Question

Select ALL CORRECT option(s) which can be considered to check whether the flexural stresses in a prestressed concrete beam are within the allowable stresses at the transfer and the service stages.

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

Hint:

Only tools built directly from the four permissible stress inequalities (at transfer and service) check flexural stress limits: the limiting zone and Magnel's diagram.

Answer 1

The Correct Option is A, B

Step 1: Understanding the Question.
In a prestressed concrete beam, the fibre stresses at the top and bottom faces must stay within allowable limits at two critical stages: at transfer (when the full prestress acts but the dead load moment is small) and at service (when losses have occurred but the full working load acts). We need to identify which listed item is actually used to check that the flexural stresses stay within these permissible limits at both stages.

Step 2: Key Formula or Approach.
The fibre stress at a section under a prestress force \(P\) at eccentricity \(e\), with bending moment \(M\), is
\[ f = \frac{P}{A} \pm \frac{Pe}{Z} \pm \frac{M}{Z} \]
For safety this stress must lie between the allowable compressive and tensile limits at transfer and again at service, at every section along the beam. Two well established techniques exist purely to choose values of \(P\) and \(e\) that satisfy all four inequalities together.

Step 3: Detailed Explanation.
(A) Limiting zone for prestressing: this is the zone (envelope) within which the resultant thrust line, or the cable, must lie so that permissible stresses are not exceeded at transfer and at service at the same time. Plotting this zone along the beam and checking the cable profile against it is a direct, standard method of verifying the flexural stress limits. This is CORRECT.
(B) Magnel's graph (Magnel diagram): this plots \(1/P\) against eccentricity \(e\), using the four stress inequalities (two at transfer, two at service) as boundary lines. The feasible region on the graph gives every combination of \(P\) and \(e\) that keeps stresses within limits at both stages, so this is CORRECT.
(C) Hoyer effect: this is the wedge action created near the ends of a pre-tensioned member as the tendon tries to shrink back to its original diameter (a Poisson's ratio effect) after release, which helps transfer the prestress force to the concrete by friction and bearing over the transmission length. It is a bond-transfer mechanism, not a check on flexural stress limits. INCORRECT.
(D) Load balancing method: this design technique (due to T. Y. Lin) chooses the upward force from the tendon's curvature to balance a chosen part of the external transverse load, mainly used to select a tendon profile and prestress force for deflection control. It is not, by itself, a stress-limit check at transfer and service. INCORRECT.

Step 4: Final Answer.
Only the limiting zone concept and Magnel's graph are methods used to check that flexural stresses stay within allowable limits at transfer and service.
\[ \boxed{\text{Options (A) and (B)}} \]