TTB$204/2023-2024/$GZ

Session $9($Week $10)$

Q$9\mathrm{.}2\mathrm{.}1$ A deep uniform cantilever beam with a length $l$ of $400mm,$ a width $b$ of $40mm$ and a thickness $d$ of $50mm$ is subjected to a concentrated load of $100kN$ at its free end, as shown in Fig. $9\mathrm{.}2\mathrm{.}1.$ If a Young's modulus $E$ and the Poisson's ratio of beam material are $204$GPa and $0\mathrm{.}33,$ respectively, determine the total deflection at its free end and the ratio of the shear deflection to the bending deflection in the total. A shear correction factor is $5/6.$

Fig. $9\mathrm{.}2\mathrm{.}1$

Answers: $25\mathrm{.}4mm$ and $1\mathrm{.}25\%.$