5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 109
© C.G. Daley
Topic 11: Indeterminate Beams – Displacement Method
Cruise Ship in Adriatic
Introduction
In this chapter we will
• introduce the displacement method used to solve structural problems
• introduce the standard stiffness components for a beam in 2D and 3D
~~~~~~~~~~~~~~~~~~~~
Indeterminate Problem
We start by considering the indeterminate beam as shown below. This could be
described as a fixed-pinned beam or a cantilever with a pinned end.
Find MA RA and RB
To solve this problem with the displacement (stiffness) method we create two subproblems,
each simpler than the whole problem. Rather than removing a support
(removing a force or moment), we remove a movement (i.e we completely fix the
structure). This becomes the problem marked * below. To the * problem, we add a
second problem, the ** problem, that fixes any errors that we created with the *
problem. In this case we have a moment MB* that should not exist, while we have a
θB* that should not be zero. So, in the ** problem, we impose θB**, (and only a θB**)
sufficiently large to cause a moment MB** that is equal and opposite to MB*.