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 F_CB, F_DC, F_DB, and F_AD.

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 F_CB as zero. Similarly, the vertical force equilibrium condition is applied to calculate F_DC 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 F_DB can be resolved into its horizontal and vertical components. Applying the vertical force equilibrium equation, F_DB is calculated to be 33.33 N. Furthermore, the horizontal force equilibrium yields force F_AD as 36.67 N.

As the force F_DB points away from the joint, it is tensile. The force F_DC is compressive as it points towards joint C. Also, F_AD points towards joint D and is compressive.