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

Question

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

Answer 1

δ_st = δ_co = δ

(F.l/S.E)_co = (F.l/S.E)_st

δ_co.l/14.10⁹ = δ_st.l/210.10⁹

14 . δ_st = 210 . δ_co

When δ_st = 150.10⁶ Pa

14.150.10⁶ =210.δ_co →δ_co=10.10Pa > 6.10⁶Pa

When δ_co= 6.10⁶Pa

14.δ_st = 210.6.10⁶ → δ_st = 90.10⁶ Pa < 150.10⁶ Pa

Use δ_st = 90.10⁶ Pa; δ_co = 6.10⁶ Pa

F_st + F_co = 850000

δ_st . S_st + δ_co + S_co =850000

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

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

For one steel bar

S_0st = 6976/4 = 1744mm²

π.D²/4 = 1744 → D = 47.1mm