In vehicle suspension design it is desirable to minimize the mass of all components. You have been
Question:
In vehicle suspension design it is desirable to minimize the mass of all components. You have been asked to select a material and dimensions for a light spring to replace the steel leaf spring of an existing truck suspension. The existing leaf spring is a beam, shown schematically in the figure. The new spring must have the same length \(L\) and stiffness \(S\) as the existing one, and must deflect through a maximum safe displacement \(\delta_{\max }\) without failure. The width \(b\) and thickness \(t\) are free variables.
You will need the equation for the midpoint deflection of an elastic beam of length \(L\) loaded in three-
point bending by a central load \(F\) :
\[\delta=\frac{1}{48} \frac{F L^{3}}{E I}\]
and that for the deflection at which failure occurs \[\delta_{\max }=\frac{1}{6} \frac{\sigma_{f} L^{2}}{t E}\]
where \(I\) is the second moment of area; for a beam of rectangular section, \(I=b t^{3} / 12\) and \(E\) and \(\sigma_{f}\) are the modulus and failure stress of the material of the beam.
Use the index you derive to rank the following candidate material for this application. High carbon steel, low alloy steel, titanium alloys and Carbon-fiber reinforced polymers (CFRP) (carbon fibre reinforced polymers).
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