Page 32 - Mechanics of Microelectromechanical Systems
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1. Stiffness basics 19
In shearing, the variant generally accepted is that the shear force is positive
when it tends to rotate the portion of the structure in a clockwise direction,
whereas in bending, a component of the bending moment (either force or
moment) produces a positive bending moment if the analyzed structural
segment deforms in a sagging manner (by compressing the upper fiber). All
these situations are sketched in Fig. 1.12.
The normal force N, shearing force S, torsion moment and bending
moment are defined at a specific point on the linear member by
calculating the sum of all relevant components that are applied between one
end point of the member (the free end of Fig. 1.12 is a convenient choice
because it does not introduce any reactions, which are usually unknown
amounts) and the specific point, as given in the equations:
Example 1.4
Determine the axial, shearing and bending moment equations for the
fixed-free microcantilever, which is loaded with the tip forces and as
shown in Fig. 1.13.
Figure 1.13 Cantilever under tip axial force and shearing force
Solution
The axial force, as generally defined in the first Eq. (1.59), is in this case:
