## 5 Numerical Example  
The truss shown in the Section 4 was characterized by a small number of bars and unknowns. The set of solutions for a structure with a greater number of unknowns and bars, which causes an increase of the dimensions of the matrix \(\mathbf{B}\), lies in a multidimensional space. The application of the present algorithm to such a structure leads to obtaining much more complex sets of inequalities.  
Let us consider a truss shown in Figure 4. The truss is composed of ten bars, which are characterized by uncertain cross-section area with nominal value of \(1\,\text{cm}^{2}\). The Young's modulus, force \(P\) and length \(L\) are assumed to be \(100\,\text{GPa}\), \(20\,\text{kN}\) and \(500\,\text{cm}\), respectively.  
Figure 4: Truss geometry and supports with (**a**) loads and (**b**) degrees of freedom.  
Figure 3: Solution set \(\Xi_{\text{uni}}\).  
The extension matrix, elasticity matrix and load vector are given as follows  
\[\mathbf{B}=\left(\begin{array}{cccccccc}0&0&0&1&0&0&0&0\\ 0&0&\frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}&0&0&0&0\\ 0&1&0&0&0&0&0&0\\ -\frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}&0&0&0&0&0\\ -1&0&1&0&0&0&0&0\\ 0&0&0&-1&0&0&0&1\\ -\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}&0&0&0&0&\frac{1}{\sqrt{2}}&\frac{1}{ \sqrt{2}}\\ 0&-1&0&0&0&1&0&0\\ 0&0&\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}&\frac{1}{\sqrt{ 2}}&0&0\\ 0&0&0&0&-1&0&1&0\end{array}\right), \tag{43}\]  
\[\left[\mathbf{E}\right]=\left[\mathbf{p}\right]\widehat{\mathbf{E}},\quad \left[\mathbf{p}\right]=\text{diag}\left(\left[p_{1}\right],\left[p_{2}\right],\ldots,\left[p_{10}\right]\right), \tag{44}\]  
\[\widehat{\mathbf{E}}=\frac{Y}{L}\text{ diag}\left(1,0,\frac{1}{\sqrt{2}},1, \frac{1}{\sqrt{2}},1,1,\frac{1}{\sqrt{2}},1\right), \tag{45}\]  
\[Q=\left(0,0,0,P,0,0,-P,P\right)^{\intercal}\text{ kN}. \tag{46}\]  
The maximum number of inequalities necessary for definition of the solution set \(\Xi_{\text{uni}}\) equals \((\begin{smallmatrix}e\\ s-1\end{smallmatrix})=(\begin{smallmatrix}10\\ 7\end{smallmatrix})=120\) and the set \(\mathcal{U}\) consists of vector products of all \((s-1)\)-element combinations of vectors \(\mathbf{B}^{(i)}\)\((i=1,2,\ldots,e)\), which, after deletion of duplicates, is 42. The set of vectors, basing on which it is possible to build the inequalities defined by (16), is presented in Appendix B.  
The proposed truss is analysed in [22], where authors obtain an exact bound of horizontal displacement of node 6 with the use of sensitivity bound techniques. Due to the convexity of the solution set \(\Xi_{\text{uni}}\) the maximum possible value of the analysed displacement is defined by vertices or edges of polytope \(\Xi_{\text{uni}}\). It should be mentioned that the analysis of all possible cases of uncertain parameters bounds leads to the set of solution points, not all of which are the vertices of the solution polytope [23]. The set of inequalities (16), which defines the exact solution set \(\Xi_{\text{uni}}\), allows the verification of the obtained result.  
It should be noted that the proposed technique can be applied not only to trusses, but also to other structures that can be described by a system of algebraic equations. It is not rational to try to solve larger problems directly with the proposed algorithm. Such an implementation is possible, but there is a need to develop a different procedure. This, however, should be the subject of further research beyond this article. Proposals for applying the method in its current form are presented in the next section.