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5.1 Pure bending of thin plates  123




















               Fig. 5.1  Plate subjected to pure bending.
               are given by
                                               1         Z
                                           Ex=-,    Ey’-
                                               Px       PY
               Referring to Eqs (1.47) we have
                                       1                 1
                                                        E
                                      E
                                  &,=-(cJx-vcry);  Ey=-(cry-Vcrx)                  (5.2)
               Substituting for E,  and   from Eqs (5.1) into Eqs (5.2) and rearranging gives
                                              EZ

                                                                                   (5.3)
                                              Ez
                                        cr  =-(’+;) 1-2  py

























                                   (a)                                 (b)
               Fig. 5.2  (a) Direct stress on lamina of plate element; (b) radii of curvature of neutral plane.
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