## Balanced Section, Under Reinforced Section & Over Reinforced Section

###### Parameters Used Here are:
• Ast= Area of Steel in Tension Zone
• fst or σst= Stress in Steel
• fst.u or σst.u= Ultimate Stress in Steel
• fc or σc = Stress in Concrete
• fy = Yield strength of steel
• fck = Characteristics strength of concrete
• ϵc= Strain in concrete
• ϵst = Strain in Steel
• Nc or nor Xu = Critical Neutral Axis
• N or n= Actual Neutral Axis
• D= Total Depth of Beam
• d= Effective depth of beam (from centroid of steel in tension zone to topmost fiber of concrete in compression zone).
• Note: The value of stress and strain shown in the definition below for each sections of concrete when the section is Design by limit state method (LSM), because it beyond the elast region of stress strain curve.

### Balanced Section

Definition: “The RCC Section which is reinforced with such amount of steel that when extreme fiber of compression zone of concrete reaches to its permissible allowable stress and strain value c =0.0035 and fc=0.45fck), the steel provided in tension zone also reaches to its permissible yield allowable strain and stress value st= (0.002+(0.87fy/Es)) and fs= 0.87fy) at same time then that section will be a Balanced or Critical Section.”

• The failure of such section may be due to compression or tension. So balanced section is basically the combination of both brittle and ductile section.
• The Neutral Axis of such sections lies in the middle of the section (n=nc) is called Critical Neutral Axis, normally denoted by nc or Xubal.
• The Moment of resistance (Mr) of such sections can be determined by Multiplying the lever arm of the stressed section either by Compression force or Tension force because the centroidal of both the areas (Compression and Tension zone) are almost at same distance from neutral axis.

(Moment of Resistance) Mr= Compressive Force*(d-0.42d)

or Mr= Tensile Force*(d-0.42d)

### Over-Reinforced Section

Definition: “The RCC Section which is reinforced with such amount of steel that when extreme fiber of concrete in compression zone reaches to its permissible allowable Strain and stress valuec =0.0035 and fc=0.45fck), while the allowable stresses in steel provided in tension zone doesn’t reaches to its permissible allowable yield strain and stressst= (0.002+(0.87fy/Es)) and fs= 0.87fy) then that section will be an Over-Reinforced Section.”

• It means that the percentage of reinforcement provided more than the requirements.
• That RCC element or section will fail due to brittleness which is dangerous to any section.
• The section is uneconomical due to high percentage of reinforcement provided.
• In such sections the actual Neutral Axis (NA) will move downward below Critical Neutral Axis (Nc) or n>nc.
• The Moment of resistance(M r) of such sections will be always more than the Balance section.

(Moment of resistance) Mr=b.n.(fst/2) *(d-n/3)

### Under-Reinforced Section

Definition: “The RCC Section which is reinforced with such amount of steel that when extreme fiber of concrete in compression zone doesn’t reach to its permissible allowable strain and stress valuec =0.0035 and fc=0.45fck), while the allowable stresses in steel provided in tension zone doesn’t reaches to its permissible allowable yield strain and stressst= (0.002+(0.87fy/Es)) and fs= 0.87fy) then that section will be an Under-Reinforced Section.”

This is the most desirable section(Under-Reinforced) because:

• It means that the percentage of reinforcement provided less than the requirements, so saving steel cost.
• That RCC element or section will fail in Ductile behavior which is the most desirable condition for any structure.
• Show enough warning before failure because first steel has to reach its yield stress before concrete.
• The Moment of resistance of such sections will be always less than the Balance section.
• In such sections the actual Neutral Axis (NA) will move upward above Critical Neutral Axis (Nc) or n<nc.
• Moment of resistance (Mr) of such sections can be determined by considering the stress of steel.

(Moment of Resistance) Mr=fst.Ast(d-n/3)