Pedestrian Bridge Cantilever Overhang Assessment in Portland, Oregon

Case Study 2: Pedestrian Bridge Cantilever Overhang Assessment in Portland, Oregon

Scenario: A new timber–steel hybrid pedestrian bridge crosses a stormwater channel in Portland’s Pearl District. One end features a 2.8 m cantilevered steel overhang supporting glass railings and lighting fixtures. The overhang is fixed at the main girder (modeled as a cantilever beam), not simply supported—so the tool’s default formulas require reinterpretation. Local code mandates ≤ 8 mm deflection under live load (2.4 kN/m uniform + 1.5 kN point at free end) to prevent railing misalignment and user discomfort. Environmental constraints include high humidity (corrosion risk) and seismic Category D — requiring stiffness verification before ductility checks.

Given data:

• Uniform Load (w) = 2,400 N/m (lighting, railing dead + pedestrian live load surcharge)
• Point Load (P) = 1,500 N (maintenance worker + tool load at tip)
• Length of Beam (L) = 2.8 m (cantilever span)
• Modulus of Elasticity (E) = 210 GPa = 210,000,000,000 Pa (weathering steel ASTM A588)
• Moment of Inertia (I) = 7.8 × 10⁻⁶ m⁴ (custom hollow structural section, verified via CAD)

Calculation: Although the tool assumes simply supported beams, its underlying formulas were adapted for cantilever boundary conditions:

• Deflection under uniform load (free end): δ = (w × L⁴) / (8 × E × I)
  = (2400 × 2.8⁴) / (8 × 210e9 × 7.8e−6)
  = (2400 × 61.4656) / (8 × 210e9 × 7.8e−6)
  = 147,517.44 / 13,104,000 ≈ 0.01126 m = 11.26 mm

• Deflection under point load (free end): δ = (P × L³) / (3 × E × I)
  = (1500 × 2.8³) / (3 × 210e9 × 7.8e−6)
  = (1500 × 21.952) / (3 × 210e9 × 7.8e−6)
  = 32,928 / 4,914,000 ≈ 0.00670 m = 6.70 mm

Superimposed total = 11.26 + 6.70 = 17.96 mm — exceeds 8 mm limit.

Result and decision: The original HSS 152×152×6.4 section was inadequate. The engineer upsized to HSS 178×178×8.0 (I = 1.42 × 10⁻⁵ m⁴). Recalculating:
δ_uniform = (2400 × 61.4656) / (8 × 210e9 × 1.42e−5) = 147,517.44 / 23,856,000 ≈ 6.18 mm
δ_point = (1500 × 21.952) / (3 × 210e9 × 1.42e−5) = 32,928 / 8,946,000 ≈ 3.68 mm
Total = 9.86 mm — still marginal. Final solution: added a discreet diagonal brace anchored to the abutment, converting the overhang into a propped cantilever — reducing tip deflection by 42% (validated via hand calc and FEA). Approved design achieved 4.6 mm total deflection.

Lesson: Standard deflection calculators assume idealized boundary conditions — never apply them blindly to cantilevers or indeterminate systems without adjusting formulas or validating with structural modeling; bracing can be more cost-effective than oversized members when space and aesthetics constrain geometry.