This article analyzes a class of distributed parameter systems, which consist of a boundary-controlled partial differential equation (PDE) and a static boundary-value problem (BVP) generating the measured output. We focus on the steady-state reachability of given output profiles and construct corresponding input signals using modal decomposition techniques. Furthermore, we identify which PDE modes contribute to the output and establish state estimates. An Euler-Bernoulli beam that deforms under thermal load is chosen as an illustrative example.