Analysis of Determinate Structures - Concept Map
Determinate Structure Analysis
Related concepts
Structural Determinacy
Sub concepts
- Degree of Static Indeterminacy (DI)
- Stability Assessment
- Equations of Condition
- Internal Releases
Relationship to central
Foundation – establishes whether a structure can be solved by equilibrium equations alone
Reactions
Sub concepts
- Equilibrium Equations (ΣFx, ΣFy, ΣM)
- Support Types (Pin, Roller, Fixed)
- Equations of Condition at Hinges
- Compound Beam Analysis
Relationship to central
First step after classifying determinacy – solve for support forces and moments
Internal Forces
Sub concepts
- Axial Force (N)
- Shear Force (V)
- Bending Moment (M)
- Free Body Diagram Method
Relationship to central
Primary output – axial, shear, and moment within members from reaction equilibrium
Three-Hinged Arches
Sub concepts
- Crown Hinge Equation (ΣMc = 0)
- Horizontal Thrust (H)
- Reaction Determination
- Moment Reduction Effect
Relationship to central
Special determinate structure type – uses crown hinge condition for horizontal thrust
Frame Analysis
Sub concepts
- Portal Frames
- Member Axial-Shear-Moment Distribution
- Sign Conventions
- L-Frames and Complex Geometries
Relationship to central
Application of determinacy and internal forces to rigid structures
Concept connections
- Structural DeterminacyReactionsDeterminacy confirms that equilibrium equations alone suffice to solve for all reactions—no compatibility equations needed
- ReactionsInternal ForcesReaction values are the boundary conditions; they anchor the free-body-diagram method used to find internal N, V, M at any section
- Equations of ConditionThree-Hinged ArchesThe crown hinge creates one equation of condition; this fourth equation solves for the unique horizontal thrust that makes the arch determinate
- Internal ForcesFrame AnalysisFrame analysis applies the axial-shear-moment method to each member; results are plotted as member-specific diagrams
- Equilibrium EquationsReactionsThree equations (ΣFx, ΣFy, ΣM) form the core of reaction determination; equations of condition extend this system when hinges exist
- Support TypesDegree of Static IndeterminacyThe number and type of reaction components (r) directly determines DI; fixed supports contribute 3 unknowns each, pins contribute 2, rollers contribute 1
- Three-Hinged ArchesHorizontal ThrustHorizontal thrust H is the defining output of arch analysis; it emerges from the crown moment condition and makes the arch more efficient than a beam
- Free Body Diagram MethodInternal ForcesFBD of a cut segment is the direct method for finding N, V, M; equilibrium of the cut face yields all three internal forces
- Compound Beam AnalysisEquations of ConditionEach internal hinge in a compound beam contributes one equation of condition; suspended-span-first analysis exploits these conditions systematically
- Stability AssessmentStructural DeterminacyStability is checked after determinacy; even a determinate structure (DI=0) is unstable if reactions are concurrent or parallel
- Sign ConventionFrame AnalysisConsistent sign convention across all members is essential for correct internal-force diagrams; confusion here is a common exam error
- Portal FramesMoment DistributionPortal frame behavior depends on whether it is determinate (fixed bases, three members, gives DI=3) or indeterminate; internal moments reflect base conditions
Diagrams
Analysis of Determinate Structures – Complete Concept Hierarchy
Comprehensive mind map showing the hierarchical structure of determinate structure analysis. Root concept branches into five major domains: Determinacy & Stability (methods to classify structures), Support Reactions (how to find reaction forces), Internal Forces (axial, shear, moment), Three-Hinged Arches (special determinate arch type), and Frame Structures (application to rigid structures). Each branch includes relevant sub-concepts and practical formulas used in licensure-level analysis.
Determinacy Classification Procedure (NSCP 2015 Approach)
Step-by-step flowchart for classifying structural determinacy per NSCP 2015 guidelines. This is a critical first step before solving any determinate structure problem. The procedure guides users through formula selection, calculation of the degree of indeterminacy, and verification of geometric stability—ensuring no concurrent or parallel reaction arrangements exist.
Reaction Analysis and Internal Force Determination Workflow
Complete workflow from given loads to final internal force diagrams. This flowchart integrates reaction determination with the method of sections, showing how equilibrium equations (both global and local) are applied systematically. The process emphasizes verification steps and leads to construction of axial, shear, and moment diagrams—essential deliverables for determinate structure analysis.
Three-Hinged Arch Analysis Procedure
Detailed procedure for analyzing a three-hinged arch, the most common determinate arch type in licensure exams. Key steps: (1) find vertical reactions from overall equilibrium, (2) apply the crown hinge moment condition to find horizontal thrust, (3) verify all four reactions. The horizontal thrust H is what makes the arch structurally efficient—it carries load with less bending than an equivalent simple beam, a critical concept for understanding arch behavior.
Determinate Frame Internal Force Sign Convention
Establishes consistent sign conventions for internal forces in frame analysis. Proper sign convention is critical for exam success—students must understand that positive shear produces clockwise rotation on the right face of a section, and positive moment places compression in the top fibers (sagging). This diagram clarifies conventions used throughout determinate frame analysis.
Structural Stability vs Determinacy Decision Matrix
State diagram showing the decision tree for classifying a structure as stable, determinate, or indeterminate. Emphasizes that stability and determinacy are independent properties: a structure must have (1) sufficient reactions AND (2) a proper geometric arrangement of those reactions to be stable. Even if DI = 0 (determinate), concurrent or parallel reactions make the structure unstable and unable to resist certain load directions.
Compound (Gerber) Beam Analysis Strategy
Critical procedure for analyzing compound (Gerber) beams, common in licensure exams. The key principle: always analyze suspended spans first and work backward toward fixed supports. Each suspended span's reaction becomes a point load on the span that supports it. This bottom-up approach reduces complexity and prevents errors in subsequent span calculations.