Simple Stresses and Strains - Concept Map
Stress and Strain Analysis in Structural Members
Related concepts
Normal (Axial) Stress
Sub concepts
- Tensile stress
- Compressive stress
- Stress formula σ = P/A
- Saint-Venant's Principle
Relationship to central
Primary stress type; force perpendicular to cross-section
Shear Stress
Sub concepts
- Single shear τ = V/A
- Double shear τ = V/2A
- Connector design
- Bolt and rivet analysis
Relationship to central
Secondary stress type; force parallel to area
Bearing Stress
Sub concepts
- Formula σ_b = P/(d·t)
- Projected bearing area
- Hole tear-out
- Plate crushing
Relationship to central
Contact pressure between bodies
Strain
Sub concepts
- Normal strain ε = δ/L
- Shear strain γ
- Axial deformation
- Lateral deformation
Relationship to central
Deformation measure; fundamental to stress-strain relationship
Hooke's Law
Sub concepts
- Axial form σ = Eε
- Shear form τ = Gγ
- Proportional limit
- Elastic limit
Relationship to central
Linear elastic relationship between stress and strain
Elastic Constants
Sub concepts
- Modulus of elasticity E
- Shear modulus G
- Poisson's ratio ν
- Bulk modulus K
- Interrelationships
Relationship to central
Material properties governing deformation
Axial Deformation
Sub concepts
- Formula δ = PL/(AE)
- Composite bar analysis
- Segmented members
- Integration for varying loads
Relationship to central
Quantitative calculation of member shortening/elongation
Thermal Effects
Sub concepts
- Free thermal expansion δ_T = αLΔT
- Thermal stress σ_T = EαΔT
- Restrained members
- Partial restraint gap analysis
Relationship to central
Temperature-induced stress and deformation
Statically Indeterminate Members
Sub concepts
- Equilibrium equations
- Compatibility equations
- Force-deformation substitution
- Double-fixed bar analysis
Relationship to central
Complex loading requiring compatibility equations
Stress-Strain Diagram
Sub concepts
- Proportional limit
- Elastic limit
- Yield point
- Ultimate strength
- Rupture strength
Relationship to central
Graphical representation of material behavior
Generalized Hooke's Law
Sub concepts
- Biaxial stress state
- Triaxial stress state
- Poisson effect in all directions
- Volumetric strain
Relationship to central
Multi-directional stress-strain relationships
Design and Safety
Sub concepts
- Allowable stress
- Factor of safety
- Yield versus ultimate criteria
- NSCP 2015 provisions
- AISC 360 standards
Relationship to central
Application of stress-strain concepts to safe design
Concept connections
- Normal StressStrainStress causes strain; related through modulus E via Hooke's Law
- Shear StressShear StrainShear stress produces angular distortion; related through shear modulus G
- Bearing StressHole Tear-outBearing stress at contact determines hole failure mode in connections
- Hooke's LawElastic ConstantsHooke's Law defines the role of E and G; connects through Poisson's ratio
- Axial DeformationComposite MembersDeformation formula δ = PL/AE applied separately to each material; compatibility equates deformations
- Thermal EffectsRestrained MembersThermal stress arises only in restrained members; free expansion causes no stress
- Statically IndeterminateCompatibility EquationsIndeterminate problems solved by adding compatibility constraint to equilibrium
- Stress-Strain DiagramMaterial BehaviorDiagram maps stress regions from elastic through plastic to rupture; informs allowable stress selection
- Poisson's RatioGeneralized Hooke's LawPoisson's ratio couples strains in perpendicular directions; essential for multi-axial stress
- Design and SafetyAllowable StressFactor of safety and allowable stress derived from yield or ultimate strength via stress-strain curve
- Saint-Venant's PrincipleNormal StressPrinciple justifies use of average stress σ = P/A away from load application points
- Single ShearDouble ShearDouble shear has factor of 2 in denominator; both are variants of τ = V/A
- Axial DeformationThermal DeformationBoth govern total deformation; thermal δ_T = αLΔT added to or subtracted from mechanical δ
- Modulus of ElasticityAxial RigidityProduct AE is axial rigidity; higher AE means less deformation for same load
- Elastic LimitProportional LimitProportional limit is typically the lower bound; elastic limit is where permanent set begins
- Composite MembersLoad SharingLoad distributes between materials inversely proportional to their AE products
- Segmented BarsSummation FormulaDeformation of segments summed: δ_total = Σ(P_i L_i / A_i E_i)
- NSCP 2015Design and SafetyPhilippine code specifies allowable stresses and design factors; governs civil engineering practice
- AISC 360Steel Connection DesignAISC standards apply to bolt shear and bearing design; used in conjunction with NSCP
- ACI 318Concrete PropertiesACI provides concrete modulus and material properties; used in composite concrete-steel analysis
Diagrams
Simple Stresses and Strains - Complete Concept Hierarchy
Comprehensive mind map showing the hierarchical organization of all key concepts in Simple Stresses and Strains, organized into six major branches: stress types, strain fundamentals, material properties, Hooke's Law, deformation analysis, advanced analysis, and design applications.
Axial Deformation Analysis Process
Step-by-step flowchart for analyzing axial deformation in structural members, from problem identification through material property selection, force determination, and deformation calculation—including pathways for determinate, indeterminate, and composite members.
Stress Type Identification and Calculation Decision Tree
Decision tree for identifying stress types based on loading direction and configuration, with pathways for calculating strain and deformation using Hooke's Law within the elastic range.
Thermal Stress Analysis - Restrained Member Process
Flowchart for analyzing thermal stress in restrained and partially restrained members, showing the three cases: free expansion (no stress), full restraint (maximum stress), and partial restraint (equilibrium with gap closure).
Statically Indeterminate Axial Member Solution Strategy
Complete systematic approach for solving statically indeterminate axial member problems, including free body analysis, equilibrium equations, compatibility conditions, force-deformation substitution, and verification steps.
Composite Bar Analysis - Load Sharing Between Materials
Systematic analysis of composite members showing how load is shared between materials based on their axial rigidity (AE). The key insight is that load sharing depends on relative stiffness, not on stress or strain equality.
Material Behavior Through Stress-Strain Curve Regions
State diagram showing the progression of a ductile material (mild steel) through the stress-strain curve from elastic behavior through yielding, strain hardening, ultimate strength, and rupture, with notation of recovery paths on unloading.
Poisson Effect and Generalized Hooke's Law in Multi-axial Stress
Flowchart tracing the concept of Poisson's ratio from simple uniaxial loading through biaxial and triaxial stress states, showing how generalized Hooke's Law governs multi-directional deformation and volumetric strain.