(Solved): 3. A cantilever beam with a uniform load has a height \( \mathrm{h} \) equal to \( 1 / 8 \) of the ...

3. A cantilever beam with a uniform load has a height \( \mathrm{h} \) equal to \( 1 / 8 \) of the length \( \mathrm{L} \). The beam is a steel wide-flange section with \( \mathrm{E}=208 \mathrm{GPa} \) and an allowable bending stress of \( 130 \mathrm{MPa} \) in both tension and compression. Calculate the ratio \( \delta / L \) of the deflection at the free end to the length, assuming that the beam carries the maximum allowable load. The end deflection for a cantilever beam loaded as shown is \( \delta_{\text {end }}=\frac{q L^{4}}{8 E I} \)