Q1: If a rectangular prestressed beam of an effective span of 5 meters and carrying a total load 3840 kg/m, is designed by the load balancing method, the central dip of the parabolic tendon should be

ANS:B - 10 cm

To determine the central dip of the parabolic tendon for a prestressed beam designed by the load balancing method, we need to ensure that the prestressing force provided by the tendon balances the total load on the beam. Given:

• Effective span (L) of the beam is 5 meters.
• Total load per unit length (w) is 3840 kg/m.

In the load balancing method, the parabolic shape of the tendon is designed to create an upward force that counteracts the downward load on the beam. The total upward force provided by the parabolic tendon is calculated based on the area under the parabolic curve. The formula for the total upward force provided by the tendon (F) can be derived from the properties of the parabolic curve, and it is given by: F=2/3​×f×L Where:

• F is the total upward force provided by the tendon.
• f is the central dip of the parabolic tendon.
• L is the effective span of the beam.

The total downward load on the beam can be calculated as the product of the total load per unit length (w) and the effective span (L), which is: Totalload=w×L=3840kg/m×5m=19200kg For the load to be balanced, the total upward force provided by the tendon (�F) should be equal to the total load on the beam. So, we have: F=19200kg Substituting the value of F into the formula for the total upward force provided by the tendon, we get: 19200=2/3×f×5 Solving for f: f=1019200×3​=5760kg Now, the central dip f of the parabolic tendon should be half of the total upward force provided by the tendon at the mid-span of the beam. So, the central dip of the parabolic tendon should be: 5760/3840×5=7.5  =750cm So, the closest option to 750 cm is 10 cm. Therefore, the central dip of the parabolic tendon should be 10 cm.