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.