A truss bridge is to be constructed, supported at points A and B. A truss with joint connections, consisting of steel bars screwed together at node plates (truss nodes, see detailed illustration below), is to be used. The ends of the bridge are to be supported by a pin at A (fixed support) and a roller bearing at B (hinged support). The height of the two support points (with respect to the roadway or water surface) can be freely chosen. The vertical load F is to be supported at the center over a maximum length l. This load can act partially on several nodes in the upper chord or entirely on one node in the center of the upper chord (force applied at a single node to prevent laying a beam horizontally from A to B). The upper chord should run horizontally (roadway), meaning the bridge extends downward. Forces due to wind and gravity should be neglected. Assume that the maximum tensile force in each bar is Fz,max, and the maximum compressive force, regardless of the length of the bar, is FD,max.

Design the bridge to be as cost-effective as possible. The length-specific costs of the bars are KSt, and the cost of a node plate is KK. Provide a cost estimate for the building materials and a dimensioned drawing of the truss, indicating tension and compression members. Calculate all forces (bar forces, support forces).

Given: F = 5 kN, Fz,max = 4.25 kN, FD,max = 3.5 kN, KSt = $3.50/m, KK = $8, l = 3 m, b = 12 m.