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SCEE$08002$ Structural Mechanics $2-$ December $2023$

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$($a$)$ Figure $2$a shows a planar pin$-$jointed truss, with pinned supports at A and B$.$ A horizontal load of $20kN,$ and a vertical load of $P$ are applied as shown. Horizontal spacing between each node along the top and bottom chords is $5m,$ the height between the top and bottom

i$)$ Calculate the support reactions at A and $B.P$ is initially $100kN$

ii$)$ By making an appropriate cut and using the method of sections, or otherwise, find the forces in the three bars, labelled $a,b$ and $c,$ stating for each whether they are in tension or compression.

$($b$)$ The bars a and c carry the largest magnitude of internal forces in the truss. The axial load capacity of the bars in tension and compression is $150kN.$ Calculate the maximum force $P$ that can be resisted by the truss. Without further calculation, explain briefly how the structure un$....$ and how your calculations would be affected.