Question

Week 11 – Cantilever Deflection at Maximum Launch

Estimated Time: 6–7 min | PDH/CPD: 1.0 hr | Difficulty: Advanced

Background: The Sombrio bridge is a two-span composite steel plate girder bridge (40 m + 82 m) launched across a deep ravine in Port Renfrew, BC. Four plate girders were incrementally launched without a temporary pier or launch nose, using precast deck panels as tail counterweight, thickened pier-segment bottom flanges, and crane-assisted final lift. (Parameters simplified for conceptual learning. Allow +25% for cross-frames, connection & splice plates. Girders launched without formwork; ignore wind.)

Engineer's Mind: At maximum launch (81 m cantilever, 41 m tail), estimate downward tip deflection—critical for crane lift planning and bearing alignment. The system acts as single span beam overhanging one support with uniformly distributed load. Using standard beam deflection formula accounts for restraining effect of back span on cantilever deflection.

Question: During this launch stage, the fully spliced and connected girders reach maximum cantilever. The girders are supported on roller supports at the abutment and pier. Estimate the downward tip deflection of the 81 m cantilever. Given:

• Single span beam overhanging one support cantilever deflection: δ = w/(6EI) × [3ab² - b³ + 6a²b - 3a²]
• a = 81m and b = 41m
• w = 7.13 kN/m per girder (incl. secondary steel)
• E = 200 GPa
• Strong Axis Moment of Inertia, I per girder = 0.21 m⁴ (average section)