Equilibrium of Particles and Rigid Bodies - Concept Map
Equilibrium of Particles and Rigid Bodies
Related concepts
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
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
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
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
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
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
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
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
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
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
Concept connections
- Free-Body DiagramEquilibrium EquationsFBD provides visual input; equations are the mathematical tools applied to FBD
- Equilibrium EquationsSupport ReactionsEquations are solved to find the unknown reactions at supports
- Particle EquilibriumLami's TheoremLami's Theorem is a specialized fast-solution method for three concurrent forces in particle equilibrium
- Rigid Body EquilibriumMoment ConceptsMoment equilibrium is essential for rigid bodies; particles need only force balance
- Distributed LoadsEquilibrium EquationsDistributed loads must be converted to resultants before equilibrium equations can be applied
- Support Types and ReactionsFree-Body DiagramSupport types determine what reactions to draw on the FBD
- Two-Force MembersRigid Body EquilibriumTruss members are special case of rigid bodies with axial force only
- Three-Force MembersConcurrent Force SystemsThree-force members must have concurrent or parallel forces for equilibrium
- Particle EquilibriumRigid Body EquilibriumParticles are limiting case of rigid bodies where moment effects are negligible
- Moment ConceptsSupport ReactionsMoment summation about a support strategically simplifies reaction calculations
- Support Types and ReactionsEquilibrium EquationsNumber of unknowns (reactions) must equal number of independent equations (3 for 2D)
- Lami's TheoremComponent MethodBoth solve concurrent three-force systems; Lami is faster but component method is more general
Diagrams
Equilibrium of Particles and Rigid Bodies — Complete Concept Hierarchy
Hierarchical mind map showing all major concepts in equilibrium analysis, from fundamental FBD concepts through particle and rigid body equilibrium methods, support reactions, special member types, distributed loads, and moment calculations. This is the complete conceptual framework for the chapter.
Equilibrium Analysis Procedure — Step-by-Step Solution Method
Step-by-step flowchart showing the decision-making and procedural logic for solving equilibrium problems. Separates particle equilibrium (using Lami's theorem or component method) from rigid body analysis (using all three equilibrium equations). Includes verification step.
Support Reaction Determination — Support Type Decision Tree
Decision tree for identifying support types and their corresponding reactions. Routes the user through proper classification of roller, pin, and fixed supports, then applies the three equilibrium equations in logical sequence to find all reactions.
Lami's Theorem Application — Three-Force Particle Equilibrium
Specialized flowchart for applying Lami's Theorem to three concurrent forces. Shows both the direct Lami method (using sine ratios) and the component method as an alternative. Includes angle verification check.
Distributed Load Conversion — UDL to Resultant Force
Procedural flowchart for converting distributed loads (UDL, triangular, trapezoid) into equivalent point loads at their centroids. Essential for applying equilibrium equations to beams with extended loading.
Equilibrium State Transitions — From Free Body to Solved Reactions
State diagram showing the progression through equilibrium problem-solving stages, from initial FBD creation through identification, conversion, equation application, solution, and verification. Includes feedback loop for error correction.
Equilibrium Problem Distribution — Exam Content Emphasis
Pie chart showing typical distribution of equilibrium topics in PRC licensure exams. Indicates that rigid body reaction problems (35%) form the largest category, followed by particle equilibrium (25%) and distributed loads (20%). Used for study priority planning.