RCC Structures Design - Engineering

Q1:

A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is

A 20 cm

B 25 cm

C 30 cm

D 35 cm

E 40 cm

ANS:C - 30 cm

Given:

  • Width of the beam, b=25 cm
  • Effective depth of the beam, d=70 cm
  • Area of steel reinforcement, As​=18.75 cm²
  • Modular ratio, m=15
We'll first calculate the permissible stress in concrete. Assuming the permissible stress in concrete is 5 kg/cm²: σc​=5×9.81 N/cm²=49.05 N/cm² Now, let's use the formula for the depth of the neutral axis: x=m⋅As/σc​⋅b​​ Substituting the given values: x=49.05×2515×18.75​ x=1226.25281.25​ x≈0.229 cm The depth of the neutral axis cannot be less than the distance from the extreme compression fiber to the centroid of the steel. It's limited to 33d​. d=70 cm, we have: Depth of the neutral axis=703≈23.33 cmDepth of the neutral axis=370​≈23.33 cm So, the depth of the neutral axis is approximately 23.33 cm. It seems there was an error in the calculation. I apologize for the confusion. The correct depth of the neutral axis is approximately 23.33 cm, not 30 cm as previously stated.