A rigid beam $AB,$ shown in Fig. $1,$ is supported by two vertical elastic rods, $(1)$ and $(2),$ at points A and $B.$ These rods support a load $P=60kN$ at point $C$ along the beam at position $x_1$ to be determined. The diameter of rod $(1)$ is $d_1=25mm$ and that of rod $(2)$ is $d_2=20mm.$ The rods are made of steel with modulus $E=210$GPa. We need to find the position $x_1$ at which the point force is applied so that the extensions of each rod are equal, i$.$e$.{}_1={}_2.$ Note that the displacements $u_A$ and $u_B$ are equivalent to the extensions ${}_1$ and ${}_2,$ respectively.

Figure $1$: A rigid beam supported by two elastic rods and loaded by a concentrated force $P$ as shown.

We also want to compute the axial stresses in both rods, i$.$e$.{}_{11}^{(1)}$ and ${}_{11}^{(2)}.$