CELE Engineering Mechanics — Equilibrium of Particles and Rigid BodiesConcept Map

Concept

Free-Body Diagram (FBD)

Sub Concepts

• Isolation of the body
• Identification of all external forces
• Support reactions
• Applied loads and weights
• Correct force directions and magnitudes

Relationship To Central

Foundation for all equilibrium analysis; visualizes all external forces and reactions

Concept

Equilibrium Equations

Sub Concepts

• Sum of horizontal forces = 0
• Sum of vertical forces = 0
• Sum of moments = 0
• 2D systems (3 equations)
• 3D systems (6 equations)
• Choice of moment center

Relationship To Central

Mathematical expressions that define the equilibrium state; core solving tool

Concept

Particle Equilibrium

Sub Concepts

• Concurrent force systems
• Two equilibrium equations only
• Lami's Theorem application
• Weight hanging from cords
• Tension and compression analysis

Relationship To Central

Special case dealing with point objects and concurrent forces

Concept

Rigid Body Equilibrium

Sub Concepts

• Non-concurrent force systems
• All three equilibrium equations required
• Support reactions at beams and frames
• Cantilever boundary conditions
• Simply supported configurations

Relationship To Central

General case dealing with extended bodies; includes moment effects

Concept

Support Types and Reactions

Sub Concepts

• Roller support (1 reaction)
• Pinned support (2 reactions)
• Fixed support (3 reactions)
• Inclined roller
• Reaction direction perpendicular to support surface

Relationship To Central

Defines how external constraints transmit forces and moments to the structure

Concept

Lami's Theorem

Sub Concepts

• Three concurrent forces condition
• Sine rule application
• Angle between force pairs
• Direct tension calculation
• Avoids component method

Relationship To Central

Rapid solution method for three-force particle equilibrium

Concept

Two-Force Members

Sub Concepts

• Truss members
• Force along line of action
• Collinearity principle
• Pin connections at both ends
• Tension or compression only

Relationship To Central

Structural elements with special equilibrium properties; pure axial loading

Concept

Three-Force Members

Sub Concepts

• Three external loads condition
• Concurrency requirement
• Parallel force condition
• Graphical solution methods
• Direction determination shortcut

Relationship To Central

Structural elements where equilibrium requires concurrent or parallel forces

Concept

Distributed Loads

Sub Concepts

• Uniform distributed load (UDL)
• Triangular load distribution
• Resultant force magnitude
• Resultant location (centroid)
• Integration method

Relationship To Central

Extended loads requiring conversion to resultants for equilibrium analysis

Concept

Moment and Torque Concepts

Sub Concepts

• Moment about a point
• Perpendicular distance (lever arm)
• Sign convention (clockwise/counterclockwise)
• Moment units (N·m, kN·m)
• Moment summation about any point

Relationship To Central

Rotational equilibrium requirement; determines support reactions and internal forces

To

Equilibrium Equations

From

Free-Body Diagram

Strength

strong

Relationship

FBD provides visual input; equations are the mathematical tools applied to FBD

To

Support Reactions

From

Equilibrium Equations

Strength

strong

Relationship

Equations are solved to find the unknown reactions at supports

To

Lami's Theorem

From

Particle Equilibrium

Strength

strong

Relationship

Lami's Theorem is a specialized fast-solution method for three concurrent forces in particle equilibrium

To

Moment Concepts

From

Rigid Body Equilibrium

Strength

strong

Relationship

Moment equilibrium is essential for rigid bodies; particles need only force balance

To

Equilibrium Equations

From

Distributed Loads

Strength

strong

Relationship

Distributed loads must be converted to resultants before equilibrium equations can be applied

To

Free-Body Diagram

From

Support Types and Reactions

Strength

strong

Relationship

Support types determine what reactions to draw on the FBD

To

Rigid Body Equilibrium

From

Two-Force Members

Strength

moderate

Relationship

Truss members are special case of rigid bodies with axial force only

To

Concurrent Force Systems

From

Three-Force Members

Strength

moderate

Relationship

Three-force members must have concurrent or parallel forces for equilibrium

To

Rigid Body Equilibrium

From

Particle Equilibrium

Strength

moderate

Relationship

Particles are limiting case of rigid bodies where moment effects are negligible

To

Support Reactions

From

Moment Concepts

Strength

strong

Relationship

Moment summation about a support strategically simplifies reaction calculations

To

Equilibrium Equations

From

Support Types and Reactions

Strength

strong

Relationship

Number of unknowns (reactions) must equal number of independent equations (3 for 2D)

To

Component Method

From

Lami's Theorem

Strength

moderate

Relationship

Both solve concurrent three-force systems; Lami is faster but component method is more general