I would recommend that you obtain a copy of the Crane Manufacturers Association of America (CMAA) Specification #70,
Specification for Top Running Bridge & Gantry Type Multiple Girder Electric Overhead Travelling Cranes. (CMAA is a division of the Material Handling Institute (MHI). It publishes several specifications for the design of various types of cranes and gantries, all regularly reviewed by manufacturers, electrical engineers, mechanical engineers, structural engineers and OSHA.)
Those specifications provide thorough background reasoning and mathematical derivations for the design requirements that you will find useful.You can obtain copies of those specifications on line.
------------------------------
Robert Crossno P.E., M.ASCE
Structural Engineer, Civil Engineer
Albuquerque NM
------------------------------