In architecture and structural engineering, a truss is a structure consisting of one or more triangular units constructed with straight members whose ends are connected at joints known as nodes. Trusses are composed of triangles because of their structural stability. A plane truss has all its members and nodes in a plane.
The figure below depicts a 13-member plane truss bridge structure with loads of W1, W2, and W3, as indicated. The left end of the truss is rigidly fixed horizontally and vertically, and the right end (G) is fixed vertically but not horizontally. The truss members that are inclined with respect to the vertical are all at an angle of 45 degrees.
For the truss to be in static equilibrium, the horizontal and vertical components of the net force at each node must be equal to zero (Newton's 1st Law). Assume the force vectors caused by the truss members are directed away from each node (i.e., assume they are all compression forces like the example in the notes). Since we are not interested in the forces exerted by the end supports, you only need to determine each of the 13 truss-member (internal) forces.
You do this by summing the horizontal components of the forces at each node (A thru G) and setting each sum equal to zero. Also, sum the vertical components of the forces at each node (A thru F) and set each sum equal to zero. Don't forget the gravitational forces at nodes B, D, and F: these are labeled W1, W2, and W3. This will result in 13 equations for the 13 unknown truss-member forces.
CONSTANT TERMS TO THE RIGHT-HAND SIDE. You will now have a system of equations of the form A*u=b, where u is the vector of unknown forces and b is a (known) vector of constants. Write a MATLAB script that will determine (using the "left divide command") the 13 forces and then print them to 2 decimal places, using fprintf. Set the values for the loads as W1=250 N, W2=400 N, and W3=200 N. For the forces you determine, a positive force represents a compression force and a negative force represents a tension force. Use the alphabetical ordering below (A thru G) for the vector containing all of the internal forces that your script solves for so that we all end up printing the same force vector (if the physics is done correctly, that is).
A
C
E
3
5
7
6
11
12
G
Ta W1
10 Ta W2 W3
13
11/111I
