In this question, we build a truss a supporting structure

for something like a roof. These work by taking on a force (often a straight-down

gravitational force, but sometimes it is angled) and distributing it to a couple of points

attached to something that is very solid. A point that cannot move (e.g. at A below)

experiences a force directly along the beam attached to it. A point that can move around,

but is sitting on a surface due to gravity (e.g. at B) will experience a force in reaction to the

gravitational pull so the vector points straight up.

(a) A triangular truss is to be built. It will consist of a horizontal member AB, with A attached

to a wall and B supported on a roller at a point 20 m away. The third joint, C, needs to be

10 m above AB. It will be subjected to 500 kN of force horizontally in the direction from A

to B. If C can be placed above any point along the member AB, where should it be put to

minimize the largest force on the truss?

(b) Repeat the question above, but this time with the force on C being angled down by 30