BENDING DEFORMATION OF A STRAIGHT MEMBER

In this section, we will discuss the deformations that occur when a straight
prismatic beam, made of homogeneous material, is subjected to bending.
The discussion will be limited to beams having a cross-sectional area that
is symmetrical with respect to an axis, and the bending moment is applied
about an axis perpendicular to this axis of symmetry, as shown in Fig. 6–18.
The behavior of members that have unsymmetrical cross sections, or are
made of several different materials, is based on similar observations and
will be discussed separately in later sections of this chapter.
Consider the undeformed bar in Fig. 6–19a, which has a square cross
section and is marked with horizontal and vertical grid lines. When a
bending moment is applied, it tends to distort these lines into the pattern
shown in Fig. 6–19b. Here the horizontal lines become curved, while the
vertical lines remain straight but undergo a rotation. The bending moment
causes the material within the bottom portion of the bar to stretch and
the material within the top portion to compress. Consequently, between
these two regions there must be a surface, called the neutral surface, in
which horizontal fibers of the material will not undergo a change in
length, Fig. 6–18. As noted, we will refer to the z axis that lies along the
neutral surface as the neutral axi