Q1: If At is the gross area of steel in tension, d is the effective depth of the beam and y is the depth of the centre of gravity of the resultant compression, the moment of resistance M of the beam, is given by

ANS:C - M = Atf(d + y)

The moment of resistance (M) of a reinforced concrete beam is typically given by the equation: M=At​×fy​×(d−3y​) Where:

• At​ is the gross area of steel in tension,
• fy​ is the yield strength of the steel reinforcement,
• d is the effective depth of the beam,
• y is the depth of the center of gravity of the resultant compression force.

In this equation, At​×fy​ represents the resisting moment due to the tensile strength of the steel reinforcement. The lever arm (3d−3y​) represents the distance between the centroid of the tension reinforcement and the centroid of the compression force, which provides the mechanical advantage for resisting bending. Therefore, the moment of resistance (M) of the beam is given by the product of the resisting moment due to the tensile strength of the steel and the lever arm. This equation accounts for the combined action of both the steel reinforcement and the concrete in resisting bending moments in the beam.