Problem 4 Consider the linearly elastic beam of stiffness E, Poisson's ratio v, density p, length L, thin, solid rectang

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Problem 4 Consider The Linearly Elastic Beam Of Stiffness E Poisson S Ratio V Density P Length L Thin Solid Rectang 1 (155.24 KiB) Viewed 10 times

Problem 4 Consider the linearly elastic beam of stiffness E, Poisson's ratio v, density p, length L, thin, solid rectangular cross-section (width W and thickness h, with h<<W) shown in the figure below. It is subjected to the effect of gravity (acceleration g in the negative z-direction) and to the effect of a line load P (in N/m) applied along an edge of the top surface over the second half of the beam, as indicated in the figure. The beam is cantilevered at x=0 and is supposed to have an elastic boundary condition (with linear spring stiffness k) at x=L. (a) Write the boundary value problem (BVP) describing the beam transverse deflections in the y- and z-directions and the beam rotation around the x-axis, giving the expression of every parameter (inertia, torsion constant, shear modulus, ...) entering the BVP. (b) Is the structure statically determinate or indeterminate? Why? (c) Solve for the beam rotation around the x-axis, putting your solution in a non-dimensional form. Perform a 'unit check' to make sure your solution for the beam rotation is indeed non-dimensional. N Ch Y W L P (N/m) www k