Truss Design Algorithm

I collaborated with a team to design and construct a truss that met specific constraints: the truss had to withstand a 32 oz load placed 12.5 to 13.5 inches from the pin support, cost under $300, have a joint-to-joint span between 7 and 14 inches, span 31 inches, and follow the equation members = 2*Joints - 3. Additionally, the truss was required to consist solely of triangular members with no overlaps or crossings.

 The project unfolded in three key phases:

1. Buckling Lab: We measured the buckling strength of acrylic strips, which were later used in constructing the final truss, as a function of their length.

2. Preliminary Design: We devised potential truss designs adhering to the specified constraints and created a truss analysis program.

3. Final Design: We refined the optimal design from the preliminary phase and proceeded to construct the physical truss.

To test these designs, we created input files for two truss designs we came up with by creating  multiple matrices that represent the different truss designs as matrices of joint and member connections. Then, the main code file is utilized that outputs: the force each member bears, the support reaction forces, the maximum theoretical load, the cost of the truss, the cost-to-load ratio, and which member buckles first. These are factors that allow us to determine the best candidate truss.  Usually, truss analysis is done via two methods, the method of joints and the method of sections. Our code uses the method of joints because we have to calculate the force in each member. The basic principle underlying the method of joints is that if a system is an equilibrium, all forces acting on any joint must be an equilibrium as well.