Consider a tie rod tr mitting a tensile force F. The corresponding tensile stress is given by \sigma=F / A, where A is the area of the cross section. The deflection of the rod is given by Eq. (4-3), which is \delta=(F l) /(A E), where l is the length of the rod. Using the Ashby charts of Figs. 2-16 and 2-19, explore what ductile materials are best suited for a light, stiff, and strong tie rod. Hint: Consider stiffness and strength separately.
Eq. (4-3),
\delta=\frac{F l}{A E}
\underline{\text { For stiffness, }} k=A E / l, or, A=k l / E.
Thus, m=\rho A l=\rho(k l / E) l=k l^{2} \rho / E . Then, M=E / \rho and \beta=1
From Fig. 2-16, lines parallel to E / \rho for ductile materials include steel, titanium, molybdenum, aluminum alloys, and composites.
For strength, S=F / A, or, A=F / S
Thus, m=\rho A l=\rho F / S l=F l \rho / S . Then, M=S / \rho and \beta=1
From Fig. 2-19, lines parallel to S / \rho give for ductile materials, steel, aluminum alloys, nickel alloys, titanium, and composites.
Common to both stiffness and strength are steel, titanium, aluminum alloys, and composites. .
