JNTU B.Tech III DESIGN OF REINFORCED CONCRETE STRUCTURES Previous Question Paper (March - 2021 - R16)

• Balanced Section: A section where the strain in concrete reaches its ultimate limit (0.0035) simultaneously with the strain in steel reaching its yield strain (0.002 + 0.87fy/Es). The depth of the neutral axis is equal to the limiting depth (xu = xu,max). Failure is sudden and brittle.
• Under-Reinforced Section: A section where the area of steel is less than that required for a balanced section. The steel reaches its yield strain before the concrete reaches its ultimate strain. The failure is ductile, characterized by large deflections and cracks, providing warning before collapse.
• Over-Reinforced Section: A section where the area of steel exceeds that required for a balanced section. The concrete reaches its ultimate strain before the steel yields. This leads to a sudden, brittle, and catastrophic failure without warning.

Sketch representation:

The stress block parameters in the Limit State Method are derived based on the parabolic-rectangular stress distribution of concrete. The total compressive force (C) and its point of application (lever arm) are determined as follows:

• Total Compressive Force (C): The area of the stress block is the integral of the stress diagram over the neutral axis depth (xu). For a rectangular section of width (b), the force is:
C = 0.36 fck b xu
• Point of Application (Centroid): The centroid of the stress block is calculated by taking the moment of the stress area about the extreme compression fiber. The distance from the extreme compression fiber to the centroid of the compressive force is:
y = 0.42 xu
• Lever Arm (z): The distance between the compressive force (C) and the tensile force (T) acting at the centroid of the steel reinforcement is:
z = d - 0.42 xu

Where (fck) is the characteristic compressive strength of concrete, (b) is the width of the section, (xu) is the depth of the neutral axis, and (d) is the effective depth.