Q.2 A reinforced concrete column is 300mm x 300mm in section .Es=210 GN/m2 and Ec= 14 GN/m2 .

Question

Q.2 A reinforced concrete column is 300mm x 300mm in section .The column is provided with 8 bars each of 20mm diameter .The column carries a load of 360kn.Find the stresses in concrete and the steel bars .Take Es=210 GN/m2 and Ec= 14 GN/m2 .

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Answer 1

Area of column = 300mn x 300

= 90000 mm²

Area of steel bar = 8 x \(\Big(\frac{\pi}{4}\Big)\)x (20)²

= 8 x \(\frac{\pi}{4}\) x 400

= 2513.27 mm²

Strain in concrete = Strain in bars

\(\frac{σ_c}{E_c}\) =\(\frac{σ_s}{∑_s}\) .........(1)

total load

ρ = σ_sA_s + σ_cA_c

360 x 10³N = σ_sA_s + σ_cA_c  .....(ii)

σ_c = \(\frac{∑_c}{∑_c}\) ∑_s

σ_c = \(\frac{14 \times10^9}{210\times10^9}\) x σ_s

σ_c = \(\frac{σ_s}{15}\) ....(iii)

Putting the value  σ₀ in equation (ii)

360 x 10³ = σ_s 2513.27 +  \(\frac{σ_s}{15}\) x 90000

360 x 10³ = σ_s (2513.27 + 6000)

360 x 10³ = σ_s x 8513.27

σ_s = 42.2869 N/mm³

putting the value of F_s in eqution (iii)

σ_s = \(\frac{42.2869}{15}\) N/mn²

σ_c = 2.819 N/mm²