$1)(20$ Points$)$ Use a two linear element FE solution to determine the transverse deformation and the reaction in the given simply supported beam.

a$)$ Determine elemental equilibrium equation. $(4$ points$)$

b$)$ Determine global equilibrium equation. $(4$ points$)$

c$)$ Calculate transverse displacement and reaction in global coordinates. $(4$ points$)$

d$)$ Plot transverse displacement that is valid for each element. $(4$ points$)$

e$)$ Plot transverse displacements over an entire beam. $(4$ points$)$

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E$=1\backslash$cdot $10^\{6\}\backslash$mathrm$\{$kPa$\}$

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