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

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.