Page 347 - Mechanics of Microelectromechanical Systems

334 Chapter 5
generates the normal stress and generates such that the resultant
stress is their algebraic sum at any point of the cross-section. As Fig. 5.64
shows‚ at points A and B the sum is maximum‚ positive at A and negative at
B. In addition to bending‚ the axial force N also produces tensile stresses
which are constant over the cross-section. It follows that the maximum
normal stress is found at A‚ and is tensile (positive):

It is also known – see Boresi‚ Schmidt and Sidebottom [3] for instance‚ that
for a narrow cross-section the maximum torsion-produced stress occurs also
at one of the edge points – so either A or B – and is equal to:

By recalling that the equivalent stress represents a maximum value‚ it follows
that Eq. (5.195) becomes‚ by means of Eqs. (5.196) through (5.198):

The equivalent stress of Eq. (5.199) gives which is smaller
than the yield stress.

Example 5.24
A U-spring connects to a shuttle mass as in Fig. 5.65 (a). The spring is
acted upon by the forces and The U-spring is constructed of a ductile
material with a yield stress of and the spring’s cross-section is
a narrow rectangle‚ as shown in Fig. 5.65 (b) with and
Known are also and Determine
the force which will keep the maximum stresses in the microsuspension
at the yield threshold.

Solution:
When ignoring the stresses produced by axial and shearing effects‚ the
three segments of the half-model of Fig. 5.65 (a) are subject to the combined
action of bending and torsion. The maximum moments occur at the fixed
position 4‚ namely: