5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 89
© C.G. Daley
This completes the manual integration method for
solving example 3. To check this we will be solving
the same problem in 2 other ways.
Macaulay Functions
Macaulay functions (also called singularity
functions) are simply a generalization of the idea
of a step function. These functions provide a
convenient way of describing point forces,
moments and piece-wise continuous functions. And
when a few special rules of integration are
employed, it becomes very easy to use Macaulay
functions to solve beam problems.
The fundamental Macaulay functions are shown
on the left. Each function in the sequence
represents the integral of the previous function
(with the small exception noted later). Any of the
functions can be multiplied to a constant to change
the magnitude.
For example, a unit moment at