Max Johannes Alois Fritzsche

Design codes for pedestrian-induced vibration on footbridges treat each pedestrian asa prescribed vertical force on the deck. This convention ignores the feedback by which deck motion modifies the gait, and at resonance overpredicts the measured field amplitudes.This paper introduces a load model for vertical human-structure interaction that closes this feedback loop. The per-step force each pedestrian exerts on the bridge splits into two parts. The first is the classical rigid-ground walking force. The second is an interaction component proportional to the deck velocity, which acts on the deck like an amplitude-dependent damper. At resonance this damping is negative and the pedestrian injects energy into the deck. The response self-limits at a finite equilibrium amplitude, because the negative damping weakens as the deck amplitude rises. Away from resonance the coupling reduces to the positive damping the pedestrian's own body contributesA main advantage of the proposed model is that its stability criterion and equilibrium amplitude require no prescribed driving force, unlike classical moving-force models. Furthermore, its parameters transfer to any bridge through the first-mode frequency. Another advantage is that for groups the per-pedestrian damping contributions add linearly across the deck.Without recalibration, the model reproduces the reported field amplitudes of four independently documented footbridges within ratios 0.93 to 1.43, while classical moving-force models overestimate them by factors 3.3 to 33.

Design codes for pedestrian-induced vibration on footbridges treat each pedestrian as a prescribed vertical force on the deck. This convention ignores the feedback by which deck motion modifies the gait, and at resonance overpredicts the measured field amplitudes.This paper introduces a load model for vertical human-structure interaction that closes this feedback loop. Each pedestrian is modelled as a single-degree-of-freedom oscillator whose leg stiffness varies over the gait cycle. On a vibrating deck this periodic stiffness couples the pedestrian to the deck motion. The per-step force on the bridge is then the classical rigid-ground walking force plus an interaction component proportional to the deck velocity, which acts on the deck like an amplitude-dependent damper. At resonance this damping is negative and the gait pumps energy into the deck. The response self-limits at a finite equilibrium amplitude, because the negative damping weakens as the deck amplitude rises. Away from resonance the damping stays positive.A main advantage of the proposed model is that its stability criterion and equilibrium amplitude require no prescribed driving force, unlike classical moving-force models, and that its parameters transfer to any bridge through the first-mode frequency, with the amplitude scales of the coupling tied to the comfort thresholds of design codes. A second advantage is that for groups the per-pedestrian damping contributions add linearly across the deck.Without recalibration, the model reproduces the reported field amplitudes of four independently documented footbridges within ratios 0.93 to 1.43, while classical moving-force models overestimate them by factors 3.2 to 33.The framework yields a closed-form stability criterion and a self-limiting equilibrium amplitude, both obtained without coupled crowd simulation and suited to footbridge serviceability assessment.

Force plates are the gold standard for measuring ground reaction forces, but their reliance on equilibrium equations limits them to single-contact measurements. During the double support phase of walking, when both feet touch the ground simultaneously, conventional force plates yield only the combined force and center of pressure. The individual foot contributions cannot be separated. This paper applies influence surface theory to extend force plate analysis beyond equilibrium-based methods. Instead of evaluating global force and moment balances, influence surfaces characterize how loads at different positions contribute to structural responses at individual supports. This enables load identification for multiple simultaneous contacts, with the number of separable loads determined by the available sensor count.The influence surfaces are trained from walking data using Gaussian Process Regression, capturing the real plate behaviour without requiring finite element modelling. To reduce complexity, the inverse problem is addressed sequentially. First, load positions are estimated. Second, the horizontal force components are determined.The method is validated on a 2.5m x 1.0m force plate using static tests with known load positions and walking trials with synchronized instrumented insoles providing the load distribution. The results show that the approach successfully reconstructs positions and three-dimensional ground reaction forces for both contacts, generally achieving accuracy comparable to equilibrium-based single-contact measurements while preserving natural gait.