Behavior of Reinforced Concrete Beam in Bending


Beams
 are structural members that are primarily subjected to forces acting transverse to its axis which causes flexure or bending in beams.


Let us discuss the behavior of a Reinforced concrete Beam subject to increasing moment:




 

Uncracked Section:


  • Since Bending causes tensile and compressive stresses in the cross section of the beam, and the nature of these stresses depends on the position of the fibre in the beam and also the type of support conditions.
  • Assuming gravity loading, the top fibre near the mid-span of a simply supported beam will be under compression and the bottom fibres will be in tension.
  • As long as the moment is small and does not induce cracking, the strains across the cross section of the beam are small and the neutral axis is at the centroid of the cross section.
  • The stresses are related to the strains and the deflection is proportional to the load, as in the case of isotropic, homogeneous, linearly elastic beams. The following formula for pure flexure holds good-
Flexure Formula

Where
M= Bending Moment
I = Moment of inertia of the section about the bending axis.
clip_image002=fibre stress at a distance ‘y’ from the centroidal or neutral axis.
E = Young’s Modulus.
R = Radius of curvature of the bent beam.


Cracked Section:


  • As the load is increased, extensive cracking occurs. The cracks also widen and spread gradually towards the neutral axis.
  • Since concrete is weak in bearing tensile forces. Now the cracked portion of the concrete beam become ineffective in resisting the tensile stresses. There is a sudden transfer of tension force from the concrete to the steel reinforcements in the tension zone. All the tension forces are borne only by reinforcement.
  • This results in increased strains in the reinforcements. If the minimum amount of tensile reinforcement is not provided, the beam will suddenly fail.





 

Yielding of Tension Reinforcement and Collapse:


  • If the loads are increased further, the tensile stress in the reinforcement and the compression stress in the concrete increase further.
  • The stresses over the compression zone will become non-linear. However, the strain distribution over  the cross section is linear. This is called the ultimate stage.
  • At one point, either the steel or concrete will reach its respective capacity; steel will start to yield or  the concrete will crush.