Question

Which of the following methods are used to check whether the flexural stresses in a prestressed concrete beam remain within permissible limits at transfer and final stages? Select all the correct option(s).

• A. Hoyer's effect
• B. Limiting zone of prestress method
• C. Magnel's graph
• D. Load balancing method

Hint:

For prestressed concrete design, remember that "Magnel's graph" and "Limiting zone" are graphical methods to find valid combinations of prestressing force and eccentricity, while "Load balancing" is a conceptual method that simplifies stress calculations.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to identify the standard analysis and design methods used to ensure that the stresses at the top and bottom fibers of a prestressed concrete beam do not exceed the allowable limits under different loading conditions (at transfer and in service).
Step 2: Detailed Explanation of Options:

• (a) Hoyer's effect: This refers to the mechanism of bond and stress transfer in pretensioned concrete members when the prestressing force is released. The tensioned wire, upon being cut, expands laterally (Poisson's effect), creating a "wedge" that anchors it within the concrete. This is a physical phenomenon, not a design method for checking overall flexural stresses.
  
• (b) Limiting zone of prestress method: This is a method that defines a "safe" or "limiting" zone for the centroid of the prestressing steel. If the steel profile lies within this zone, it guarantees that the flexural stresses in the concrete will remain within the permissible limits at all stages. This is a direct method for checking stress compliance.
  
• (c) Magnel's graph: This is a graphical design aid. It plots the inequalities for stress limits (four inequalities: top and bottom fibers at transfer and service stages) on a graph of prestressing force (\(P\)) versus eccentricity (\(e\)). The resulting feasible region on the graph shows all combinations of \(P\) and \(e\) that satisfy the stress conditions. This is a classic method used for this exact purpose.
  
• (d) Load balancing method: This is a powerful concept for analysis and design. The prestressing tendon is profiled in such a way that its upward force component "balances" a portion of the dead and live loads. The stresses are then calculated based on the net moment (from unbalanced loads) and the axial compression from prestress. This method is fundamentally used to design for and check stresses.

Step 3: Final Answer:
The limiting zone method, Magnel's graph, and the load balancing method are all established techniques used to analyze and design prestressed concrete beams to ensure stresses remain within allowable limits. Hoyer's effect is a related physical phenomenon but not a design/checking method in this context.