Machines: Problem Solving II

To find the force on member AB, create a free-body diagram for section DAF and apply the moment equilibrium condition at joint F. Substitute known values including the calculated forces from joint E analysis into the equilibrium equation. For the 100 kg lifting tong example, this yields a force of 2423.76 N along member AB, which represents the internal force required to support the load.

Two-force members, such as ED and EC in a lifting tong, carry forces directed along their length toward the connected joints. These forces simplify analysis because they act only along the member axis. By resolving these forces into horizontal and vertical components and applying force equilibrium conditions, engineers can systematically determine internal forces throughout the machine structure.

Structural symmetry about a central point, such as point E in a lifting tong, ensures that forces are distributed equally on both sides. This symmetry means that forces FED and FEC are equal in magnitude, simplifying calculations and reducing the number of unknowns. Symmetry also guarantees balanced load distribution, which is critical for safe and efficient machine operation.

Force equilibrium conditions state that the sum of forces in any direction must equal zero. Applying horizontal and vertical equilibrium at joint E determines individual member forces. For the lifting tong, horizontal equilibrium confirms FED equals FEC, while vertical equilibrium yields the member force as 953.46 N. These conditions are essential for method of joints problem solving.

The cable tension force must balance the load's weight, which is calculated as mass times gravitational acceleration. For a 100 kg load, the weight equals 981 N. The cable tension acts vertically upward and equals this weight, creating the primary force that drives the entire force distribution throughout the lifting tong structure.

The angle between members and horizontal components directly influences force resolution and equilibrium equations. In the lifting tong example, the angle between member ED and the horizontal is 30.96 degrees. This geometric relationship determines how forces decompose into components, affecting the magnitude of internal forces calculated through equilibrium conditions.

Force equilibrium ensures linear motion does not occur, while moment equilibrium prevents rotational motion. In lifting tong analysis, applying moment equilibrium at joint F captures the rotational effects of forces acting on section DAF. Together, both conditions fully constrain the system and allow calculation of all internal forces, including the critical force along member AB.