Reinforced Concrete Design: Chapter 15.7 - Development length requirements at simple supports

In the previous section we saw the least possible length (on which bond stress will be exerted to prevent pulling out) that is available at a simple support. This length is a portion of that 'length of the bar which is coming between the points of zero moments'. If any length is available beyond these points of zero moments, then concrete will exert grip on that length also. So that length will also assist in preventing the pull out.

Let us denote the extension beyond the point of zero moment as L₀. This L₀ can be given in a number of different ways. We will now see each of these methods in detail.

Fig.15.34

Simple extension

Development length requirements at simple supports

In the above fig.15.34, the bar is given a simple extension (that is., with out any bends or hooks) beyond the point of zero moment. But the bar cannot continue indefinitely. It can be continued upto a maximum point where the concrete cover C_c at the end becomes just sufficient. C_c is specified by the code. Details can be seen here.

In many of the worked out examples that we did until now, 'moderate' exposure conditions were assumed, and so C_c was taken as 30 mm for the bottom bars. This much cover is to be given from the outer surface of the stirrups. So the main bars get even more cover. But in our present case, the cover is taken from the end surface of the beam. Diameter of stirrups does not come into the picture. So we can assume 30 mm from the end of the bar to the end surface of the beam. However, it is important to consider the exposure conditions and other code requirements while fixing up C_c for each design problem.

From the fig.15.34, we can easily calculate L₀ if the width of support and C_c are known.

In some cases, the CL of the support may not coincide with the Point of zero moment. This happens when the effective span is different from the c/c distance between the supports. In such cases necessary adjustments should be made in the calculation of L₀.

Now we consider the case when the bar is given a standard 90^o bend at the support as shown in the fig.15.35 below:

Fig.15.35

Extension with a standard 90^o bend

We can see that a small portion of the 'original straight portion' of the bar extends beyond the CL of the support. This is denoted as BA' in the fig.15.36 below. In an actual beam, depending upon the width of the support and C_c, there may or may not be such a small portion. In the above fig.15.35, we have to calculate the length of this portion.

Before that, let us see the other features of this arrangement: We can see that the bend portion begins at the end of the straight portion. We can also see that after the bend portion, a straight length of 4Φ is given to make it a standard 90^o bend. We know that the radius of the bend is 4Φ. So the calculations can be done based on the fig.15.36 given below:

Fig.15.36

Calculation of L₀

Bends provided at the ends of bars at simply supported ends

From the fig., we can see that

• C_c + Φ + r + BA’ = half of the width of support = ws/2

• But r = 4Φ. So we can write

• C_c + 5Φ + BA’ = ws/2. From this we will get BA’.

• Now, the anchorage value of the bend from B to D is 8Φ.

• So the value of L₀ = BA’ + 8Φ

Finally we consider the case when an extension is given to the bar even beyond point D in the above fig. This is shown in the fig.15.37 below:

Fig.15.37

Extension beyond point D

In this case, the calculation of BA’ is same as the previous one. Also, the value from B to D is 8Φ.

• So we get L₀ = BA’ + 8Φ + DE

So now we know how to calculate L₀. This length L₀ will also help to prevent the pull out. So the total length available to us is equal to M_uR ⁄ V_u , + L₀, and this much available length should be greater than or equal to L_d. So we can write:

15.6

L_d (unique value) ≤ M_uR ⁄ V_u + L₀

This is the same expression given in the cl.26.2.3.3 (c) of the code. In the code, the ultimate moment of resistance M_uR is denoted as M1, and the factored shear force V_u is denoted as V.

Next, we will see a modification that has to be made to the above expression, when the simply supported end of the beam satisfies a 'special condition'. In the topic on design for shear, we discussed about the critical sections for shear design. There we saw that, when a 'transverse compression' is present at a support, the shear strength of the beam is increased near the support region. Figs. 13.62 to 13.65 of that section were used to illustrate the support conditions were such compression will occur. The same is applicable for our present discussion also. That is., when such a compression is available, the ends of the bars of the beam which are extended into the support will experience a confining effect. So a greater force will be necessary to pull the bars out. This is in effect, having a longer length of bars to resist the pull out. So the code allows us to increase MuR ⁄ Vu by 30 per cent. Thus, the expression that we can use when the ends of bars are under transverse compression is:

15.7: