Accurate estimation of wind loads on side surfaces of structures in turbulent flow is crucial for ensuring the safety of buildings. However, inaccurately simulating the turbulence integral scale in wind tunnel tests leads to discrepancies in measured wind pressures, potentially causing structural damage. In this paper, the influence of different turbulence integral scales on the side fluctuating pressure of CAARC scaled model in wind tunnel is studied. A novel empirical model of aerodynamic admittance is introduced, which modifies the root-mean-square (RMS) of the fluctuating pressure coefficients, addressing the unique three-dimensional aerodynamic effects particularly flow separation and re-attachment occurred on side surfaces. The results show that the fluctuating pressure coefficient increases with the increase of the ratio of turbulence integral scale to model thickness, while the turbulence integral scale exerts minimal influence on the mean pressure coefficient. The larger integral scale not only increases the energy transfer of fluctuating pressure, but also significantly affects the power spectrum and vortex shedding frequency of fluctuating pressure. Without accurate integral scale simulation, RMS values of fluctuating pressures can deviate by up to 37%. Applying the proposed empirical model reduces these errors to within 5%. The results confirm the empirical model's necessity and effectiveness in correcting errors from improper turbulence integral scale simulation in wind tunnel tests.