Question

Week 3 – LTB-Limited Flexural Capacity
Estimated Time: 4–5 min | PDH/CPD: 0.5 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: Quiz 1 ignored lateral-torsional buckling. During launching, the bottom flange at the pier is in compression, unbraced except at cross-frames (8 m spacing). Detailed LTB analysis shows capacity reduces to ~65% of yield strength. Apply CSA S6-19 resistance factor φ = 0.90.

Question: Given that LTB analysis shows capacity reduces to 65% of yield strength, and CSA S6-19 requires resistance factor φ = 0.90 for steel in flexure, what is the factored LTB-limited moment resistance? Given:
•    M_y = 52 MN·m (from Quiz 1)
•    LTB reduction factor = 0.65
•    φ = 0.90 (CSA S6-19 Clause 10.3)