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093.Ph.D.QE.MoM - mm as shown in Fig 3 The dimensions of...

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Ph.D. Qualifying Exam Mechanics of Materials (Fall 2009) Name:________________________________ ID #:_________________________________ 1. The state of stress of an element at O is represented in Fig. 1, where 0. z σ = ( a ) Draw the three Mohr’s circles for stresses in the xy , yz , and zx planes. ( b ) Determine the range of values of θ for which the normal stress x in the xy ′′ plane is equal to or less than 130 MPa. ( c ) What is the maximum shear stress developed in this element? Fig. 1 Fig. 2 2. The beam ABC of length 2 L has a constant flexural rigidity EI and carries a moment 0 M at A and a distributed load with intensity w in the segment BC as shown in Fig. 2, where 2 0 1.5 . L = M w Determine ( a ) the reaction at B , ( b ) the deflection at A , ( c ) the slope at A . 3. A sign is supported by a pipe having outside diameter of 100 mm and inside diameter of 80
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Unformatted text preview: mm as shown in Fig. 3. The dimensions of the sign are 2 m × 0.75 m and its lower edge is 3 m above the support. The wind pressure against the sign is 1.5 kPa. Determine the following: a) The internal forces and moments at the base of the pipe at section a-a . Draw the appropriate free-body diagram. b) Determine the normal stress and shear stress at point A on the cross section at section a-a . c) Determine the normal stress and shear stress at point C on the cross section at section a-a . d) Draw the stress state at point A on a differential volume element located at this point. e) Is this a statically determinate or statically indeterminate problem? Explain. Note: Be sure to clearly show all work and state units. Fig. 3...
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