Previous Quizzes
Winner of the Quiz
Jimmy Fortier
Parsons Inc
Incremental Launch Quiz Series
04 - 10 Dec 2025
Week 4 – Maximum Cantilever Length
Estimated Time: 5–6 min | PDH/CPD: 0.75 hr | Difficulty: Intermediate
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: With factored LTB-limited resistance of 30 MN·m (Quiz 3), determine maximum cantilever length. This reveals the self-launch capability of the girders to assess auxiliary measures required to launch across the longer span.
Question: What is the maximum cantilever length before factored self-weight moment equals factored flexural resistance of 30 MN·m of the pier girder segment? Given:
- M_r = 30 MN·m (from Quiz 3)
- w = 8.62 kN/m per girder (from Quiz 2)
- Load factor α_D = 1.25
- Factored moment: M_f = α_D × (w × L² / 2)
- 75 m
- 72 m
- 68 m
- 78 m
Explanation
Calculation:
Set: Factored Moment Demand = Factored Moment Resistance
- 1.M_f = α_D × (w × L² / 2) = 30 MN.m
- .1.25 × (8.62 × L² / 2) = 30,000 kN.m
- 35.3875 × L² = 30,000
- L² = 5,569
- L = 74.6 m ≈ 75 m
The maximum self-supporting cantilever is 75 m, revealing a critical progression from the previous quizzes. Quizzes 1-2 suggested adequacy: elastic capacity of 52 MN·m (Quiz 1, no LTB or factors) exceeded the 27.6 MN·m unfactored demand at 80 m (Quiz 2). However, after applying resistance reductions for LTB and φ factor (Quiz 3: capacity drops to 30 MN·m) and construction load factors (demand at 80 m increases to 34.5 MN·m), the reality emerges: 34.5 > 30 MN·m—inadequate!
Solving for equilibrium (1.25 × 8.62 × L²/2 = 30,000) yields L = 75 m. This 5 m difference between initial impression (≥80 m) and factored reality (75 m) demonstrates why stability effects and code factors cannot be deferred to detailed design—ignoring them during conceptual calculations leads to fundamentally incorrect conclusions that require costly mid-design corrections. The remaining 6 m shortfall (75 m capable vs. 81 m target) necessitates strengthening (Quiz 5) or auxiliary launching measures.
Learning Resources:
- CSA S6-19 Table 3.5.1 – Load Factors
- CSA S6-19 Clause 10.5.7 – Resistance Factors
- CSA S6-19 Clause 10.10.2 – Lateral-Torsional Buckling