The beams shown in Figures P7.90 are made of an elastic material of elastic modulus \(210 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\) and have a cross-sectional moment of inertia \(1.3 \times 10^{-5} \mathrm{~m}^{4}\). Determine the flexibility matrix when a three degree-of-freedom model is used to analyze the beam's vibrations. Use the displacements of the particles shown as generalized coordinates. Use Table D. 2 for deflection calculations.

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-40 40 cm 40 cm FIGURE P7.90 40 cm- 40 cm