Question

The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modeled as a cantilever. The left tank is filled with water to a depth of 4 m, and the right tank to a depth of 1 m, both measured from the common base where the barrier is fixed. Taking the density of water as 1000 kg/m³, and g=10 m/s², the maximum absolute bending moment developed in the cantilever is __________ kN·m (round off to the nearest integer).

Accepted Answer

The correct answer is 105 kN·m (± 1). Measuring z downward from the left (taller) water surface, net pressure p_net(z) = ρg·z for 0≤z≤3 (only the left side wets this zone) and p_net(z) = 3ρg (constant, both sides contribute) for 3≤z≤4, with ρg=10,000 N/m³. Bending moment at the base = ∫p_net(z)(4−z)dz over [0,4]: the 0-3 m zone contributes 10,000×[2z²−z³/3]₀³ = 90,000 N·m, and the 3-4 m zone (constant pressure 30,000 Pa) contributes 30,000×[4z−z²/2]₃⁴ = 15,000 N·m. Total = 90+15 = 105 kN·m.

Explanation