Q1: If the maximum dip of a parabolic tendon carrying tension P is h and the effective length of the prestressed beam is L, the upward uniform pressure will be

ANS:B -

To find the upward uniform pressure exerted by the parabolic tendon on the prestressed beam, we need to consider the equilibrium condition. The total force exerted by the tendon must be balanced by an equal and opposite reaction force from the beam. Since the tendon is parabolic, we can consider it as a distributed load with varying intensity. The total force exerted by the tendon can be calculated by integrating the force distribution along its length. Since the tendon carries tension P, and assuming the tendon has a parabolic shape, the force at any point y along its length is proportional to the depth of the tendon at that point. The equation for the parabolic shape of the tendon can be given by: y=4h/L^2​x(L−x) Where:

• y = depth of tendon at a distance x from one end
• x = distance from one end of the tendon
• ℎ = maximum dip of the tendon
• L = effective length of the prestressed beam

To find the total force exerted by the tendon, we integrate this equation over the length of the tendon (from 0 to L): Ftotal​=∫0L​L24h​x(L−x)dx After integrating and simplifying, we get: Ftotal​=3/2​Ph Now, to find the upward uniform pressure (p) exerted by the tendon, we divide the total force (Ftotal​) by the area over which it acts. Since the pressure is uniform, we consider it to act over the entire area beneath the tendon, which is the cross-sectional area of the beam. p=L⋅hFtotal​​ Substituting the expression for Ftotal​, we get: p=3/2​⋅L⋅h/Ph​ p=32​⋅L/P​ So, the upward uniform pressure exerted by the parabolic tendon on the prestressed beam is 2332​ times the tension P in the tendon, divided by the effective length L of the prestressed beam.