Types of R.C.C. beam, Fundamental assumptions of elastic theory of bending

R.C.C. Structure design Working Stress method
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Types of R.C.C. beam,Singly,doubly and T, Flanged Reinforced Beams,fundamental assumptions of elastic theory, Assumptions in the theory of simple bending of R.C.C. beams(Working stress method)

Plain Cement Concrete has low tensile strength. A beam made up of plain cement concrete will have low load carrying capacity and will fail by cracking in the tension zone. It is therefore reinforced by placing steel bars in the tensile zone. These bars will take up the tensile stresses and thus increase the load carrying capacity or strength of the beam. The steel placed in the tensile zone, is called as longitudinal steel or main steel.

 TYPES OF R.C.C. BEAM

           Types of  R.C.C. beam are of following :

            (i)        Singly Reinforced Beams :

This is the one of Types of  R.C.C. beam in which steel reinforcement is placed in the tensile zone only are called as singly reinforced beams.

            (ii)       Doubly Reinforced Beams :

The beams in which reinforcement is placed in the tensile as well as compression zone are called as doubly reinforced beams.

            (iii)     Flanged Beams (T beams and L beams) :

In most reinforced concrete structures, the slab and beams are case monolithic. Thus, the beam forms a part of the floor system. When the beam bends, a part of the slab also bends along with the beam. So, the intermediate beams in a floor system act as T beams and the end beams as L beams. The beams in which a portion of the slab acts together with the beam for resisting compressive stresses are called as flanged beams. Figure 2.1 shows singly reinforced, doubly reinforced and T-beam sections.

Singly Reinforced,Doubly Reinforced and T-Beam

 ASSUMPTIONS IN THE THEORY OF SIMPLE BENDING OF R.C.C. BEAMS (WORKING STRESS METHOD)

The elastic theory of bending or simply straight line theory forms the basis of working stress method of design. In this method, the ultimate compressive strength of concrete and the yield stress of steel are divided by the appropriate factors of safety to get the allowable or permissible stresses in the materials under working loads. This theory is applicable only in the narrow range of stress-strain curve where Hook’s law is applicable.

Fundamental assumptions of elastic theory of bending

The fundamental assumptions of elastic theory of bending are explained below:

A section which is plane before bending remains plane after bending. This assumption implies that the strain above and below the neutral axis are proportional to the distance from the neutral axis i.e. the strain distribution is triangular, linearly varying from zero at the neutral axis to maximum value at the extreme fibre.

The concrete and steel reinforcement are perfectly bonded.It means that the tensile strain in steel reinforcement is equal to the tensile strain in concrete surrounding the steel.

All tensile stresses are taken up by steel and none by concrete.This assumptions implies that the contribution of concrete to take tension is completely neglected and the concrete is assumed to be cracked in the tension zone.

The stress-strain relationship of steel and concrete under working loads is a straight line.It implies that stress distribution is also linear like strain distribution, with a zero at the neutral axis to maximum value at the extreme fibres.

The modulli of elasticity of steel Es and concrete Ec are constant.

The modular ratio (m) has the value

    \[\frac{280}{3\sigma _{cbc}}\]

, where σcbc is the permissible compressive strength of concrete in bending in N/mm2.

There are no initial stresses in steel and concrete.

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