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Displacements ux and uy and the longitudinal rotation

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Unformatted text preview: Element Type(s): Stiffness, Damping, or Mass Matrix Element (MATRIX27) 2-D Elastic Beam Element (BEAM3) Input Listing: vm41.dat Test Case A very stiff beam of length L, subjected to a lateral load F, is initially at position AB on a horizontal table. Point A is pinned to the table and restrained from rotation by a relatively weak torsion spring. Determine the final position of the beam in terms of δx, δy, and Θ. Show that the bending stress in the beam σbend is negligible. Figure 41.1 Rigid Beam Problem Sketch Material Properties Kθz = 10,000 in-lb/rad Geometric Properties L = 10 in Loading F = 10 lb E = 30 x 106 psi Analysis Assumptions and Modeling Notes The problem is solved using two approaches: • thick beam geometry approach • constraint equation approach In the thick beam approach, the "rigid" beam properties are arbitrarily selected as area = 100 in2, I = 1000 in4, thickness = 10 in. In the constraint equation approach, a constraint equation is used to enforce the assumption of a rigid beam. The constraint equation is...
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