In working-stress analysis of reinforced concrete, the expression [A + (m − 1)Asc] representing the equivalent concrete area of an R.C.C. section corresponds to which method of analysis?

Introduction / Context:
Before limit-state design became universal, working-stress (elastic) analysis used transformed sections so that concrete and steel could be analysed with a single material by scaling areas using a modular ratio m.

Given Data / Assumptions:

• A = gross concrete area of the section under consideration.
• Asc = area of steel in compression (if any).
• m = modular ratio = Es / Ec.

Concept / Approach:
The modular ratio method converts steel area to an equivalent concrete area: steel in compression is multiplied by m to reflect its higher stiffness compared to concrete. The transformed (equivalent) concrete area becomes A + (m − 1)Asc because the steel already displaces its own area in concrete (hence m − 1).

Step-by-Step Solution:
Start with steel in compression Asc.Transform to concrete: equivalent = m*Asc.Add to concrete area but subtract the displaced concrete area Asc → net addition (m − 1)Asc.Total equivalent area = A + (m − 1)Asc.

Verification / Alternative check:
Similar transformations are used to compute transformed second moment of area for elastic stress checks at service loads.

Why Other Options Are Wrong:

• Load factor/ultimate load methods belong to plastic or limit-state philosophy; they do not use this transformed-area expression.
• None of these: Incorrect since the modular ratio method explicitly uses it.

Common Pitfalls:
Forgetting that tension steel is ignored in concrete (cracked) tension zone; using the wrong m value; mixing service and ultimate stress checks.

Final Answer:
modular ratio method