6.4: Method of Joints: Problem Solving I
The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint. Consider a truss structure with two forces of 20 N and 10 N acting at joints C and D, respectively. The method of joints can be used to determine the forces FCB, FDC, FDB, and FAD.
To begin the analysis, a free-body diagram of joint C is considered, and force equilibrium conditions are applied.
The horizontal force equilibrium condition gives FCB as zero. Similarly, the vertical force equilibrium condition is applied to calculate FDC as 20 N.
Next, a free-body diagram of joint D is considered. The angle between members BD and AD, calculated using the tan inverse of the ratio of the lengths of AB and AD, is 36.87°. The force FDB can be resolved into its horizontal and vertical components. Applying the vertical force equilibrium equation, FDB is calculated to be 33.33 N. Furthermore, the horizontal force equilibrium yields force FAD as 36.67 N.
As the force FDB points away from the joint, it is tensile. The force FDC is compressive as it points towards joint C. Also, FAD points towards joint D and is compressive.
