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About design of beams, effective span, effective depth, reinforcement, nominal cover to reinforcement, curtailment of tension reinforcement

## BASIC RULES FOR DESIGN OF BEAMS

While designing R.C.C. beams, following important rules must be kept in mind:

### Effective Span (CI. 22.2, IS 456)

The effective span of the beams are taken as follows :

#### (a) Simply Supported Beam or Slab

The effective span of a simply supported beam or slab is taken as least of the following:
(i) Clear span plus the effective depth of beam or slab.

(ii)Centre to centre distance between supports.

(b) Continuous Beam or Slab

In case of continuous beam or slab if the width of the supports is less than $\frac {1}{12}$of the clear span, the effective span is taken as in (a). If the width of the support is greater than $\frac {1}{12}$ of the clear span or 600 mm whichever is less, the effective span is taken as:

(i)For the end span with one end fixed and the other continuous or for intermediate spans, the effective span shall be the clear span between the supports.

(ii)For end span with one end free and other continuous, the effective span shall be equal to the clear span plus half the effective depth of the beam or slab or clear span plus half the width of discontinuous support whichever is less.

#### (c) Cantilever Beam or Slab

The effective span of the cantilever beam or slab is taken as :

• Length of over hang plus half the effective depth
• Except where it forms the end of a continuous beam where the length up to the centre of support is taken.

### Effective Depth

Effective depth of a beam is the distance between the centroid of the area of tension reinforcement and the topmost compression fibre. It is equal to total depth of the beam minus effective cover.

### Control of Deflection (Cl. 23.2, IS 456)

For beams and slabs, the vertical deflection limits may be assumed to be satisfied if the span to depth ratios are not greater than the following :

(a)For span upto 10 m

(i)Simply supported beam$\frac{Span}{Effective depth}=20$

(ii)Cantilever beam $\frac {Span}{Effective depth}=7$

(iii)Continuous beam $\frac {Span}{Effective depth} =26$

(b)For span above 10 m, the values given in (a) should be multiplied by 10/span (m), except for cantilever for which is to be calculated the exact deflection.

(c)Depending upon the area and stress of steel for tension reinforcement, the values in (a) or (b) shall be modified by multiplying with the modification factor obtained from Fig.1.

In Fig.1. fsis the stress in steel at service loads.

(d)Depending on the area of compression reinforcement, the value of span to depth ratio can be modified as per modification factor given in Fig.2.

### Reinforcement (Refer CI. 26.5.1, IS 456)

#### (a) Minimum Reinforcement

The minimum area of tension steel shall not be less than that given by following:

$\frac {A_{s}}{bd}=\frac {0.85}{fy}$

whereAs = Minimum area of tension steel

b = Breadth of the beam or the breadth of the web of T-beam.

d = Effective depth

fy = Characteristics strength of reinforcement in N/mm2.

#### (b) Maximum Reinforcement

The maximum area of tension reinforcement shall not exceed 0.04 bD.

#### (c) Side Face Reinforcement

When the depth of the web in a beam exceeds 50 mm, it is a deep beam. So side face reinforcement should be provided along the two faces. The total area of such reinforcement shall not be less than 0.1 percent of the web area which shall be distributed equally on both the faces. The spacing of side face spacing should not be more than 300 mm or web thickness whichever is less.

#### (d) Transverse Reinforcement in Beams for Shear

The shear reinforcement in beams shall be taken around the outermost tension and compression bars.  Design of shear reinforcement

#### (e) Spacing of Reinforcement Bars

(i)The horizontal distance between two parallel main bars shall not be less than the greatest of the following:

• Diameter of the bars are of same diameter.
• Diameter of the larger bar if the diameter are unequal.
• 5 mm more than the nominal maximum size of coarse aggregate.

(ii)When the bars are in rows, they should be vertically in line and the minimum vertical distance between the bars shall be greater of following :

• 15 mm
• 2/3rd of nominal maximum size of aggregate.
• Maximum diameter of the bar.

### Nominal Cover to Reinforcement (CI. 26.4, IS 456)

Nominal cover is the depth of concrete cover to all steel reinforcement including links, shear stirrups or column ties. It is the dimension used in design and indicated in the drawings.

It shall not be less than the diameter of the bar in any case. The nominal cover is provided in R.C.C. design for following reasons :

(a)To protect the reinforcement against corrosion.

(b)To provide cover against fire.

(c)To develop the sufficient bond strength along the surface area of the steel bar.

• The code IS 456 :2000 gives values of nominal cover to meet durability as given in Table 6.1. (Table 16, IS 456)

#### Table  Nominal Cover to Meet Durability Requirements

 Esposure Condition Nominal Cover (mm) not less than Mild 20 Moderate 30 Severe 45 Very severe 50 Extreme 75

(i)For a longitudinal reinforcement bar in a column, the nominal cover shall not be less than 40 mm or diameter of such bar. But in case of columns of minimum dimensions of 200 mm or under whose reinforcement bars do not exceed 12 mm, a nominal cover of 25 mm may be used.

(ii)For footings minimum cover taken is 50 mm.

### Curtailment of Tension Reinforcement

The reinforcement shall extend at least d or 12φ (whichever is greater) beyond the point of theoretical cut off. (Theoretical cut off or centailment point is that point beyond which the bar is not longer required to resist bending at the section).

The rules governing the curtailment explained in the following articles.

#### Conditions for Curtailment of Bars

The area of tensile reinforcement (A_{st}) in a beam is calculated for the maximum bending moment.

$A_{st}=\frac {M}{\sigma_{st}jd}$

In a beam the bending moment varies along the length of the beam and hence the requirement of steel also. The number of bars required at any section is directly proportional to the bending moments at that section i.e., $A_{st}\infty M.$

It is understood that maximum number of bars are required at the section of maximum bending moment, but some of these bars may not be required at the sections having less bending moment. So, some of these bars can be curtailed at this section. (Fig. 6.3).

The point after which the bar is no longer required to resist flexure is called as theoretical curtailment point. The number of bars which can be curtailed or bent up at any distance x, from the centre of the span of beam is given by

$x=\frac {1}{2}\sqrt{\frac {n_{s}}{n_{c}}}$

wherec = Number of bars at the centre

nx = Number of bars which can be curtailed at section xx

#### Simplified Curtailment Rules for Tension Reinforcement in Beams (As Per SP 34)

The curtailment of tension reinforcement in beams is related to the bending moment diagram and rules given above. However, simplified curtailment rules are given in SP 34 (handbook on concrete reinforcement and detailing) and are given in Figs. 6.4 and Fig. 6.5.

As per Fig. 6.4, 50% of the main bars, in a cantilever beam can be curtailed at a distance $\frac{l}{2}\left ( but\frac{l}{2}>L_{d} \right )$or more from the support. In the case of simply supported beams, 50% of the main bars can be curtailed at distance 0.08l from the face of the support.