Coastal Pedestrian Bridge Cantilever Overhang Assessment

Case Study 2: Coastal Pedestrian Bridge Cantilever Overhang Assessment

Scenario A new seaside boardwalk in Monterey, California includes a 2.8 m cantilevered concrete walkway extending from a fixed abutment. Due to aggressive marine environment (salt-laden air, cyclic humidity), the design team selected fiber-reinforced polymer (FRP) composite beams for corrosion resistance. Local jurisdiction mandates ≤3 mm total deflection under pedestrian live load (5 kN/m² converted to line load). Critical constraint: no field adjustments possible post-installation due to tidal access limitations.

Given Data

• Uniform load: 3,200 N/m (5 kN/m² × 0.64 m tributary width)
• Beam length: 2.8 m (cantilever span — note: tool assumes simply supported; but per tip #3, boundary condition verification confirmed use of cantilever formula is required — however, user mistakenly applied the tool’s default simply supported formula initially; subsequent correction revealed need for manual recalculation using correct boundary condition)
• Modulus of elasticity: 32,500,000,000 Pa (manufacturer-tested E for pultruded FRP beam at 25°C, reduced 15% for long-term creep)
• Moment of inertia: 4.12 × 10⁻⁵ m⁴ (verified via 3D laser scan of as-fabricated section)

Calculation Initial (incorrect) tool input yielded:
$\delta_{\text{SS}} = \frac{5 \cdot 3200 \cdot (2.8)^4}{384 \cdot 3.25 \times 10^{10} \cdot 4.12 \times 10^{-5}} \approx 0.000132\ \text{m} = 0.132\ \text{mm}$ — misleadingly low.

Correct cantilever calculation:
$$ \delta_{\text{max}} = \frac{w L^4}{8 E I} = \frac{3200 \cdot (2.8)^4}{8 \cdot 3.25 \times 10^{10} \cdot 4.12 \times 10^{-5}} = \frac{3200 \cdot 61.4656}{1.0712 \times 10^7} \approx \frac{196,689.92}{10,712,000} \approx 0.01836\ \text{m} = 18.36\ \text{mm} $$

Result and Decision Cantilever deflection = 18.36 mm — exceeding the 3 mm limit by >6×. The design was rejected. Engineers upsized to a hybrid FRP-steel box beam (I = 1.15 × 10⁻⁴ m⁴), reducing deflection to 6.5 mm. Final solution added discrete elastomeric bearings at the fixed end to limit rotation, achieving 2.8 mm — compliant and constructible within tidal window.

Lesson Boundary condition mismatch is a leading cause of nonconservative deflection estimates; never rely solely on calculator defaults—always cross-validate formula selection against physical supports, especially for cantilevers, fixed ends, or continuous spans.