Page 38 - Mechanics of Microelectromechanical Systems
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1. Stiffness basics 25
After performing the needed calculations, the sought slope is:
Equation (1.79) took into account that the dummy moment is actually zero in
the bending moment expression, and that the reaction is given in Eq.
(1.76).
Example 1.6
Solve the problem of Example 1.5 by considering that the beam is
relatively short, and compare the results with the results of the previous
example.
Solution:
The shearing force needs to be taken into account in the strain energy
equation, and therefore the deflection can be written as:
where the shear force is simply Solving Eq. (1.73) with the particular
expression of Eq. (1.80) gives:
with:
The slope at midspan is calculated by means of Eq. (1.79) and its equation is:
A comparison is made now between Eqs. (1.79) and (1.83) by means of the
following ratio:
