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62                                                          Chapter 1
         Problem 1.8
             Compare the  compliance       of  a fixed-free  straight beam  with the
         same  compliance of a fixed-free curved beam  that subtends  an  arc  of
         The two  beams have  identical lengths  and  rectangular  cross-sections.
         Consider both the case where torsion is and is not taken into account.


         Answer:
             When torsion is ignored, the compliance ratio is:




             When the torsion is taken into account, the compliance ratio becomes:




         Problem 1.9
             Compare the bending rigidity of the sandwich beam in Fig.  1.34 for the
         particular case where                                   to the bending
         rigidity of the homogeneous microcantilever of length and thickness













                                 Figure 1.34  Sandwich  beam



         Answer:



         Problem 1.10
             Calculate the stiffness about the x-direction (horizontal) at point 2 for the
         parallel  beam  structure of Fig.  1.35.  The two side beams are  identical and
         parallel to the center beam whose length is twice the length of the side beams.
         Consider that the three beams have identical  cross-sections and are built of
         the same material.

         Answer:
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