Correct : A,B,D

The question asks which methods can be used to verify that flexural stresses in a prestressed concrete beam stay within allowable limits at both transfer and service stages.
Option A — Limiting zone — True
The limiting zone defines the region of eccentricity within which the prestressing cable must lie to ensure all four stress conditions (top and bottom fibre stresses at transfer and service) are satisfied simultaneously. It is a direct and standard method for checking stress limits.
Option B — Magnel''s graph — True
Magnel''s diagram plots 1/P versus eccentricity e. Each of the four stress conditions produces a linear boundary, and the feasible region enclosed by all four lines gives all valid (P, e) combinations. It directly checks whether stresses are within allowable limits and is one of the most powerful design tools in prestressed concrete.
Option C — Hoyer effect — False
The Hoyer effect relates to the bond mechanism in pre-tensioned beams — when the prestressing wire is cut, it expands laterally due to Poisson''s effect, creating a wedge action that transfers prestress into the concrete. This is a bond/anchorage concept, not a method for checking flexural stress limits.
Option D — Load balancing method — True
T.Y. Lin''s load balancing method treats the prestress as an equivalent transverse load. The net stress at any section is computed as P/A ± the stress from any unbalanced load. This can be used to verify stresses against allowable limits at both transfer and service stages.
Correct answer: A, B, D