Abstract: In order to solve the problem of development roadway supporting on frequent abandoned workings and broken roof area,the theoretical analysis,numerical calculation and field measurement are combined to analyze the interaction mechanism of “fractured roof- I-beam”,two kinds of trapezoid shed beam mechanical calculation models are built,and the problem of determining the passive support strength of the trapezoidal shed of the soft-breaking surrounding rock during re-mining and residual mining is studied;and according to the geometric parameters of trapezoidal roadway and mechanics parameters of the overlying strata,the different span lengths of different sill beams are calculated.The pressure value of the lower roof is compared with the maximum supporting load of the I-beam.The numerical calculation of the plane strain mechanics model of the surrounding rock of the solid mining road and the fractured roof area is carried out.The study results showed that the trapezoidal shed column and the top beam are simplified as a compression bending composite model,which is more in line with the reality; when shed beam span is 3.2 m,the maximum allowable shed distance of the single beam is 0.7 m.The roof pressure of the roadway is less than the tensile strength and yield strength of the trapezoidal sill beam,which can meet the support requirements of the roadway for re-mining roadway.The study provides a theoretical basis for the determination of trapezoidal shed support schemes in similar complex mining.