Assertion (A): In Pre-stressed Concrete, the concept of "Load Balancing" is used to determine the tendon profile such that the upward pressure from the cable counteracts a specific portion of the external gravity loads. Reason (R): For a parabolic tendon profile, the cable exerts a uniform upward pressure along the entire length of the beam. Choose the correct answer: (A) Both (A) and (R) are correct and (R) is the correct explanation of
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)Correct
- BBoth (A) and (R) are correct, but (R) is not the correct explanation of (A)
- C(A) is correct but (R) is incorrect
- D(A) is incorrect but (R) is correct
Solution
Concept
Load Balancing Concept in Pre-stressed Concrete
Formula
wu = 8Pe / L2
Step-by-step solution
1. Identify the concept of load balancing in pre-stressed concrete, where tendon profiles are designed to counteract external gravity loads. 2. Recall that for a parabolic tendon profile, the upward uniform load exerted by the cable is calculated using the formula w\_u = 8Pe / L2. 3. Evaluate Assertion (A) and Reason (R): both statements are true, and the upward uniform pressure directly explains how load balancing is achieved, making Option (a) the correct answer.
Explanation
In load balancing, curved steel tendons are shaped so that their upward pressure counteracts downward gravity loads on a concrete beam. When a tendon has a parabolic profile, it exerts a uniform upward force along the entire length, which directly balances uniform gravity loads and reduces bending. Therefore, both statements are correct, and Reason (R) directly explains Assertion (A).
Shortcut
To remember the Load Balancing concept for parabolic tendons, use the rule "Parabola = Uniform Push Up": - Parabolic Cable: Exerts a uniform upward load (wu = 8Pe / L2) across the beam. - Load Balance: The upward uniform pressure directly counteracts uniform gravity loads, which is why a parabolic profile is chosen.
Common mistake
A common mistake is selecting option B by believing that Reason (R) is merely a standalone correct statement rather than the direct explanation for Assertion (A). Students often fail to recognize that the uniform upward pressure exerted by a parabolic cable profile is the exact physical mechanism behind load balancing, which directly explains why the tendon profile is selected to counteract gravity loads.
Correct answer: A) Both (A) and (R) are correct and (R) is the correct explanation of (A)