Q1: If a bent tendon is required to balance a concentrated load W at the centre of the span L, the central dip h must be at least

ANS:D -

When a concentrated load W is placed at the center of a span L of a simply supported beam, and a bent tendon is used to balance this load, the central dip ℎh of the tendon must be such that it creates a moment equal to the applied load W at the center of the span. The formula to calculate the required central dip ℎh of the tendon is derived from the principle of moments, which states that the moment created by the tendon must be equal and opposite to the moment created by the applied load to achieve equilibrium. The formula to calculate the required central dip ℎh is given by:h=8PWL2​ Where:

• W = Concentrated load applied at the center of the span
• L = Span of the beam
• P = Tension force in the tendon

This formula is derived from the equilibrium condition where the moment created by the tendon equals the moment created by the applied load. The tension force P in the tendon is assumed to be uniformly distributed, and the maximum dip occurs at the midpoint of the span. Therefore, to ensure equilibrium and balance the concentrated load W at the center of the span L using a bent tendon, the central dip ℎh of the tendon must be calculated using the formula provided above: h=WL^2​/8P This equation provides the minimum required central dip ℎh of the tendon to balance the concentrated load W at the center of the span L.