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84 Chapter 2
The axial stiffness and torsional stiffness are:
For the particular condition where the trapezoid becomes a
rectangle, and consequently by taking the limit in Eqs. (2.58)
through (2.65), the stiffness equations for a constant, rectangular cross-
section cantilever – Eqs. (2.27), (2.28), (2.29) and (2.30) – should be
retrieved, which indeed occurs, as it can easily e checked.
Example 2.7
Compare a constant cross-section, rectangular microcantilever to one of
trapezoid configuration, which has the same length and by
analyzing the and stiffnesses. Consider that and c
spans the [1, 5] range. Also consider that the microcantilever’s cross-section
is very thin (t << w).
Solution:
The following stiffness ratios can be formulated:
where the * superscript indicates the constant rectangular cross-section
microcantilever. By utilizing Eqs. (2.27), (2.30), (2.58) and (2.65), together
with the given width relationship, Eqs. (2.66) transform into:
