Because the stepped shaft existed the
discontinuities of second moment of inertia, which
arise in the change of cross-section, and loading
condition on a shaft consisted of a mixture of
concentrated and distributed loads, there needed to
separate the whole shaft into segments and then to
write the each loading several equation in the
conventional shaft analysis. In these discontinuities,
one may use the compatibility equations to satisfy the
continuity conditions. For this conventional way,
there was a lot of cumbersome work to evaluate the
continuities of the adjacent section. However, the
advantage of bi-singularity functions is that the
loading equation and the stepped moment of inertia
can be written in a single expression
