Other components of the strain tensor are zero, so that:

(12.3)

Integrating, the displacements can be given as

(12.4)

The formulae for the displacements show that the cross-sections remain plane but the planes are rotated so that they pass through the centre of curvature. Shape of the cross-sections is changed. For example if the cross sections initially are rectangular with boundaries in a plane , these boundaries will become the curves given respectively by,

(12.5)

For a rod with rectangular cross-section (sides ) the principal moments of inertia are

(12.6)

For a rod with circular cross-section, with radius , the moment of inertia is

(12.7)