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38                                                          Chapter 1





















               Figure 1.23 Geometry and loading for out-of-the-plane compliance derivation

          The out-of-the-plane  displacements at  point 1  can  be  again  calculated by
          means of Castigliano’s  second theorem as:





















          where the strain energy is:








          After performing the calculations of Eqs.  (1.134), (1.135) and (1.136), the
          out-of-the-plane displacements and loads can be connected as:
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