Passive fully grouted bolts have been widely utilized in civil and mining engineering. However, existing anchorage theories inadequately capture the deformation characteristics and mechanical behaviors of bolts within jointed rock masses. To address this limitation, the tension-shear coupling beam model, which depicts the elastic responses of the bolts, was refined to accommodate the plastic stage, taking into account the geologic characteristics of fully grouted bolts under combined tension and shear loads, as well as the bending deformation effects during the plastic phase. By introducing the Logistic function to characterize the geometric shape of the bolt after yielding and integrating plastic bending theory, geometric constraints, and failure criteria, a method for calculating the internal forces and contributions of the bolts was developed. Comparisons between the proposed model, existing models, and shear test results were conducted, systematically analyzing the effects of bolting angle, bolt diameter, and joint friction angle on anchorage performance. The results indicate that, compared to existing models, the developed model more accurately predicts the test results, demonstrating an error reduction of approximately 8.16% to 14.68%, thus validating the model′s rationality. Additionally, an optimal bolting angle was identified, slightly larger than the joint friction angle. The bolt contribution exhibits a parabolic growth trend with respect to the bolt diameter. This research enhances the understanding of the anchorage mechanism for bolts undergoing plastic deformation and provides essential theoretical foundations for strength calculations and the optimized design of bolting in jointed rock masses.