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The present report is a summary of the structural analysis of the pump nozzles applying the finite element method by using the Ansys computer program. The IEA-R1 RR is an open pool-type moderated and cooled by light water using beryllium/graphite as a reflector. The reactor can reach up to 5MW of thermal power cooled by the primary and secondary systems. The primary coolant system consists of a piping arrangement, a decay tank, two pumps, and two heat exchangers. The primary pump B1-B presented some failures requiring refurbishment by a new one. The pump used in the IEA-R1 must meet the requirements inherent to the nuclear installation, in addition to the operational requirements for rotating equipment, such as flow and pressure, and structural integrity of the body and nozzles. The supplier specified the type of pump suitable for the System. The pump furnished granted mechanical allowable loads for the nozzles that were lower than the loads imposed by the piping on the nozzles. To enable the installation of the pump in the primary circuit, new support was inserted in the piping system next to the pump minimizing efforts and deformations. A piping stress analysis was carried out to obtain the new efforts imposed on the nozzles. For validation of the motor pump set, a verification of the nozzles was done compared with API 610 standard loads, and the allowable loads of the provider. Finally, a structural analysis of the pump nozzles with the new loads was developed using the finite element method. The calculated stresses meet the limits prescribed by the ASME code; therefore, the new B1-B Pump is approved for operation at the IEA-R1 Nuclear Research Reactor primary circuit.