The contour and size of the rib on the thread steel have significant effects on the anchoring strength of resin bolt in the coal mine. To analyse the effects of ribs on load transfer of thread steel bolt

theoretical analysis and numerical simulation methods were used for solving the load distribution of the bolt. By simplifying the mechanical model of the bolt as an axisymmetric model under the pull-out condition

the second-order variable coefficient differential equation has been derived for the shear displacement

in which the variable coefficient function is periodic and discontinuous. Based on MATLAB

this differential equation is solved by Fourier transforming the periodic

discontinuous and variable coefficient function into a continuous function. Thus

the shear stress distribution is obtained and then compares with that of the round steel bolt. Furthermore

a numerical simulation of the bolt has been conducted by ABAQUS to verify the correctness of theoretical solutions. Moreover

based on the results of theoretical analysis and numerical simulation

the rib stress concentration coefficient F is defined to discuss the range and degree influenced by the rib. The results show that the shear stress is a zigzag decreasing distribution along the long axis of the bolt. The rib stress concentration coefficient F is in a range of 1.875 and 2.156 in the effective bearing zone of the bolt. For pull-out force of 300 MPa

the shear stress peak value reaches 36 MPa

which indicates that the initial damage and failure zone commonly occurred near the rib in the anchoring system.