Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

CHAPTER
Statically Indeterminate
beams
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11.1 Introduction
A beam is classified as statically indeterminate if the number of unknown support reactions
exceeds the available number of equilibrium equations. In such cases, the deformation of
the loaded beam is used to derive additional relationships that are needed to evaluate the
unknown reactions (or other unknown forces). The calculation methods presented in Chapter
10 will be employed, along with known beam slopes and deflections at supports (and
other constraints), to develop compatibility equations. Together, the compatibility and
equilibrium equations provide the basis needed to determine all beam reactions. Once all
loads acting on the beam are known, the methods of Chapters 7 through 10 can be used to
determine the required beam stresses and deflections.
11.2 Types of Statically Indeterminate Beams
A statically indeterminate beam is typically identified by the arrangement of its supports.
Figure 11.1a shows a propped cantilever beam with loads and reactions illustrated. This
type of beam has a fixed support at one end and a roller support at the opposite end. The
fixed support provides three reactions: translation restraints A x and A y in the horizontal and
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