A 14 ft. column is subjected to total compressive load of 550 kips.

Question

1. Design it as reinforced concrete square tied column. Use concrete fc’= 5 ksi, steel fy = 60 ksi.
2. Design it as steel column. Use K=1, Fy= 35 ksi.
3. Is steel cross-section W10x49 a safe design. Use K=1, Fy=50 ksi
4. Is steel W10x49 a safe design if the column is braced about the y-axis to reduce the unbraced length about y-axis to 8 ft? 

Answer 1

1) Assume a cross section, say 16"x16".

fc =5ksi, fy = 60ksi.

RC tied column, Φ =0.65

Pu = 550 kips, L =14'

As per AACI 318,

Pu< ΦP_n, where Pn = 0.8[0.85fc'(Ag-Ast)+Asfy]

Ag = 16x16 =256 in², Ast (Say 8- #6 bars) =8*0.44 = 2.64 in²,

Ag- Ast = 252.18.

ΦP_n = 0.8x0.65 x[(0.8x5x252.18)+ (2.64x60)] =639.68 kips

As Pu<ΦP_n, hence safe. Provide 16"x16" square column with 8 No.(6) bars evenly distributed on each face.

2) For fy = 35ksi, K=1, Lc=KL = 14' or 168"

Let's assume a section: W12x79.

ry = 3.05in, Lc/ry = 55.08, Ag = 23.2, E =29000ksi

Pu< ΦP_n

ΦP_{n =} F_cr*Ag

Check 4.71 √(E/Fy) = 135.57

If L/ry< 4.71 √(E/Fy;Fcr = [0.658 ^(Fy/Fe)]*Fy ;

else Fcr = 0.877Fe,

Fe = π²*E/(Lc/ry)²

Fe = 94.34 ksi.

As L/ry < 135.57, Fcr = [0.658^(35/94.34)]*35 = 29.9 ksi.

ΦP_n = 0.9*29.9 * 23.2 = 625.67 kips

As ΦP_n > Pu, hence section is safe.

3) Check W10x49 for L= 1, Fy =50 ksi.

Ag = 14.4 in², ry = 2.54 in

Lc/ry = 66.14 , Fe = 65.42 ksi,

4.71 √(E/Fy) = 113.4. As Lc/ry < 113.4,

Fcr = [0.658 ^(50/65.42)]*50 = 36.31 ksi.

ΦP_n = 470.57 kips.

As ΦP_n < Pu, hence section is unsafe.

4) If Ly = 8ft,

Ag = 14.4 in², ry = 2.54 in,

Lc/ry = 37.79, Fe = 200.42 ksi

Fcr = [0.658 ^(50/200.42)]*50 = 45.04 kips,

ΦP_n = 0.9*45.04* 14.4 = 583.71 kips.

As ΦP_n > Pu, hence section is safe.