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

CHAPTER7
Equilibrium of beams
7.1 Introduction
The behavior of slender structural members subjected to axial loads and to torsional
loadings was discussed in Chapters 5 and 6, respectively. This chapter begins the consideration
of beams, one of the most common and important components used in structural and
mechanical applications. Beams are usually long (compared with their cross-sectional
dimensions), straight, prismatic members which support loads that act perpendicular to the
longitudinal axis of the member. They resist transverse applied loads by a combination of
internal shear force and bending moment.
The term transverse refers to
loads and sections that are
perpendicular to the longitudinal
axis of the member.
Types of Supports
Beams are normally classified by the manner in which they are supported. Figure 7.1
shows graphic symbols used to represent three types of supports:
• Figure 7.1a shows a pin support. A pin support prevents translation in two orthogonal
directions. For beams, this condition means that displacements parallel to the longitudinal
axis of the beam (i.e., the x direction in Figure 7.1a) and displacements perpendicular to
the longitudinal axis (i.e., the y direction in Figure 7.1a) are restrained at the supported
joint. Note that, while translation is restrained by a pin support, rotation of the joint is
permitted. In Figure 7.1a, the beam is free to rotate about the z axis and reaction forces
act on the beam in the x and y directions.
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