Today’s invention is a program to optimise the strength of a telescopic crane.
When using such a crane either fully (1) or minimally extended, the loading allowed will be well defined. I’ve often seen them used in configuration (2), however, which seems like it has potential to damage the mechanism (unless it’s so over engineered as to be much more costly than it need be).
The program envisaged would, for a given intermediate reach, work out p,q,… etc which would minimise the maximum bending stress in the booms.
In practice, it seems these cranes are often operated with p at its maximum length and all other booms fully withdrawn ie q etc=0. This looks like it creates a huge stress concentration at the point where the beam marked p emerges from all the other coincident booms. I haven’t done the full stress analysis but it would make a nice undergraduate project (if no-one wants to pay me to break out the old FEA code).