3rd midterm - oriented element c Determine the maximum...

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EM-319 M.E.Mear An4reaJ Ne./son WED1-9r~ Fall 2006 Exam III Problem 1: The cantilever beam shown below DJs flexural rigidity EI and length L, and it is subjected to two couples of magnitude Mo at the locations indicated in the figure. Determine the deflection of the beam as a function of x. In your analysis, employ the second order differential equation EI d2v/dX = M. , Problem 2: Consider the structure shown in the figure. Both beams have flexural rigidity EI, and the rod has axial rigidity AE. Determine the force induced in the rod by the uniformly distributed load q (which acts on the upper beam as indicated in the figure). Cb 1 ~ 1 .h. ~- 1..
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Problem 3: A material element (in plane stress) is subjected to the stresses indicated in the sketch below. Using Mohr's circle: a) Determine the stresses acting on an element that is inclined at a 45° angle (relative to the original element). b) Detemllne the principal stresses and show the results on a sketch of a properly
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Unformatted text preview: oriented element. c) Determine the maximum shear stresses and show the results on a sketch of a properly oriented element. (Note: If any normal stress also acts on the planes on which the maximum shear stress acts, make sure you include [email protected] your sketch thO of the properly oriented element.) ,$ D Problem 4: A cylindrical pressure vessel is constructed from steel plate by wrapping the plate around a mandrel and then welding along the edges of the plate to form a helical joint. The helical weld makes an angle a=55° with the longitudinal axis as indicated in the~figure. The vessel has inner radius r = 1.8 m and wall thickness t = 20 mm, and the internal pressure is p = 800 kPa. Determine the normal stress and shear stress acting perpendicular and parallel, respectively, to the welded seam....
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