Short RCC column under axial load — working stress method A 200 mm × 200 mm reinforced concrete column is provided with four steel bars having a total steel area of 1200 mm². If the permissible stress in concrete is 5 N/mm² and the modular ratio m = Es/Ec is 15, compute the safe axial load on the column (use transformed area method: Aeq = Ac + m * Ast).

Introduction / Context:This problem checks the working stress method for short axially loaded reinforced concrete columns. Under axial compression, the steel is transformed into equivalent concrete using the modular ratio, and the safe load is obtained by multiplying the permissible concrete stress by the transformed area.

Given Data / Assumptions:

• Column size = 200 mm × 200 mm → gross area Ag = 40000 mm².
• Total steel area Ast = 1200 mm² (4 bars combined).
• Permissible concrete stress σc,perm = 5 N/mm².
• Modular ratio m = Es/Ec = 15.
• Short, concentrically loaded column; eccentricity neglected.

Concept / Approach:Working stress method uses transformed section area: Aeq = Ac + m * Ast, where Ac = Ag − Ast. Safe axial load P = σc,perm * Aeq.

Step-by-Step Solution:

Verification / Alternative check:You may also check using percentage steel p = Ast/Ag = 1200/40000 = 3 percent (approx) and ensure that the assumed short-column, concentric load assumptions hold. The value aligns with standard transformed area computations.

Why Other Options Are Wrong:

• 264 kN, 274 kN, 294 kN: These arise from using wrong gross area, ignoring modular ratio, or arithmetic slips.
• None of these: Not correct because 284 kN matches the correct calculation.

Common Pitfalls:Using gross area Ag instead of Ac; forgetting to subtract steel area before adding m * Ast; mixing units (N vs kN).

Final Answer:284 kN