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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» 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 = σsAs + σcAc 360 x 103N = σsAs + σcAc .....(ii) σc = \(\frac{∑_c}{∑_c}\) ∑s σc = \(\frac{14 \times10^9}{210\times10^9}\) x σs σc = \(\frac{σ_s}{15}\) ....(iii) Putting the value σ0 in equation (ii) 360 x 103 = σs 2513.27 + \(\frac{σ_s}{15}\) x 90000 360 x 103 = σs (2513.27 + 6000) 360 x 103 = σs x 8513.27 σs = 42.2869 N/mm3 putting the value of Fs in eqution (iii) σs = \(\frac{42.2869}{15}\) N/mn2 σc = 2.819 N/mm2 |
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