This paper describes two optimization problems for determining the optimal locations of intermediate supports for a multi-span non-uniform beam using the modified applied theory of variable-thickness plates. In the first problem, the left end of the beam is free, whereas the right end is hinged. In the second problem, the left end remains free, whereas the right end is clamped. The two optimal support locations are determined by formulating a minimax optimization problem, aimed at minimizing the global maximum absolute deflection of the beam. The analysis accounts for the beam's variable stiffness. The finite difference method is employed for the numerical solution. The optimal coordinates of the two intermediate supports are then evaluated for different values of the shear stiffness parameter, satisfying the equioscillation condition, under which the maximum deflection is equalized over all spans. The results demonstrate that variations in the shear deformation require specific repositioning of the intermediate supports to maintain the global balanced state, providing a robust approach to the optimal design of structural components.
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