers

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Stairs with overhanging Landings
Now, we can discuss the arrangement of bars in another type of longitudinal stairs. In this type, the supports are at the ends of the sloping slab as shown in the fig.16.26 below:

Fig.16.26
Supports at the ends of sloping slab

From the fig., we can see that the supports are at the ends of the sloping slabs. The intermediate landing and the top landing are overhanging beyond the supports. In other words, the landings are cantilevers. This type of stairs are more economical. Let us see how this economy is achieved: As shown earlier, the thickness of the waist slab is taken as 1/20 of the effective span. In the fig. above, the effective span is reduced because, the supports are now nearer to each other. So the waist slab thickness can be reduced. The bending moment will also be reduced because of the reduced effective span.

A cantilever structure will produce more bending moment than a simply supported structure. So at a glance, we may feel that more steel will be required for resisting the bending moment from the cantilevers. But here, the cantilevering span is small when compared to the simply supported span between the supports. Also the load on the cantilever landings is less than the load on the sloping portion.
However, it is important to note that hogging moments will be produced at the supports because of the cantilever action. This is shown in the figs. below:

Fig.16.27
Bending moment diagram for flight AB

Fig.16.27
Bending moment diagram for flight CD

From the above figs., it is clear that hogging moments will be present at the supports in this type of stairs. The values of maximum hogging moments and sagging moments can be easily calculated from basic principles. Then we can determine the steel required to resist these moments. The steel required to resist the hogging moments should be given as top steel at the supports. The arrangement of bars for this type of stairs is shown in the figs. below:

Fig.16.28
Arrangement of bars for flight AB

Fig.16.29
Arrangement of bars for flight CD

In the above figs., a new type of bar denoted as 'd' is given as top bars at all supports where overhang is present. These are the bars which resist the hogging moment. They must have sufficient embedment as indicated by 'y' in the figs. Also note that these bars are taken to the farther face of the sloping slab, and then bent to make them parallel to the slope. This is to give maximum embedment inside concrete.

In the next section, we will discuss about another type of longitudinal stairs in which, the second flight takes a right angled turn from the first flight.

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