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A reinforced concrete circular section of 50,000 mm2 cross-sectional area carries 6 reinforcing bars whose total area is 500 mm2. If the concrete is not to be stressed more than 3.5 MPa and modular ratio for steel and concrete is 18, the safe load the column can carry will be nearly

A reinforced concrete circular section of 50,000 mm2 cross-sectional area carries 6 reinforcing bars whose total area is 500 mm2. If the concrete is not to be stressed more than 3.5 MPa and modular ratio for steel and concrete is 18, the safe load the column can carry will be nearly Correct Answer 205 kN

Concept:

To solve this problem, we need to convert steel into equivalent concrete section.

Total area of equivalent concrete section, Ae = Ac + mAsc

Where,

Ac is the area of concrete i.e. portion of circular column where concreter is present actually.

Ac = total area of circular column – area of steel = A - Asc

‘m Asc ‘ is the area of concrete when steel converted to its equivalent concrete

Where m is the modular ratio and Asc is area of steel reinforcement

Now finally,

Ae = A-Asc + mAsc = A + (m-1) Asc

Let ‘P’ is the safe load a column can carry and it is given by

P = permissible stress (σ) × equivalent concrete section area (Ae)

Calculation:

Permissible stress, σ = 3.5 MPa

P = 3.5 × {50000 + (18-1) × 500} = 204750 N

∴ P = 204.75 kN or P ≈ 205 kN

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