JNTU B.Tech III Year DESIGN OF REINFORCED CONCRETE STRUCTURES Previous Question Paper (October - 2020 - R16)

Given: M = 250 kNm, b = 300 mm, D = 450 mm, fck = 25 N/mm², fy = 415 N/mm². Assuming effective cover d' = 50 mm, effective depth d = 450 - 50 = 400 mm.

1. Check for limiting moment of resistance (Mu,lim):

Since Mu (250 kNm) > Mu,lim (165.6 kNm), the section must be designed as a doubly reinforced beam.

2. Calculate reinforcement for the singly reinforced portion (Mu1 = Mu,lim):

3. Calculate reinforcement for the additional moment (Mu2 = Mu - Mu,lim = 250 - 165.6 = 84.4 kNm):

Total tension steel: Ast = Ast1 + Ast2 = 1385 + 581 = 1966 mm². Provide 4 bars of 25 mm diameter (1963 mm²).

4. Calculate compression reinforcement (Asc):

Assuming fsc ≈ 353 N/mm² for d'/d = 50/400 = 0.125:

Provide 2 bars of 22 mm diameter (760 mm²).

In the limit state design of reinforced concrete, the stress-strain relationship of concrete is represented by a simplified rectangular-parabolic stress block. The parameters of this stress block are derived from the actual stress-strain curve to simplify the calculation of the ultimate moment of resistance.

The stress block parameters are defined as follows:

• Compressive Stress Magnitude: The maximum compressive stress in the concrete is taken as 0.67fck, where fck is the characteristic compressive strength of concrete. This value accounts for the difference between the strength of concrete in a structure and the strength of a standard test cube, incorporating a partial safety factor of 1.5. Thus, the design stress is (0.67fck / 1.5) = 0.446fck.
• Depth of Stress Block: The depth of the rectangular portion of the stress block is taken as 0.42xu, where xu is the depth of the neutral axis from the extreme compression fiber.
• Total Compressive Force (C): The total compressive force acting on the concrete section is the product of the average stress, the width of the section (b), and the depth of the stress block. It is calculated as C = 0.36fck * b * xu.
• Lever Arm (z): The resultant compressive force acts at the centroid of the stress block. The distance between the centroid of the compressive force and the centroid of the tensile force (in the steel) is the lever arm, given by z = d - 0.42xu, where d is the effective depth.

These parameters ensure that the internal moment of resistance calculated using the simplified block is equivalent to the moment calculated using the actual parabolic stress distribution, providing a reliable basis for the design of beams and slabs under flexure.