6.4:
Method of Joints: Problem Solving I
Consider a truss structure where two forces act at joints C and D, connected with frictionless joints. Determine the forces in each truss member and identify tension or compression in each truss member.
The method of joints can be used to determine all forces acting at each joint.
The analysis begins with joint C as it has the least unknown forces.
Draw a free-body diagram of joint C. Using the equilibrium equations, the unknown forces can be determined.
The angle between the members BD and AD can be determined as the tan inverse of the ratio of the length of AB and AD.
Next, consider joint D and draw a free-body diagram. The joint D consists of two known and two unknown forces.
Resolve the force in the member BD into its components, and by using the equation of equilibrium, the unknown forces can be determined.
Members experiencing the forces pointing away from the joint are in tension, while the members experiencing forces pointing towards the joint are in compression.
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.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. pp 276-277.