![]() The structure is determinate and it holds the weight in place.Įven if we replace the pin joints by a small plate (known as gusset plate) with two or three pins in these, the analysis remains pretty much the same because the pins are so close together that they hardly create any moment about the joints. Thus we see that the weight is held with these three rods. ![]() Balance of forces in the vertical direction gives ![]() Since the direction of F 13 is coming out to be negative, the direction should be opposite to that assumed. It is in equilibrium under forces F 23, normal reaction N and a horizontal force F 13. Thus forces acting on pin 2 look like shown in figure 4.Īpplying equilibrium condition to pin (2) gives Further, it is pulled down by the weight W. The only forces acting on pin 2 are F 12 due to rod (12) and F 23 due to rod (23). If the actual forces are tensile, the answer will come out to be negative. Notice that we have taken all the forces to be compressive. Thus rods (12), (23) and (13) experience forces as shown in figure 3. Thus each rod is under a tensile or compressive force. As I discussed in the previous lecture, in this situation the forces have to be collinear and therefore along the rods only. The first thing we note that each rod in equilibrium under the influence of two forces applied by the pins at their ends. To get the forces I look at all the forces on each pin and find conditions under which the pins are in equilibrium. For simplicity I take the lengths of all rods to be equal. Let us now analyze forces in the structure that just formed. Generally, in a truss each joint must be connected to at least three rods or two rods and one external support. However these two forces cannot be collinear so without the rod (13) the system will not be in equilibrium. Rod (13) has two forces acting on it: one vertical force due to the wheel and the other at end 2. It is because point 3 will otherwise keep moving to the right making the whole structure unstable. Note: One may ask at this point as to why as we need the horizontal rod (13). The triangle made by rods forms the basis of a plane truss. This is the bare minimum that we require to hold the weight is place. To counter this, we attach a wheel on point 3 and put it on the ground. 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. All the joints in this structure are pin joints. 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). 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). Now I put a pin (pin2) at point 2 at the upper end and hang a weight W on it. 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). In this course, we will be concentrating on plane trusses in which the basis elements are stuck together in a plane. ![]() Thus there are two categories of trusses - Plane trusses like on the sides of a bridge and space trusses like the TV towers. On the other hand, a microwave or mobile phone tower is a three-dimensional structure. The structure shown in figure 1 is essentially a two-dimensional structure. Schematic diagram of a structure on the side of a bridge is drawn in figure 1. The examples of these are the sides of the bridges or tall TV towers or towers that carry electricity wires. We know the basics of equilibrium of bodies we will now discuss the trusses that are used in making stable load-bearing structures. Analysis of trusses by the methods of joints and by the methods of section is explained in the article. □ Reading time: 1 minuteLearn truss analysis methods with examples. ![]()
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