Advanced Structural Analysis - Lecture 2 Notes

Overview of the Lecture

• Continuation of advanced structural analysis course.
• Focus on:
  • Statically determined structures
  • Work and energy methods (next class)
• Referencing the textbook "Structural Analysis" authored by the lecturer.

Structure Modeling

• Skeletal Structure: Essential elements include:
  • Space frame elements
  • Plane frame elements
  • Grid or beam elements
  • Truss elements
• Interconnections: Joints can be rigid, pin, or semi-rigid.
• Supports: Types include:
  • Fixed, guided, hinged, roller (most generic is elastic).

Load Types

• Direct Actions: Indicated by arrow marks.
• Indirect Actions: Include support settlements, construction errors, and environmental changes.
• Interest in both force response and displacement response.

Indeterminacy in Structures

• Indeterminacy Types: Static vs. kinematic indeterminacy.
• Analysis Methods:
  • Force method
  • Displacement method
• Emphasis on:
  • Static, linear, deterministic analysis as a starting point.
  • Understanding non-linear, dynamic, and probabilistic analyses later in the course.

Response of Structures

• Correct responses must satisfy:
  • Equilibrium: Statically admissible.
  • Compatibility: Kinematically admissible.
  • Constitutive Relationships: Based on material properties (stress-strain relationships).

Equilibrium and Analysis Techniques

• Direct Equilibrium: Using Newton's laws.
  • Six equations of equilibrium for spatial structures, reduced for planar structures (3 equations).
• Deflection Calculation Methods:
  • Direct integration method
  • Moment area method
  • Conjugate beam method
  • Principle of virtual work (to be covered later).

Example: Continuous Beam

• Application of equilibrium in a 2-span continuous beam.
• Notable observation: Potential for multiple solutions due to insufficient equations.
• Use of strain energy for compatibility checks.

Importance of Free Body Diagrams

• Distinction between free body diagrams and loading diagrams.
• Example: Drawing loading diagrams with associated deflection shapes.

Analysis of Beams

• Kinematic Variables: Deflection, slope, and curvature.
• Static Variables: Load intensity, shear force, bending moment.
• Basic differential equations relating these quantities:
  • Shear force is the derivative of bending moment.
  • Bending moment is related to curvature and deflection.

Common Misconceptions in Analysis

• Example of isolated footing and incorrect assumptions in structural analysis.
• Importance of recognizing the inconsistency in results when analyzing under incorrect assumptions.

Conjugate Beam Method

• Concept: Using the bending moment diagram to find deflections and slopes.
• Boundary conditions for the conjugate beam change based on original beam conditions.

Summary of Key Points

• Understanding Structure Responses: All structural responses must be compatible with equilibrium and material properties.
• Key Techniques: Familiarity with direct equilibrium, conjugate beam method, and understanding the kinematic and static relationships essential for effective analysis.
• Practical Applications: Recognizing how assumptions affect analysis conclusions and ensuring consistency in applied loading and resulting responses.