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Final - UCSD Spring 2010 MAE 131A SE 110A Final Exam...

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Unformatted text preview: UCSD, Spring 2010 MAE 131A / SE 110A: Final Exam Problem 1: A wood beam ABC has height h = 300 mm, and the span between A and B, L = 3.6 m (Fig. 1). The beam supports a concentrated load 3P = 18 kN and the moment M = PL / 2. (a) Calculate the reactions at A and B, and draw the shear force and bending moment diagrams. (b) Determine the required width b of the beam if the allowable bending stress is Jan = 8.2 MPa, and the allowable shear stress is Tau = 0.7 MPa. Problem 2: Two loads P = 1 kN act on a segment of the crank—shaft as shown in Fig. 2. The diameter of the upper shaft is d = 20 mm. (a) Determine the bending and torsional moments, and the transverse and normal force, acting in the cross-section through the coordinate origin. (b) Write down the expression for the normal stress oz in that section, and evaluate its value at the points A and B. (c) Calculate the shear stress at B due to torsional moment and the shear force. (d) Calculate the principal stresses at the point B. Problem 3: A propped cantilever beam (of length 2L and bending stiffness EI) with support at B is loaded by a uniformly distributed load of intensity q. (a) Use the method of superposition to calculate the reaction at B (in terms of q and L). (b) Draw the shear force and bending moment diagrams of the beam. (0) Derive the expression for the deflection at 0 (again using the superposition). IL / LLLLL'Ll L + ’ B‘ 4. z. \ a. - TY; 0") 2. 21’- ‘L L J: ._._ [gm-Hana] ZYEI . 3 2. V 2. BE... :11?“ ' ~ I. J;,vz(z;L>%§-£zv~e+m '35 :43 .215 v1 2‘; t: 3 2 Tb —/9’ 2L Y/LZ «Vomfsflfb‘fi’g: 32: Y6; E ii. ...
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