Figure P9.18 shows a three-dimensional pipe abcd clamped at a with mass m at d. All members are made of the same material and have identical cross sections. Formulate the equations of motion governing the DOFs ux , uy , and uz when the excitation is ground motion in (i) x-direction, (ii) y-direction, (iii) z-direction, and (iv) direction a–d. First express the flexibility matrix in terms of E, I, G, J , and L; then specialize it for G J = 4/5. Consider flexural and torsional deformations but neglect axial deformations.
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