Problem 6 O Consider the problem of a cantilever thin-walled box beam under torsion shown in the figure below, with t<<

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Problem 6 O Consider The Problem Of A Cantilever Thin Walled Box Beam Under Torsion Shown In The Figure Below With T 1 (102.78 KiB) Viewed 15 times

Problem 6 O Consider the problem of a cantilever thin-walled box beam under torsion shown in the figure below, with t<< a <<L. a2t Q (N/m) 2a 2t 101 It is loaded by two line-loads (of amplitude Q in N/m) acting in opposite directions over the second half of the beam (L/2≤x≤L), generating a twisting moment. The box beam is made of a single material with shear modulus , and the rectangular thin-walled cross-section has a varying thickness as indicated in the figure (t for the horizontal components, and 2t for the vertical components). (a) Write the BVP (GDE and BCs) describing the torsion response of the beam. Make sure to include the approximate expression of the torsion constant J. Ignore the effect of gravity. (b) Solve the BVP found in a) and put your solution in a non-dimensional form. Check that your solution is indeed non-dimensional. (c) Is the structure statically determinate of indeterminate and why? (d) Using a FBD, compute the internal twisting moment M/(x) along the beam. (e) Use the solution found in b) to recover the expression of the internal twisting moment. found in d) (f) Assuming that the material fails when the maximum shear stress reaches a critical value Tc, what is the maximum value of Q that the structure can sustain. Make sure to provide details on your derivations.