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

ANS:C -

To calculate the maximum stress (f) in a prestressed beam subjected to a maximum bending moment (M), we need to consider both the effects of prestress force (P) and the external bending moment (M). The maximum stress in the beam can be determined using the flexure formula for a rectangular beam: f=ZM​ Where:

• f = Maximum stress in the beam
• M = Maximum bending moment
• Z = Sectional modulus of the beam

However, in the case of a prestressed beam, the prestress force (P) also contributes to the overall stress distribution within the beam. Therefore, the total bending moment (totalMtotal​) acting on the beam is the sum of the externally applied bending moment (M) and the moment due to prestress force (P). Mtotal​=M+P×e Where:

• totalMtotal​ = Total bending moment
• P = Prestress force
• e = Eccentricity of the prestress force with respect to the centroidal axis of the beam's cross-section

Once the total bending moment (totalMtotal​) is determined, we can use it in the flexure formula to calculate the maximum stress (f) in the beam: f=Mtotal​​/Z It's important to note that the prestress force (P) should be considered as a compressive force in the beam, while the external bending moment (M) can induce both compressive and tensile stresses depending on the beam's bending behavior. Therefore, to calculate the maximum stress (f) in the prestressed beam, the total bending moment (Mtotal​) should be determined first by considering both the external bending moment (M) and the moment due to prestress force (P). Then, this total bending moment can be used in the flexure formula to find the maximum stress (f) in the beam.