In
the previous section we completed the arrangement of the required reinforcement using straight bars. Now we will see the details about distribution bars. We have seen that the area of distribution bars depend only on Ag the gross area of cross section. So the same steps that we did while using bent-up bars are applicable here also. Thus we can provide #8 @200 for the distribution bars.
So we have completed the design of slab using straight bars. We can now do the various checks. The pdf file given below gives the detailed steps involved in the various checks:
Solved example 8.1 (straight bars) final checks
Curtailment of bars
Now we will discuss about the curtailment of bars. We have seen the curtailment details while using bent-up bars here. Now we will see the details while using straight bars. As pointed out earlier, a detailed discussion about 'Development length and curtailment' can be seen here. For our present case, we will be using the recommendations given in SP16. It must be noted that, to use these recommendations, the analysis of the continuous member should be done using the 'method of coefficients'. We have indeed used it in the analysis of our slab, and the results thus obtained were used in the design.
When we discussed about the curtailment of bent-up bars, we saw that the BM progressively decreases while we move away from a particular section ( support section as well as midspan section). So the steel can also be decreased at greater distances away from the concerned sections. This is applicable for straight bars also.
We will first see the curtailment of top bars at supports. We will take support B as an example. The fig.8.18 given below shows the details.
Fig.8.18
Curtailment of top bars
Here, bar types b'' and c'' are working together to resist the hogging moment at support B. These bars are shown separately only for clarity. In reality, they are at the same level, as indicated by the 0mm distance in the fig.
We can see a distance of 0.15l (from the face of the support) marked off on either side. So there is a particular horizontal length equal to 0.15l1 + 0.15l2 + width of the support. Within this length, no curtailment is allowed. In other words, within this length, all bars (which are intended to resist the design hogging moment) should be compulsorily present. So the quantity of steel in this length is denoted as Ast,sup.B. Just the availability of a length of '0.15l1 + 0.15l2 + width of the support' is not good enough. We must ensure that 0.15 times the respective spans is available on both sides. In this length, all of b'' and c'' are working together. But beyond this distance, all bars are not present. The b'' bars are not travelling beyond this distance on either side of the support. But c'' bars are continuing their travel for a distance of 0.15l more. So in effect, within a distance of 0.15l, full capacity is present. After this distance, the capacity is reduced because all bars are not present.
But there is a restriction on the quantity of bars that can be curtailed in this way: 50% of the bars required to resist the full hogging moment must be compulsorily present beyond the 0.15l length. Thus, in the fig., the quantity of steel beyond 0.15l is denoted as 0.5Ast,sup.B. This will be readily achieved because all the alternate bars in the group are continuing their travel. There is a restriction on the length also. All the c'' must compulsorily extend a distance of another 0.15l. So they will have a length of 0.30l from the face of the support.
The above discussion about 'curtailment of top bars at an interior support' can be simply written in a few steps as follows:
• At the interior support of a continuous one way slab, there will be two types of top bars.
• The longer bars have a length of 0.30l1 + 0.30l2 + width of the support
• The shorter bars have a length of 0.15l1 + 0.15l2 + width of the support.
• These two bars are provided alternately
• Care should be taken to see that the required lengths are provided on the concerned spans. (0.15l1 and 0.30l1 on the left side and 0.15l2 and 0.30l2 on the right side). The required areas should also be satisfied
Now we will see the curtailment of bottom bars in an interior span. We will take span BC as an example. Fig.8.19 given below shows the details.
Fig.8.19
Curtailment of bottom bars
Here, the bars c' and d' are working together to resist the sagging moment at midspan BC. These bars are shown separately only for clarity. In reality, they are at the same level, as indicated by the 0mm distance in the fig.
We can see a distance of 0.25l2 (from the center of supports) marked near either supports. So there will be a portion (of length l2 -0.50l2 =0.50l2) at the middle of the slab. This is the important portion as far as the 'sagging moment in an interior span' is concerned. All the bars which are intended to resist the sagging moment at midspan should be completely present in this portion. Thus, in the fig., the quantity of steel is denoted as Ast,mid.BC. Beyond this portion, on either sides, the BM is of lower magnitude. So c' stops at 0.25l2.
