Consider a cantilevered beam shown in figure 10.3 with \(E=2.9 \times 10^{4} \mathrm{ksi}\). The width \(w\) is taken as 2.25 inches, while the height \(h\) is considered a design variable. The design should satisfy the factor of safety 1.5 .

(a) When the allowable tip displacement is \(D_{\text {allowable }}=2.5 \mathrm{in}\)., determine the height of the beam.

(b) When the allowable strength of the material is \(40 \mathrm{ksi}\), determine the height of the beam.

L= 100 in Figure 10.3 Cantilevered beam design W h F=2,000 lb