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Consider a beam element shown in the figure below. \( \mathrm{E}=70 \mathrm{GPa} \) and \( \mathrm{I}=0.0001 \mathrm{~m}^{4} \). Cross section of the beam element: If the nodal displacements (in metres and radians) of the beam element are \[ \{\boldsymbol{a}\}=\left\{\begin{array}{l} v_{1} \\ \theta_{1} \\ v_{2} \\ \theta_{2} \end{array}\right\}=\left\{\begin{array}{c} 0.002 \\ -0.0006 \\ -0.002 \\ 0.0001 \end{array}\right\} \] determine 1) the deflection and rotation at the centre of the element (i.e., \( x=1 \mathrm{~m}) \) (17 marks) 2) the strain \( \varepsilon(x) \) and stress \( \sigma(x) \) of the element at its bottom (i.e., \( y=-150 \mathrm{~mm} \) ) (8 marks)

Maximum deflection occurs at Centre of the beam=Moment at the C