The invention relates to a structure based on glass fiber coated with a resin composition designed to reinforce bonded abrasive articles, the resin composition including the following constituents in the proportions indicated, expressed in percentage by weight of solid matter: 75 to 98% of a mixture of at least one novolac having a glass transition temperature lower than or equal to 60° C. and at least one novolac having a glass transition temperature above 60° C., 0.5 to 10% of at least one wax, 0 to 3.5% of at least one plasticizing agent.