(Solved): The cantilevered beam shown in the accompanying figure is a W16 31. Determ ...

???????

The cantilevered beam shown in the accompanying figure is a W16 $$?31$$. Determine its first three natural frequencies. The beam is made of Stainless steel. 1- Model it in ANSYS to verify the results. $$\left(\mathrm{L}1=15\mathrm{ft},\mathrm{L}2=10\mathrm{ft},\mathrm{E}=30^{?}10^{?}6\mathrm{lb}/{\mathrm{in}}^{?}2,\mathrm{y}=6.685^{?}10^{?}?3{\mathrm{lb}}^{?}{\mathrm{s}}^{?}2/{\mathrm{in}}^{?}2\right)$$ - Find the details of $$\mathrm{W}16^{?}31$$ from the table Global mass matrix is: $$[\mathbf{M}{]}^{(e)}=\frac{?L}{420}\left[\begin{array}{cccc}156& 22L& 54& ?13L\\ 22L& 4L^2& 13L& ?3L^2\\ 54& 13L& 156& ?22L\\ ?13L& ?3L^2& ?22L& 4L^2\end{array}\right]$$ Global stiffness matrix is: $$[\mathbf{K}{]}^{(e)}=\frac{EI}{L^3}\left[\begin{array}{cccc}12& 6L& ?12& 6L\\ 6L& 4L^2& ?6L& 2L^2\\ ?12& ?6L& 12& ?6L\\ 6L& 2L^2& ?6L& 4L^2\end{array}\right]$$