A project for constructing a Facility just started. It involves the excavation of 40 to 60 feet deep and 60 feet wide trench to house double tunnels. A 24-inch outside diameter (22.5-inch inside diamater) water line is located in the path of the trench. A temporary bridge will be constructed to carry a flexible crib to support the water line. The bridge consists of two parallel trusses (carrying the entire load) and horizontal bracing grid system consisting of three members along the bridge and transverse braces. No load will be carried by the grid system. The weightless trusses will carry the water line, whose load is assumed to be equally distributed to all nodes of the two side trusses. Nodes A and E on both trusses are subjected to the reactionary forces only; no load from the water line and the minimum distance between A and E is 66 feet.
For each truss, the lengths of members AB, BC, ..., CD, and DE are the same and equal to "X" feet, their number is variable and depending on your design, and their cross-sectional areas could be different. The number of nodes A, B, C, ... etc.is a function of the member length "X". The length of each vertical members such as FB, GC, and HD is 4 feet. The minimum cross-sectional area ofany member of the truss is 0.5 inch2.
1.) Provide a diagram showing the stress induced in members (see Figure 4) AB, AF, FG, FB, BG, and BC as a function of BC length, plot the length on the x axis and the stress on the y axis.
2.)Provide a diagram showing the cost of the truss as a function of BC length, plot the length on the x axis and the cost on the y axis.
3.)Name the member subjected to the highest force (compression or tension) and compute the magnitude of that force.
4.)Select the length of the horizontal members and the minimum cross sectional area of any member if the allowable stress in all members of the truss is 25000 psi and the minimum specified factor of safety is 3.0.
5.)Provide an equation expressing the magnitude of the stress induced in member AB as a function of its length. (Hint, develop the equation using equilibrium equations or use excel and the best fit curve of the data).