Problem $3\mathrm{.}15$

Problem Statement: Consider the beam of circular cross section of Fig. $3\mathrm{.}29$ and Ex$.3\mathrm{.}1.$ As

before, the radius $r$ of the cross section may vary with material, and the beam is required to have

length $L$ and carry load $P.$ However, in this case, the strength requirement is replaced by a

requirement that the deflection not exceed a particular value $v_{\text{m}\text{a}\text{x}}.$

a$)$ Select a material from Table $3\mathrm{.}13$ such that the mass is minimized.

b$)$ Repeat the selection with cost being minimized.

c$)$ Briefly discuss your results, and suggest one or more materials that represent a reasonable

choice, where both lightweight and cost are important.