ANS:B -

For a balanced design of a prestressed concrete beam, the maximum bending moment due to dead load (Md), the maximum bending moment due to live load (Mt), and the total effective prestressing force (F) must satisfy a specific relationship. In a balanced design, the tensile and compressive stresses resulting from the external loads and the prestressing force are such that they balance each other, resulting in a state of equilibrium and minimal deflection under service loads. The relationship for a balanced design can be expressed as: Md+Mt=F This equation states that the sum of the maximum bending moments due to dead load and live load must equal the total effective prestressing force. Explanation:

• Md: Maximum bending moment due to dead load.
• Mt: Maximum bending moment due to live load.
• F: Total effective prestressing force.

In a balanced design, the prestressing force is chosen such that it counteracts the bending moments induced by the applied dead and live loads. This ensures that the resulting stresses in the beam are within the allowable limits and that the structure remains stable and structurally sound. By satisfying the equation Md+Mt=F, the designer ensures that the prestressed concrete beam is designed to efficiently utilize the prestressing force to resist the external loads, resulting in a structurally optimized and economical design.