Module
2
Analysis of Statically
Indeterminate
Structures by the
Matrix Force Method
Version 2 CE IIT, Kharagpur

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Lesson
8
The Force Method of
Analysis: Beams
Version 2 CE IIT, Kharagpur

Instructional Objectives
After reading this chapter the student will be able to
1. Solve statically indeterminate beams of degree more than one.
2. To solve the problem in matrix notation.
3. To compute reactions at all the supports.
4. To compute internal resisting bending moment at any section of the
continuous beam.
8.1 Introduction
In the last lesson, a general introduction to the force method of analysis is given.
Only, beams, which are statically indeterminate to first degree, were considered.
If the structure is statically indeterminate to a degree more than one, then the
approach presented in the previous example needs to be organized properly. In
the present lesson, a general procedure for analyzing statically indeterminate
beams is discussed.
8.2
Formalization of Procedure
Towards this end, consider a two-span continuous beam as shown in Fig. 8.1a.
The flexural rigidity of this continuous beam is assumed to be constant and is
taken as
EI
. Since, the beam is statically indeterminate to second degree, it is
required to identify two redundant reaction components, which need be released
to make the beam statically determinate.
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Version 2 CE IIT, Kharagpur