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
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.
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
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
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 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.
In fig 16.25(a) tension will be at top of landing slab. Why steel bars numbered 'd' is not shown on top landing?
ReplyDeleteCan we use steel design for fig 16.28,16.29 for partially fixed support or simply supported for both AB,CD.
In fig.16.25(a), the bar type 'd' comes down from near the top surface of the sloping slab and becomes horizontal in the landing. It cannot be made horizontal at the exact junction between the sloping slab and landing. Because, when it try to straighten up due to the hogging moment, cracks will develop. This is because, only the concrete cover will be available to resist the tendency to straighten up. So, the bar type 'd' is taken down upto near the bottom surface of the landing slab, and then, it is made horizontal. This gives sufficient embedment inside a 'mass of concrete' rather than just a 'concrete cover'. Similar is the case with bar type 'c'. The types 'c' and 'd' together resist the tension at top.
DeleteIn fig.16.28 and fig.16.29, a partial fixity can not arise. Because, if we construct a wall above the supporting wall, passage of pedestrians will be obstructed.
DeleteWhy For AB flight in fig.16.22 bar d is not provided?
ReplyDeleteIf it is provided then how?
For fig 16.28 why 'd'bar is straight in landing and sloping portion and in 16.29 why c and d bars are straight in landing and sloping area.
It will not try to straighten up due to hogging at top of landing?
Flight AB in fig.16.22 is the first flight. It is resting on the ground on a foundation. So it's bar arrangement is different. In it, the type 'c' will serve the purpose of taking up any possible hogging moment.Type 'd' has a different shape.
DeleteIn fig.16.28, the landing will be bending downwards. So the 'd' bar, instead of straightening up, will be bending more and more inwards.
DeleteIn fig. 16.29, 'c' and 'd' will try to straighten up. Type 'd' is having the required embedment. But 'c' should have been brought down upto near the bottom surface of the landing, and then made horizontal. Thanks for bringing it to my notice. I will make the correction soon.
DeleteFig.16.29 is now corrected.
ReplyDeletesir. fig.16.25 is valid for both simply supported span and partial fixity at intermediate support c.
ReplyDeletewhy fig.16.22 does not have d bar(extra bar) at b support.
You have a point. d bars have to be provided at the lower support in fig.16.23
ReplyDeleteFig.16.23 is now corrected
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