Like in the case of top bars, here also, there are some restrictions: Half the area of bars at the midspan should be compulsorily present after curtailment on either sides. Thus, in the fig., the quantity of steel after curtailment is denoted as 0.5Ast,mid.BC. There is a restriction on length also: All the bars remaining after curtailment should be compulsorily extended into the supports on either sides.
The above discussion about 'curtailment of bottom bars at an interior midspan' can be simply written in a few steps as follows:
• At the interior span of a continuous one way slab, there will be two types of bottom bars.
• The longer bars extend from support to support
• The shorter bars have a length of l2 -0.50l2 =0.50l2
• These two bars are provided alternately
• Care should be taken to see that the shorter bars are provided at the exact mid portion. Because 0.25l2 is marked from the center line of either supports. The required areas should also be satisfied
So we have completed the discussion on the curtailment of bars at interior supports and spans. Now we will see the curtailment at an end span. Together, we will see the curtailment at an end support also. Fig.8.20 below shows the details.
Fig.8.20
Curtailment details in end span
First we will see the details of top bars at the end support A. The length marked here is 0.1l from the face of the support. So we must ensure that all the a'' have a length of 0.1l from the face of the support. These bars are not part of any group. They are working alone to resist the hogging moment at support A. The area of these bars should not be less than half of that provided at midspan for the sagging moment.
Next we will see the bottom bars. This is similar to what we saw in fig.8.18 above, except that the distance from the center line of end support is 0.15l instead of 0.25l. So the 'important' portion in the midspan region has a length of l1 -0.15l1 -0.25l1 =0.60l1. All the bars should be present in this region. Beyond this region, the bars should have an area of half of that provided at midspan, and they must extend into supports on either sides.
So the discussion about 'curtailment of bottom bars at an end span' can be simply written in a few steps as follows:
• At the end span of a continuous one way slab, there will be two types of bottom bars.
• The longer bars extend from support to support
• The shorter bars have a length of l1 -0.15l1 -0.25l1 =0.60l1
• These two bars are provided alternately
• Care should be taken to see that the shorter bars are provided at the exact required portion. (0.15l from the end support and 0.25l from the interior support). The required areas should also be satisfied
This completes the details of the arrangement using 'straight bars'. In the next section we will see the design of a continuous beam.
So we have completed the design of slab using straight bars. We can now do the various checks. The pdf file given below gives the detailed steps involved in the various checks:
Solved example 8.1 (straight bars) final checks
Curtailment of bars
Now we will discuss about the curtailment of bars. We have seen the curtailment details while using bent-up bars here. Now we will see the details while using straight bars. As pointed out earlier, a detailed discussion about 'Development length and curtailment' can be seen here. For our present case, we will be using the recommendations given in SP16. It must be noted that, to use these recommendations, the analysis of the continuous member should be done using the 'method of coefficients'. We have indeed used it in the analysis of our slab, and the results thus obtained were used in the design.
When we discussed about the curtailment of bent-up bars, we saw that the BM progressively decreases while we move away from a particular section ( support section as well as midspan section). So the steel can also be decreased at greater distances away from the concerned sections. This is applicable for straight bars also.
We will first see the curtailment of top bars at supports. We will take support B as an example. The fig.8.18 given below shows the details.
Fig.8.18
Curtailment of top bars
Here, bar types b'' and c'' are working together to resist the hogging moment at support B. These bars are shown separately only for clarity. In reality, they are at the same level, as indicated by the 0mm distance in the fig.
We can see a distance of 0.15l (from the face of the support) marked off on either side. So there is a particular horizontal length equal to 0.15l1 + 0.15l2 + width of the support. Within this length, no curtailment is allowed. In other words, within this length, all bars (which are intended to resist the design hogging moment) should be compulsorily present. So the quantity of steel in this length is denoted as Ast,sup.B. Just the availability of a length of '0.15l1 + 0.15l2 + width of the support' is not good enough. We must ensure that 0.15 times the respective spans is available on both sides. In this length, all of b'' and c'' are working together. But beyond this distance, all bars are not present. The b'' bars are not travelling beyond this distance on either side of the support. But c'' bars are continuing their travel for a distance of 0.15l more. So in effect, within a distance of 0.15l, full capacity is present. After this distance, the capacity is reduced because all bars are not present.
