Q1: If permissible compressive stress in concrete is 50 kg/cm², tensile stress in steel is 1400 kg/cm² and modular ratio is 18, the depth d of the beam, is

ANS:A -

To determine the depth (d) of the beam, we can use the concept of modular ratio (m) in reinforced concrete beam design. The modular ratio (m) relates the modulus of elasticity of steel (Es) to the modulus of elasticity of concrete (Ec) and is given by: m=Ec/​Es​​ Given that the modular ratio (m) is 18, we can express the modulus of elasticity of steel (Es) in terms of the modulus of elasticity of concrete (Ec): Es​=m×Ec​ Now, we know that the tensile stress in steel (σs​) can be related to the compressive stress in concrete (σc​) through the modular ratio: σs​=m×σc​ Given that the permissible compressive stress in concrete (σc​) is 50 kg/cm² and the tensile stress in steel (σs​) is 1400 kg/cm², we can rearrange the equation to solve for the compressive stress in concrete: σc​=σs/m​​ σc​=(1400kg/cm2​)/18 σc​≈77.78kg/cm^2 Now, we can use the formula for compressive stress in concrete to find the depth (d) of the beam: σc​=M​/Z Where:

• M = Bending moment
• Z = Section modulus

For rectangular sections, the section modulus (Z) is given by: Z=bd^2/6​ Substituting the values: 77.78=M/bd^2/6 277.78=6M/bd^2​ 77.78bd^2=6M bd^2=6M/77.78​ Now, we need additional information such as the bending moment (M) or the dimensions of the beam (b) to solve for the depth (d) of the beam. Without this information, we cannot determine the exact depth of the beam.