1. **State the problem:** Given dead load (D) = 450 kN, live load (L) = 200 kN, roof live load (Lr) = 80 kN, find the service load using allowable stress design (ASD) and factored load using load and resistance factor design (LRFD). --- ### Allowable Stress Design Load Combinations 2. Calculate each load combination from ASD: - 1.0 D + F = $450 + 0 = 450$ kN - 1.0 D + H + F + L + T = $450 + 0 + 0 + 200 + 0 = 650$ kN - 1.0 D + H + F + (Lr or R) = $450 + 0 + 0 + 80 = 530$ kN - D + H + F + 0.75 [L + T (Lr or R)] = $450 + 0 + 0 + 0.75 \times (200 + 0 \times 80) = 600$ kN - D + H + F + (0.6 W or E) = $450 + 0 + 0 + 0 = 450$ kN 3. The maximum service load, $S = 650$ kN. --- ### Load and Resistance Factor Design Load Combinations 4. Calculate each factored load LRFD: - 1.4 (D + F) = $1.4 \times (450 + 0) = 630$ kN - 1.2 (D + F + T) + 1.6 (L + H) + 0.5 (Lr or R) = $1.2 \times (450 + 0 + 0) + 1.6 \times (200 + 0) + 0.5 \times 80 = 900$ kN - 1.2 D + 1.6 (Lr or R) + f(L or 0.5 W) = $1.2 \times 450 + 1.6 \times 80 + 1.0 \times 200 = 868$ kN - 1.2 D + 1.0 W + fL + 0.5 (Lr or R) = $1.2 \times 450 + 1.0 \times 0 + 1.0 \times 200 + 0.5 \times 80 = 780$ kN - 1.2 D + 1.0 E + fL = $1.2 \times 450 + 1.0 \times 0 + 1.0 \times 200 = 740$ kN - 0.9 D + 1.0 W + 1.6 H = $0.9 \times 450 + 1.0 \times 0 + 1.6 \times 80 = 405$ kN - 0.9 D + 1.0 E + 1.6 H = $0.9 \times 450 + 1.0 \times 0 + 1.6 \times 80 = 405$ kN 5. The maximum factored load, $U = 900$ kN. --- ### Summary: - Maximum service load (ASD): $$S = 650 \ \text{kN}$$ - Maximum factored load (LRFD): $$U = 900 \ \text{kN}$$