Page 29 - Mechanics of Microelectromechanical Systems
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16 Chapter 1
4.3 Shearing
For shear loading, the maximum stress which is generated by a shear
force S – consider it be the force in Fig. 1.9 (a) – is:
where is a coefficient depending on the cross-section shape and which is
equal to 3/2 for rectangular cross-sections – see Young and Budynas [4]. The
corresponding maximum shear strain is:
The strain energy stored in the elastic body through shearing is:
where for rectangular cross-sections – Young and Budynas [4].
4.4 Bending
The bending of a beam mainly produces normal stresses. The stress
varies linearly over the cross-section going from tension to compression
through zero in the so-called neutral axis, which coincides with a symmetry
axis for a symmetric cross-section. The maximum stress values are found on
the outer fibers as:
where c is half the cross-sectional dimension which is perpendicular to the
bending axis, is the bending moment, and I is the cross-sectional moment
of inertia about the bending axis.
When a beam is subject to the action of distributed load, point forces
perpendicular to its longitudinal axis and point bending moments, an element
can be isolated from the full beam, as sketched in Fig. 1.11, and the
following equilibrium equations can be written:
The deformations in bending consist of deflection and slope, as sketched in
Fig. 1.3. These deformations are described by the following differential
equations:
