The explicit central difference numerical time integration scheme is demonstrated to be a robust and efficient alternative to commonly used implicit schemes like the Newmark average acceleration scheme for nonlinear structural response simulation. Numerical non-convergence issues, which are frequently encountered using the Newmark average acceleration scheme, are shown to introduce conservative biases in the estimated structural capacity and hamper the efficiency of analysis. They are shown to be responsible for the underestimation of the median collapse capacity of a 9-storey steel moment frame building by 10%. Despite requiring shorter analysis time steps, the time taken to conduct an incremental dynamic analysis using the central difference scheme is 73% lower than using the average acceleration scheme.