Mid-term1a

# Mid-term1a - UNIVERSITY OF CALIFORNIA BERKELEY College of...

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UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Mechanics of Materials (CE130-I) Fall 2005 The First Mid-term Examination Problem 1. A hollow circular shaft has the dimensions shown in the ﬁgure. (a) Find the maximum shear stress in terms of inner diameter a , outer diameter b , and applied torque T ; (b) ﬁnd a solid cylinder shaft with the diameter, d that has the same maximum shear stress, i.e. determine the diameter d in terms of a and b . Figure 1: A hollow circular shaft Hint: For a solid cylinder : J p = πd 4 32 (1) τ max = Tc J p ; (2) Problem 2. Derive the equilibrium equation for a two-dimensional inﬁnitesimal element in the horizontal ( x ) direction. Note that the thickness of the element (z-direction) is taken as 1 (unit length), and X,Y are the body forces with the unit (force per unit volume). (20 points) Problem 3 1

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Figure 2: A 2D inﬁnitesimal element Figure 3: A two-bar bracket system A wall bracket is constructed as shown in the Figure 3. All joints may be considered pin con- nected. There is an external force
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Mid-term1a - UNIVERSITY OF CALIFORNIA BERKELEY College of...

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