Trusses: we are now ready to discuss the trusses that are used in making stable load-bearing structures. The examples of these are the sides of the bridges or tall TV towers or towers that carry electricity wires. Schematic diagram of a structure on the side of a bridge is drawn in figure 1.
The structure shown in figure 1 is essentially a two-dimensional structure. This is known as a plane truss. On the other hand, a microwave or mobile phone tower is a three-dimensional structure. Thus there are two categories of trusses - Plane trusses like on the sides of a bridge and space trusses like the TV towers. In this course, we will be concentrating on plane trusses in which the basis elements are stuck together in a plane.
To motivate the structure of a plane truss, let me take a slender rod (12) between points 1 and 2 and attach it to a fixed pin joint at 1 (see figure 2).
Now I put a pin (pin2) at point 2 at the upper end and hang a weight W on it. The question is if we want to hold the weight at that point, what other minimum supports should we provide? For rods we are to make only pin joints (We assume everything is in this plane and the structures does not topple side ways). Since rod (12) tends to turn clockwise, we stop the rightward movement of point 2 by connecting a rod (23) on it and then stop point 3 from moving to the right by connecting it to point 1 by another rod (13). All the joints in this structure are pin joints. However, despite all this the entire structure still has a tendency to turn to turn clockwise because there is a torque on it due to W. To counter this, we attach a wheel on point 3 and put it on the ground. This is the bare minimum that we require to hold the weight is place. The triangle made by rods forms the basis of a plane truss.
Note: One may ask at this point as to why as we need the horizontal rod (13). It is because point 3 will otherwise keep moving to the right making the whole structure unstable. Rod (13) has two forces acting on it: one vertical force due to the wheel and the other at end 2. However these two forces cannot be collinear so without the rod (13) the system will not be in equilibrium. Generally, in a truss each joint must be connected to at least three rods or two rods and one external support.
Let us now analyze forces in the structure that just formed. For simplicity I take the lengths of all rods to be equal. To get the forces I look at all the forces on each pin and find conditions under which the pins are in equilibrium. The first thing we note that each rod in equilibrium under the influence of two forces applied by the pins at their ends. As I discussed in the previous lecture, in this situation the forces have to be collinear and therefore along the rods only. Thus each rod is under a tensile or compressive force. Thus rods (12), (23) and (13) experience forces as shown in figure 3.