Page 58 - Mechanics of Microelectromechanical Systems
P. 58
1. Stiffness basics 45
This equation has been obtained by using Eqs. (1.169) and (1.170) and by
considering that:
Equation (1.171) can further be put in the standard form:
where, according to the parallel axis theorem, the moment of inertia is:
A similar approach is now followed for the composite beam of Fig. 1.25
(a). In this case, the position of the neutral axis is unknown. Because the state
of stress is of pure bending, the axial force that acts on the cross-section is
zero, which leads to:
where and are the cross-sectional areas of the two components. The
strain will however follow the linear distribution of Eq. (1.168), and
therefore Eq. (1.170) is still valid. The stresses in the two components are:
By substituting Eqs. (1.176) into Eq. (1.175), the position of the neutral axis
becomes:
When more than two layers form the composite cross-section, Eq. (1.177)
generalizes to:
