African Journal of Applied Mathematics: Theory for Engineering Systems

Box girder bridges are the predominant structural form for medium-to-long span road crossings in Sub-Saharan Africa, valued for their high torsional stiffness, aerodynamic stability, and structural efficiency. However, the dynamic response of these bridges to high-speed vehicle passages — encompassing resonance excitation, vehicle-bridge interaction (VBI) coupling, and road surface roughness effects — remains inadequately characterised for the specific conditions prevailing on African highway corridors, where vehicle speeds are increasing following road improvement programmes and vehicle weights frequently exceed design assumptions. This paper presents a comprehensive dynamic response analysis of a 40 m single-span twin-cell steel box girder bridge subjected to high-speed vehicle passages at speeds of 60–180 km/h. A coupled vehicle-bridge interaction model is formulated, combining a quarter-car vehicle model (sprung and unsprung masses, primary and secondary suspension stiffness and damping) with an Euler-Bernoulli beam model of the box girder discretised using 3D shell finite elements (4,800 elements, 29,040 degrees of freedom). Road surface roughness is generated stochastically following the ISO 8608 power spectral density classification (Classes A–D). The governing equations of motion are integrated numerically using the Newmark-beta method with time step dt = 0.002 s. Natural frequencies, mode shapes, midspan deflection time histories, bending moment and shear force envelopes, deck accelerations, and dynamic amplification factors (DAF) are computed for a comprehensive parametric matrix of vehicle speeds, vehicle weights (10–55 tonne gross vehicle weight), road roughness classes, span-to-depth ratios, and damping ratios. Key findings include: (i) the DAF for the 40 m