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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
crosssection 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.
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 Spring '07
 nesteranko

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