<p>This paper studies the optimum design of beam networks modeled with Timoshenko beams. To account for multiple load cases, an auxiliary optimal control problem is introduced. Optimal distributed control problems for Timoshenko beam networks are solved through the associated optimality system, where the shape functional of the network is defined by the optimal value of the control cost. For control problems exhibiting the turnpike property, the optimum network design is carried out using the steady-state beam model and the corresponding steady-state control problem. A domain decomposition method is adopted to handle topological changes, while the Steklov–Poincaré operator is used to reformulate the beam network model as an interface problem on subdomain boundaries. This approach is applicable under additional assumptions on the network loading. Consequently, the topological derivative of the Steklov–Poincaré operator is incorporated into the optimality system of the control problem, enabling sensitivity analysis with respect to topological changes. The topological derivative of the cost functional with respect to the size of small cycles is derived and computed. Finally, numerical experiments are presented to illustrate and corroborate the analytical results.</p>