Q1: P is the prestressed force applied to tendon of a rectangular prestressed beam whose area of cross section is A and sectional modulus is Z. The minimum stress f on the beam subjected to a maximum bending moment M is

ANS:C -

To determine the minimum stress f on a rectangular prestressed beam subjected to a maximum bending moment M, we can use the basic principles of mechanics of materials and prestressed concrete. The minimum stress in the beam occurs at the bottom fiber of the beam's cross-section, where tensile stresses are highest due to bending. When prestressing is applied, it counteracts the tensile stresses induced by bending, reducing or eliminating the tensile stresses in the beam. Given:

• P is the prestressing force applied to the tendon.
• A is the area of the cross-section of the beam.
• Z is the sectional modulus of the beam.
• M is the maximum bending moment.

The minimum stress f in the beam can be calculated using the formula: f=M/Z​−P/A​ This equation represents the stress resulting from the bending moment M and the stress resulting from the prestressing force P. The prestressing force tends to create compressive stresses in the beam, opposing the tensile stresses induced by bending. Therefore, the minimum stress f on the beam subjected to a maximum bending moment M is given by the formula above. It represents the combined effect of bending and prestressing on the beam's stress distribution.