Question

1) [Design] A reinforced concrete column is to be sized to carry pure axial compressive load. According to ACI 318, what is the smallest possible cross-sectional area (Ag) that the column can use in design supporting an axial dead load of 200 kips (unfactored) and live load of 400 kips (unfactored). Use fc = 4,000 psi and fy = 60 ksi. Assume pe = 0.08 and ties for transverse reinforcement. Be sure to include the appropriate design factors and use the pure axial capacity equation. Assume the column is to have a square cross-section (Ag = bx b). If the width of the cross-section is equal to b, present your final answer in terms of (b xb). [25 points]

Answer 1

Solm Pq - 200kips Per 400 kips fartor Pe - (Pat P.) x 1.5 - 600 x1.5 = 900 kips Pu - 0.4f6 Ac + 0.67 fy Ast 0 where 0.4 and o-by and are constants obtained by comidening partial safety factors. Ast ratio, jo=0.08 A c = 6² - Ast given reinforcement So, 0.08 = Ast ; Ast=0.08de Ac tsing equ Q, ro'x 900 = 0.4x4000x Ac + 0-67x 60 xVÓ X0-08A C 9x10r = 1600 AC + 3216 Ac = 4816 Ac A c = 186-88 in Ast = 14.95 in 2 6² = Act Ast = 201-83 bx b= 14.207 x 14.207 in