## BEAM- SINGLY REINFORCED BEAM

A beam is a structural element that primarily resists loads applied laterally to the beam’s axis. Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam’s support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, which in turn induce internal stresses, strains, and deflections of the beam. Beams are characterized by their manner of support, profile (shape of cross-section), equilibrium conditions, length, and material.

## Types of Beam

- Rectangular Beam
- L-Shape Beam
- Circular Shape Beam
- T-Shape Beam

There are 2 types of the beam for designing purpose called-

- Singly Reinforced Beam
- Doubly Reinforced Beam

## Singly Reinforced Beam

The beam that is longitudinally reinforced only in the tension zone, is known as a singly reinforced beam. In Such beams, the ultimate bending moment and the tension due to bending are carried by the reinforcement, while the compression is carried by the concrete.

Note- In practice, for singly reinforced beams, two additional bars are provided in the compression face of the beam so that stirrups can be tied with bars. These additional reinforcements are of a nominal diameter of 8mm or 10mm.

## Doubly Reinforced Beam

The doubly reinforced beam is defined as the beam in which the reinforcement is provided by the steel in both tension and compression zone of the beam.

It is provided to increase the moment carrying capacity of the section.

When the depth of a section is restricted due to any reason, the beam is designed as a doubly reinforced concrete beam.

# SINGLY REINFORCED BEAM

## STRESS-STARIN CURVE FOR STEEL

STRESS BLOCK PARAMETERS

Where,

x = Depth of Neutral Axis

b = Breadth of section

d = Effective depth of section

## Depth of Neutral Axis

The depth of neutral axis can be obtained by considering the equilibrium of the normal forces that is,

Resultant force of compression = 0.36f_{ck}bx

Resultant force of tension = 0.87f_{y}*A_{t}

Force of compression = Force of tension

0.36f_{ck}bx = 0.87f_{y}*A_{t}

x = 0.87f_{y}A_{t}/0.36f_{ck}*b

Where, A_{t}= Area of Tension Steel

## Lever Arm

The Distance between two lines of action of two forces C & T is called the **Lever arm** and is denoted by z,

z = d-0.42x

z = d- 0.42(0.87f_{y}A_{t}/0.36f_{ck}b)

z = d- f_{y}A_{t}/f_{ck}b

## Moment of Resistance

Moment of Resistance with respect to concrete = Compressive Force * Lever Arm

= 0.36f_{ck}b*z

Moment of Resistance with respect to steel = tensile force * lever arm

= 0.87f_{y}A_{t}*z

Maximum Depth of Neutral Axis (x_{m})

f_{y} N/mm^{2} | x_{m} |

250 | 0.53d |

415 | 0.48d |

500 | 0.46d |

### Limiting Moment of Resistance Values

Where MoR = Moment of Resistance

For Under reinforcement section,

MoR = 0.87f_{y}A_{t} (d – (f_{y}A_{t}/f_{ck}b))

For Balanced Section,

MoR = 0.87f_{y}A_{t }(d-0.42x_{m})

For Over Reinforced Section,

MoR = 0.36f_{ck}bx_{m}(d-0.42x_{m})

## Factored Bending Moment,

FBM = Load Factor * BM

If, Load Factor is not Given, Use 1.5.