Page 57 - Mechanics of Microelectromechanical Systems
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44 Chapter 1
Figure 1.25 Beam of composite cross-section: (a) cross-section geometry; (b) bending
strains; (c) bending stresses
6.1.1 Bending
Bending about the y-axis, which is assumed the most sensitive axis, will
be thoroughly analyzed. Assume that a homogeneous cross-section is being
studied first. The strain varies linearly about the z-axis, as sketched in Fig.
6.25 (b), and if the horizontal line that passes through the bottom of the
cross-section is chosen as a datum line, the strain can be expressed as:
The normal stress is:
The stress and strain are zero in the neutral axis, and therefore:
where gives the position of the neutral axis, and in the case of a
homogeneous cross-section this coordinate is half the beam’s thickness. The
bending moment that acts on the cross-section can be expressed as:
