To guarantee reliability and safety of engineering structures, we need to regularly measure their mechanical properties. Such measurements are often expensive and time-consuming. It is therefore necessary to carefully plan the corresponding measurement experiments, to minimize the corresponding expenses.
It is known that, in general, experiment design is NP-hard. However, the previous proofs dealt either with nonlinear systems, or with situations with low measurement accuracy. In civil engineering, however, most systems are well-described by linear systems, and measurements are reasonably accurate. In this paper, we show that experiment design is NP-hard even for civil engineering problems. We show that even checking whether the results of the previous measurements are sufficient to determine the value of the desired mechanical quantity -- or additional measurement are needed -- even this problem is, in general, NP-hard. So, crudely speaking, no feasible algorithm can always answer this question -- and thus, overspending on measurements is inevitable.