Structural systems are inherently affected by various sources of uncertainty arising from material properties, geometric parameters, modelling assumptions, and loading conditions [1]. These uncertainties play a critical role in governing structural response, particularly under extreme and highly variable loading conditions. Uncertainty quantification (UQ) is therefore a fundamental requirement for reliable analysis and performance assessment of engineering structures. Traditional deterministic approaches are inadequate for this purpose, as they fail to capture the probabilistic nature of structural demand and capacity. Monte Carlo simulation (MCS) [2] remains the most widely adopted framework for UQ due to its robustness and applicability to complex nonlinear systems. By repeatedly sampling uncertain parameters and excitations, MCS provides unbiased estimates of response statistics and failure probabilities. However, its application to large-scale, time-dependent structural systems is severely limited by its high computational cost. The number of required simulations increases rapidly with system dimensionality and target accuracy, making MCS prohibitively expensive for multi-degree-of-freedom structures under seismic loading. In this study, an efficient UQ framework based on stochastic calculus [3] is developed to overcome these limitations. The proposed approach exploits the governing stochastic calculus to directly evaluate the contribution of uncertain parameters to response variability along individual stochastic trajectories. This allows accurate estimation of response variance with a substantially reduced number of simulations. As a result, the computational burden associated with conventional sampling-based techniques is significantly reduced while maintaining high accuracy in time-domain response statistics. The methodology is demonstrated on a three-dimensional multi-storey, multi-bay frame structure subjected to stochastic earthquake excitation. The case study illustrates the scalability of the approach and its effectiveness in capturing response uncertainty in high-dimensional structural systems. Comparisons with MCS confirm substantial computational efficiency gains without compromising accuracy, highlighting the potential of the proposed framework for large-scale UQ.