Week 8 – Stability Without Counterweight

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: Girders can resist flexural demands to 81 m with strengthened pier segment (Quiz 5). However, another critical check: global stability. Will girders overturn about pier roller support as they cantilever forward? Tail section behind pier provides restoring moment—but is it sufficient?

Question: As the entire girder length is spliced together and launched, determine the maximum cantilever length (x) that can be achieved limited by global overturning equilibrium. Only the girder weight behind the pier provides overturning stability. Use appropriate load factors for stability-driving and stability-restoring moments. Given:

·        Total girder length: L = 122 m

·        Uniform average section:

o   Web = 2750 mm × 16 mm

o   Flanges (top and bottom) = 600 mm × 25 mm

o   Add 25% for secondary steel

·        Steel density ρ_s = 7850 kg/m³

·        Load factors: α_D = 1.25 (driving), α_D = 0.90 (restoring)

·        Equilibrium: Restoring Moment (M_R) = Driving Moment (M_D)