Balanced, Under-Reinforced and Over-Reinforced Beam Sections

Reinforced concrete beams are classified as balanced, under-reinforced and over-reinforced based on percentage of reinforcement it has. Details of these beam sections are discussed.

Balanced, Under-Reinforced and Over-Reinforced Beam Sections

Moment of resistance of reinforced concrete beams are calculated based on following assumptions:

1. Plane sections remain plane in bending up to the point of failure. This means that strains are proportional to distance from the neural axis.

2. Ultimate limit state of bending failure is assumed to have been reached when the strain in the concrete at the extreme bending compression fiber reaches 0.0035

Strain diagram of a beam section; (a) Section, (b) Strain diagram

3. The stress distribution across compression face will correspond to the stress-strain diagram for concrete in compression.

4. The tensile strength of concrete is neglected as the section is assumed to be cracked up to the neutral axis.

5. The stress in steel will correspond to the corresponding strain in the steel.

As given in assumption 2 above that the reinforced concrete section in bending is assumed to fail when the compression strain in concrete reaches the failure strain in bending compression equal to 0.0035.

Balanced Beam Section

Reinforced concrete beam sections in which the tension steel also reaches yield strain simultaneously as the concrete reaches the failure strain in bending are called balanced sections.

Under-Reinforced Beam Section

Reinforced concrete beam sections in which the steel reaches yield strain at loads lower than the load at which the concrete reaches failure strain are called under-reinforced sections.

Every singly reinforced beam should be designed as under-reinforced sections because this section gives enough warning before failure.

Yielding of steel in under-reinforced beam section does not mean the structure has failed, as when steel yields, excessive deflection and cracking in beam will occur before failure which gives enough time to occupants to escape before the section fails.

The failure in under-reinforced beam section is due to the concrete reaching its ultimate failure strain of 0.0035 before the steel reaches its failure strain which is much higher 0.20 to 0.25.

Under-Reinforced Beam Section

Over-Reinforced Beam Sections

Reinforced concrete beam sections in which the failure strain in concrete is reached earlier than the yield strain of steel is reached, are called over-reinforced beam sections.

If over-reinforced beam is designed and loaded to full capacity then the steel in tension zone will not yield much before the concrete reaches its ultimate strain of 0.0035. This due to little yielding of steel the deflection and cracking of beam does not occur and does not give enough warning prior to failure.

Failures in over-reinforced sections are all of a sudden. This type of design is not recommended in practice of beam design

Over-Reinforced Beam Sections

What is the difference between an over reinforced and under reinforced RCC beam?

To understand the difference between over reinforced and under reinforced, first we need to understand Balanced section.

BALANCED SECTION :

• The stresses in concrete and steel reach to permissible values at the same time.
• concrete and steel theoretically fail at the same time.
• Practically it is difficult to have a balanced section.
• Theoretically all the sections designed are balanced sections.
• The failure is by primary compression( In practise the ultimate failure is by crashing of concrete in compression zone only, even though beam is balanced section is called primary compression).
• Xu=Xumax

STRESS AND STRAIN DISTRIBUTION FOR BALANCED SECTION:

where ,

Xumax is the maximum depth of neutral axis at failure condition at which concrete reaches to a maximum strain of 0.0035, At this condition steel will be in plastic zone with continuous yielding or deformation.

Xumax Equation: Xumax / 0.0035 = d-xumax / (0.87fy/Es + 0.002)

Mu limit is Moment of resistance of balanced section.

Xu is the Neutral axis at general loading condition where concrete and steel might not have reached their maximum strains ,how ever at collapse Xu will be equal to Xumax

i.e Compressive force = Tensile force. ( 0.36*fck*b*Xu=0.87*fy*Ast)

Xu Equation: Xu= (0.87*fy*Ast)/(0.36*fck*b)

UNDER REINFORCED SECTION:

• Reinforcement available in the beam is less than that of a balanced section, i.e Xu < Xumax .
• Failure is in steel ,causes a ductile failure and gives clear warning before failure.
• Most of the practical sections are under reinforced sections.
• Failure is by primary tension.

OVER REINFORCED SECTION:

• Steel in the section is more than that of required for a balanced section, i.e Xu > Xumax.
• Failure is in concrete , causes a brittle/sudden failure without any prior warning
• As per Limit state method of design of over reinforced sections should be avoided