Dynamic loads in piping systems are mainly caused by transient phenomena generated by operating conditions or installed equipment. In most cases, these dynamic loads may be modeled as harmonic excitations, e.g., pulsating flow. On the other hand, when designing piping systems under dynamic loads, it is a common practice to neglect strong nonlinearities such as shocks and friction between pipe and support surfaces, mainly because of the excessive cost in terms of computational time and the complexity associated with the integration of the nonlinear equations of motion. However, disregarding these nonlinearities for some systems may result in overestimated dynamic amplitudes leading to incorrect analysis and designs. This paper presents a numerical approach to calculate the steady-state response amplitudes of a piping system subjected to harmonic excitations and considering dry friction between the pipe and the support surfaces, without performing a numerical integration. The proposed approach permits the analysis of three dimensional piping systems, where the normal forces may vary in time and is based in the hybrid frequency–time domain method (HFT). Results of the proposed approach are compared and discussed with those of a full integration scheme, confirming that HFT is a valid and computationally feasible option.