The method of joints is used to solve for the member forces and reaction forces on a power tower truss. Use sliders to set the point load forces at joints and , and check "show joint labels" to see the labeled joints. This truss rests on two pinned supports, which resist both vertical and horizontal forces. Member forces are shown in kN. Arrows that point outward (green) represent the member response to compression forces, and arrows that point inward (red) represent the member response to tension forces. Compression acts to shorten the member and tension acts to lengthen it. Zero members (black lines) are in neither tension nor compression, so their force is 0 kN. Zero members provide stability and extra support to the structure in case another member fails.
The reaction forces are calculated first by summing the forces, then calculating moments about joint , and then doing a force balance in the direction. , , , and are the reaction forces in the and directions at joint , and are the reaction forces at joint , , and are the point load forces in the and directions at joint , is the point load force at joint , and are the shorter and longer widths, and and are the shorter and longer heights. The second and third terms ( , ) are positive in the moment balance because they cause a clockwise rotation, and the first and fourth terms ( , ) are negative because they cause a counterclockwise rotation. The method of joints is used to calculate the member forces using the order of the calculations below. Force balances are done assuming we can determine which forces are under tension and which forces are under compression prior to solving the truss. At joint there is an upward force of , so we know that must be a compression force in order for the truss to remain stationary. Also, there is a force of in the negative direction, so must be a tension force. A labeled truss is shown in Figure 1. See the angles used in Figure 2. Joint : , , . Joint : , . Joint : , , . Joint : , . Joint : , . Joint : , . Joint : , , . Joint : , . Joint : . Joint : . For some conditions, is under compression and is under tension. [1] R. C. Hibbeler, Engineering Mechanics: Statics, 12th ed., Upper Saddle River, NJ: Prentice Hall, 2010.
