This paper presents a numerical method based on a LES approach to modelling the unsteady flow around and the vortex-induced vibration (VIV) of a 5:1 rectangular cylinder in the smooth and turbulent flow. A fluid-structure interaction algorithm was also developed to model the aerodynamic behaviour of a half of the bridge deck in the bending and torsional modes. Results from the static and heaving simulations have validated the accuracy of the proposed computational method and revealed the important role of the motion-induced vortex during the lock-in and its interaction with the von Karman vortex. By introducing the bending motion on the bridge deck, some preliminary results of the bending simulation have indicated some distinct features including the variation of the surface pressure and the separation bubble in the spanwise direction which could promote the spanwise flow. The relative strength between the motion-induced vortex and the von Karman vortex was observed to vary across the spanwise length of the bridge deck, largely influencing the response of the bridge deck in the lock-in. The project will go on to investigate these features together with the surface pressure distribution and the pressure coherence and correlation structure in order to offer a quantitative explanation on the turbulence-induced effect on the VIV and torsional flutter of a 5:1 rectangular cylinder.