$*******$ONLY DO A$*******$inned 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

chord is $8m$ and the truss is symmetrical, with an offset of $2\mathrm{.}5m$ between the nodes on

the top and bottom chords, as shown. The force $P$ is initially $100kN$

i$)$ Calculate the support reactions at A and $B.$

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.

$($c$)$ A temperature change causes all the bars in the structure to increase in length by $1\%.$

Without further calculation, explain briefly how the structure would behave, and how your

calculations would be affected.