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# Answer to Question #154893 in Civil and Environmental Engineering for eddi

Question #154893

a short reinforced concrete column of section 200mm x 22mm is to be reinforced with a 4 numbered steel bars and is required to carry an axial load of 850KN. the stress in the column must not exceed 7N/mm^2 and the stress in the steel must not exceed 150N/mm^2. determine the diameter required for the bars and subsequent stresses occurring in the concrete and the steel under the specified load.

young's modulai concrete = 14KN/mm^2 and steel = 210KN/mm^2. suitable sketch

1
2021-01-18T01:14:14-0500

δst = δco = δ

(F.l/S.E)co = (F.l/S.E)st

δco.l/14.109 = δst.l/210.109

14 . δst = 210 . δco

When δst = 150.106 Pa

14.150.106 =210.δcoδco=10.10Pa > 6.106Pa

When δco= 6.106Pa

14.δst = 210.6.106δst = 90.106 Pa < 150.106 Pa

Use δst = 90.106 Pa; δco = 6.106 Pa

Fst + Fco = 850000

δst . Sst + δco + Sco =850000

90.106. Sst + 6.106. (0.2 . 0.22 - Sst) = 850000

84.Sst = 0.85 - 0.264 → Sst = 0.006976m2 = 6976mm2

For one steel bar

S0st = 6976/4 = 1744mm2

π.D2/4 = 1744 → D = 47.1mm

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