The beam in Figure $($a$)$ is an example of a symmetric structure under a set of symmetric loads

$($the dash line indicated by $"s"$ is the axis of symmetry$).$ Based on the discussion in the handout

document $($shared on Canvas and linked here$),$ this structure can be simplified to the structure in

Figure $($b$).$

Use the displacement method to analyze the structures in Figure $($a$)$ and Figure $($b$),$ respectively,

by determining the support reactions and drawing bending moment and shear force diagrams.

Based on your results, verify that:

$(1)$ The support reactions for the structure in $($a$)$ are symmetric about the axis of symmetry;

$(2)$ The bending moment diagram for the structure in $($a$)$ is symmetric about the axis of

symmetry;

$(3)$ The shear force diagram for the structure in $($a$)$ is antisymmetric about the axis of

symmetry.

Notes:

For both structures, DO NOT define structural nodes at point loads.

$E=200$GPa,$I=5\mathrm{.}0({10}^9)m{m}^4.$ The values are constant along the entire beam.

Complete the analyses of both structures with hand calculation and FE$-$approved

calculators.