Reinforced Concrete: Columns & Shear

Worked

• A 16 in square tied column with eight No. 8 bars (A_st = 6.32 in²), f′c = 5 ksi, f_y = 60 ksi: P₀ = 0.85 × 5 × (256 − 6.32) + 60 × 6.32 = 1,061 + 379 = 1,440 kips, and φP_n,max = 0.52 × 1,440 = 749 kips.
• A normal-weight beam with b_w = 12 in, d = 20 in, f′c = 4,000 psi: V_c = 2 × √4,000 × 12 × 20 = 30,400 lb, so φV_c = 22.8 kips, and stirrups are needed above V_u = 11.4 kips.