But there is a restriction on the quantity of bars that can be curtailed in this way: 50% of the bars required to resist the full hogging moment must be compulsorily present beyond the 0.15l length. Thus, in the fig., the quantity of steel beyond 0.15l is denoted as 0.5Ast,sup.B. This will be readily achieved because all the alternate bars in the group are continuing their travel. There is a restriction on the length also. All the c'' must compulsorily extend a distance of another 0.15l. So they will have a length of 0.30l from the face of the support.
The above discussion about 'curtailment of top bars at an interior support' can be simply written in a few steps as follows:
• At the interior support of a continuous one way slab, there will be two types of top bars.
• The longer bars have a length of 0.30l1 + 0.30l2 + width of the support
• The shorter bars have a length of 0.15l1 + 0.15l2 + width of the support.
• These two bars are provided alternately
• Care should be taken to see that the required lengths are provided on the concerned spans. (0.15l1 and 0.30l1 on the left side and 0.15l2 and 0.30l2 on the right side). The required areas should also be satisfied
Now we will see the curtailment of bottom bars in an interior span. We will take span BC as an example. Fig.8.19 given below shows the details.
Fig.8.19
Curtailment of bottom bars
We can see a distance of 0.25l2 (from the center of supports) marked near either supports. So there will be a portion (of length l2 -0.50l2 =0.50l2) at the middle of the slab. This is the important portion as far as the 'sagging moment in an interior span' is concerned. All the bars which are intended to resist the sagging moment at midspan should be completely present in this portion. Thus, in the fig., the quantity of steel is denoted as Ast,mid.BC. Beyond this portion, on either sides, the BM is of lower magnitude. So c' stops at 0.25l2.
Like in the case of top bars, here also, there are some restrictions: Half the area of bars at the midspan should be compulsorily present after curtailment on either sides. Thus, in the fig., the quantity of steel after curtailment is denoted as 0.5Ast,mid.BC. There is a restriction on length also: All the bars remaining after curtailment should be compulsorily extended into the supports on either sides.
The above discussion about 'curtailment of bottom bars at an interior midspan' can be simply written in a few steps as follows:
• At the interior span of a continuous one way slab, there will be two types of bottom bars.
• The longer bars extend from support to support
• The shorter bars have a length of l2 -0.50l2 =0.50l2
• These two bars are provided alternately
• Care should be taken to see that the shorter bars are provided at the exact mid portion. Because 0.25l2 is marked from the center line of either supports. The required areas should also be satisfied
So we have completed the discussion on the curtailment of bars at interior supports and spans. Now we will see the curtailment at an end span. Together, we will see the curtailment at an end support also. Fig.8.20 below shows the details.
Fig.8.20
Curtailment details in end span
First we will see the details of top bars at the end support A. The length marked here is 0.1l from the face of the support. So we must ensure that all the a'' have a length of 0.1l from the face of the support. These bars are not part of any group. They are working alone to resist the hogging moment at support A. The area of these bars should not be less than half of that provided at midspan for the sagging moment.
Next we will see the bottom bars. This is similar to what we saw in fig.8.18 above, except that the distance from the center line of end support is 0.15l instead of 0.25l. So the 'important' portion in the midspan region has a length of l1 -0.15l1 -0.25l1 =0.60l1. All the bars should be present in this region. Beyond this region, the bars should have an area of half of that provided at midspan, and they must extend into supports on either sides.
So the discussion about 'curtailment of bottom bars at an end span' can be simply written in a few steps as follows:
• At the end span of a continuous one way slab, there will be two types of bottom bars.
• The longer bars extend from support to support
• The shorter bars have a length of l1 -0.15l1 -0.25l1 =0.60l1
• These two bars are provided alternately
• Care should be taken to see that the shorter bars are provided at the exact required portion. (0.15l from the end support and 0.25l from the interior support). The required areas should also be satisfied
This completes the details of the arrangement using 'straight bars'. In the next section we will see the design of a continuous beam.
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