5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 99
© C.G. Daley
There are two approaches for solving indeterminate systems. Both approaches use
the principle of superposition, by dividing the problem into two simpler problems,
soling the simpler problems and adding the two solutions.
The first method is called the Force Method (also called the Flexibility Method).
The idea for the force method is;
step release internal forces* or external reactions until we have one or more
determinate systems
step solve each determinate system, to find all reactions and deflections. Note
all incompatible deflections
step re-solve the determinate structures with only a set of self-balancing
internal unit forces* (at internal releases) or unit reaction forces at
removed reactions. This solves the system for the internal or external
forces removed in . Observe the magnitude of incompatible deflections
that occur per unit force.
step a scale the unit forces to cause the opposite of the incompatible deflections
noted in
step Add solutions (everything: loads, reactions, deflections…) from and a.
Note that this will result in no incompatible deflections.
*note: forces include both forces and moments
Overview of Force Method
The structure: a beam over multiple supports:
step cut the structure to have one or more determinate systems