Engineering Mechanics: Force Analysis

Engineering Mechanics - Part 1: Statics - Force Analysis

• Force is defined as the action of one body on another.
• Force is a vector quantity, requiring magnitude, direction, and point of application for full specification.
• When only resultant external effects are relevant, a force can be treated as a sliding vector.
• SI units for force are Newtons (N) and kiloNewtons (kN).
• U.S. customary units for force are pounds (lb) and kilopounds (kip).
• Force direction is defined by the line of action and the sense of the force.
• The line of action is an infinite straight line along which the force acts. It's defined by the angle it forms with a fixed axis.
• The principle of transmissibility states that a force acting on a rigid body can be considered to act at any other point on its line of action, provided that point is rigidly connected to the body. This allows for simplified analysis.
• A force acting on a body can change its motion, cause rotation about an axis, retard motion, bring the body to rest or equilibrium, and generate internal stresses within the body.
• Force systems can be categorized as coplanar, collinear, concurrent, coplanar concurrent, non-coplanar concurrent, and non-coplanar non-concurrent, based on lines of action.

Types of Forces

• External force: Applied by a different object.
• Internal force: Applied by one part of an object on another part.
• Distributed force: Applied over a large area.
• Concentrated force: Applied over a small area compared to the body's other dimensions.
• Gravitational force (weight): Represented by a vector from the center of mass, pointing vertically downwards toward the center of the Earth. Weight (w) = mass (m) × acceleration due to gravity (g).

Other Force Considerations

• Body force: Acts throughout the volume of an object (e.g., gravity).
• Surface force: Acts on the surface of an object; generated by direct physical contact between two objects.
• Contact forces: Result from contact between objects. These forces can include contact with surfaces, ropes, cables, pulleys, and springs.
• Surface contact force and friction force: Two surfaces in contact exert forces on each other; these forces are equal in magnitude but opposite in direction and can be resolved into normal (N) and tangential (f - friction) components and depends if the surface are rough or smooth
• Ropes and Cables: A force exerted by a rope or cable is equal to the cable's tension (T), with its line of action collinear with the cable.
• Pulleys: Used to change the direction of a rope or cable. Tension is approximately equal on both sides of a stationary or constant-rate pulley.
• Springs: Exert contact forces in mechanical devices. Force (F) exerted from stretching a spring of unstretched length (Lo) to a length (L): F = ks where s = |L − L₀| and ‘k’ is the stiffness constant

Composition and Resolution of Forces

• Forces are treated as vectors.
• Composition (finding the resultant of multiple forces) and resolution (breaking a force into components) require vector operations.
• Graphical methods (parallelogram law, triangle law, polygon law) are used for the composition of coplanar forces.
• Analytical methods using components (x and y) and coordinate direction angles are used to determine the resultant force and components of a force..
• Vector notation is used in resolving forces into their Cartesian components in 2D or 3D systems

Solved Examples and Problems

• Solved examples demonstrate the calculation of resultant forces and direction angles.
• Problem sets are typically provided to practice the concepts covered.