Figure 4

A map of dependencies between the quantities in this paper. A relation \(a \rightarrow b\) means that a is one of the factors which determine b. For example, \(\hat{s}_{0}\) is determined by \(\mathcal{L}_{\mathbf{M}}[\mathbf{b},w]\) and ρ through (5.5) and is a factor determining \(s_{\mathrm{min}}\) and \(s_{\mathrm{max}}\) through (5.6) and (5.7). It is also a factor determining r and R through Definition 5.2. The dashed arrow from f to ρ means that ρ is determined by f with some freedom. All the quantities here are explicitly computable from the inputs f, w, M, b. The springs represent Assumptions (F), (A), (B) and the quantities involved with them. Here, the effects of the flexural rigidity EI and the length 2l of the beam, which are assumed to be fixed positive constants, are omitted