Chapter 15.14 - Curtailment of bars when Moment coefficients are used

In the previous section we saw the anchorage requirements and curtailment details of bent-up bars. In this section we will see a general scheme.

Curtailment when moment coefficients are used 
So far we have discussed about the curtailment of bars based on Bending moment diagrams. When we analyse the structure, we will be able to draw the BM diagrams based on the results of the analysis. These diagrams are used for the design of steel at various sections. These diagrams are also used for determining the sections at which curtailment of steel can be done. But in chapter 7 (cont..3) we saw a method of designing steel 'without doing actual analysis and drawing the BM diagram'. In this method (if the structure satisfies certain conditions), moment coefficients given in Table 12 of the code are used to find the Bending moments . So in this method, there will not be any BM diagrams to calculate the theoretical points of curtailment.

In such a case, we can do the curtailment based on the fig.8.15 of SP 34: Handbook of Concrete Reinforcement And Detailing. Based on that fig., the method of curtailment of the top bars at the end support of a continuous beam (when the beam is framing into a column at that end support) can be shown as in the fig.15.81 below:

Fig.15.81
Curtailment of top bars at end support when moment coefficients are used

In the above fig., A_st is the maximum top steel provided at the support. This much steel is not required at regions away from the support. So curtailments can be done. The first curtailment is done at a distance of 0.15 l₁ from the face of the support. The remaining bars continue towards the next support. The area of these remaining bars should be greater than or equal to 60% of A_st. 

Out of these continuing bars, some can be curtailed at a distance of 0.25 l₁ from the face of the support. The area of the remaining bars after this curtailment should be greater than or equal to 20% of A_st . These bars continue uninterrupted to the last end support, and will take part in resisting the hogging moments at various supports.

So we know the lengths at which curtailments are done and the areas that should remain after each curtailment. One more important aspect that we have to consider is that of development length. Each and every bar in the above fig requires an embedment in the column, This embedment should be greater than or equal to L_d. We know that the bars will be pulled from both ends, and so the development length should be provided on both sides of the section. For those bars which are curtailed at 0.15 l₁, the only length available for anchorage at the right side of the section (that is., section through the face of the support) is 0.15 l₁. So this 0.15 l₁ must be greater than or equal to 'L_d of those bars which are curtailed at 0.15 l₁'. For example if l₁ = 3250 mm, 0.15 l₁ = 487.5 mm. This is less than 564.14 mm. (L_d of 12 mm dia. bars of Fe 415 grade steel when M20 concrete is used).

If the condition that 0.15 l₁ ≥ L_d is satisfied, our first impression will be that 0.25 l₁ will be naturally greater than L_d. But this need not be true if the bars curtailed at both the sections are not of the same diameter.

For example,
• Let the bars curtailed at 0.15 l₁ have a diameter of Φ1 and a development length of L_d1
• Let the bars curtailed at 0.25 l₁ have a diameter of Φ2 and a development length of L_d2
• Then, if 0.15 l₁ ≥ L_d1
    ♦ 0.25 l₁ ≥ L_d1 will be true. But
    ♦ 0.25 l₁ ≥ L_d2 need not be true.
So, if the bars are of different diameters, we must check that 0.25 l₁ is also greater than the L_d of those bars which are curtailed at 0.25 l₁.

This completes the discussion on the above fig.15.81. Next we will see the curtailment at an intermediate support. This is shown in fig.15.82 below:

Fig.15.82
Curtailment of top bars at intermediate support when moment coefficients are used

From the above fig., we can see that the length requirements and area requirements are exactly same as those at the end support. The development length requirements should also be checked in the same way that we discussed for end support, based on fig.15.81 that we saw earlier.

Now we will see how the rules related to area can be applied to an actual beam. Let there be 3-20# and 2-16# as top bars at an intermediate support. A sectional view is shown in the fig.15.83 below:

Fig.15.83
Top bars at a support

We must remember a general rule in curtailment: The bars in the layer closer to the NA of the beam are curtailed first. So when curtailment of top bars at a support is done, the bars in the bottom most layer of the bar group is curtailed in the first stage. In the second stage, the bars in the second bottom most layer is curtailed. Similarly, when the curtailment of bottom bars in a span is done, the bars in the top most layer of the bar group is curtailed in the first stage. In the second stage, the bars in the second top most layer is curtailed.

So, in the first stage, the two 16 mm bars can be curtailed, and at the second stage, one 20 mm bar can be curtailed. The calculations are shown in the fig.15.84 below:

Fig.15.84
Calculations of the areas after curtailments

From the calculations we can see that:
After the first curtailment, 3-20# bars remain. This much steel gives an area which is 70.09% of the A_st at support. This is greater than the required 60%. Hence OK

After the second curtailment, 2-20# bars remain. This much steel gives an area which is 46.73% of the A_st at support. This is greater than the required 20%. Hence OK

The 2-20# which remain after the second and final curtailment will continue as stirrup hangers, and also will take part in resisting the hogging moments at various supports. The fig. showing this arrangement is given below:

Fig.15.85
Arrangement after curtailment

However, the above arrangement should be finalised only after the development length checks using the values of l₁ and l₂.

In the next section we will see more such curtailments.

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