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190                                                         Chapter 4



















          Figure 4.8  Bloc  force in a bent beam as a function of cross-sectional width and thickness

         Example 4.3
             Compare a  fixed-free bar and a bent  beam  half model in  terms of their
         free displacement and bloc force assuming they have identical lengths‚ cross-
         sections‚  material  properties and  are subjected to the  same  temperature
         increase.

         Solution:
             It is useful  to  analyze the  following two  ratios  that relate the  output
         displacement and bloc force of the two thermal actuators‚ namely:







          where the subscripts bb and s denote bent beam and straight‚  respectively.



















            Figure 4.9  Bent  beam versus straight bar in terms of free displacement as a function of
                                  inclination angle and length

          By using Eqs. (4.8) and (4.6)‚ the first ratio of Eq. (4.10) becomes:
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