Analytical Evaluation of Internal Forces In Metal Mine Supports Under Combined Vertical And Variable Lateral Rock Pressure

The structural response of metal mine supports is strongly influenced by the interaction between vertical roof pressure and laterally varying rock pressure acting along the support height. This paper presents an analytical evaluation of internal forces in metallic underground reinforcements subjected to combined vertical loading and horizontally varying distributed pressure. The formulation is based on the force method and provides generalized expressions for bending moment, normal force [1, 2, 3], and shear force in any section of the support structure. The horizontal pressure is introduced as a continuous function of the vertical coordinate, allowing realistic representation of rock–support interaction [4, 5]. The horizontal thrust is determined through compatibility conditions, accounting for both bending and axial deformability of the support profile. Dimensional verification and limiting case analysis confirm the mathematical consistency of the derived expressions. The model provides a rigorous analytical tool for assessing stress distribution and optimizing metallic support systems in underground excavations.