Structural Analysis Summary

Introduction to Structural Analysis

Structural Theory

  • Structural analysis predicts a structure's performance under loads/external effects.
  • Performance characteristics include:
    • Stresses/stress resultants (axial forces, shear forces, bending moments).
    • Deflections.
    • Support reactions.
  • Analysis determines these quantities caused by loading.

Historical Background

  • Early structures relied on trial and error.
  • Galileo Galilei (1564–1642) is considered the originator of structural theory.
    • Analyzed simple structures like cantilever beams.
    • His work laid the foundation for future developments.

Key Contributors:

  • Robert Hooke (1635–1703): Hooke’s law (linear force-deformation).
  • Sir Isaac Newton (1642–1727): Laws of motion, calculus.
  • John Bernoulli (1667–1748): Principle of virtual work.
  • Leonhard Euler (1707–1783): Theory of column buckling.
  • C. A. de Coulomb (1736–1806): Bending analysis of elastic beams.
  • L. M. Navier (1785–1836): First textbook on modern strength of materials (1826).
  • B. P. Clapeyron (1799–1864): Three-moment equation for continuous beams.
  • J. C. Maxwell (1831–1879): Method of consistent deformations, reciprocal deflections.
  • Otto Mohr (1835–1918): Conjugate-beam method for deflections, Mohr’s circles.
  • Alberto Castigliano (1847–1884): Theorem of least work.
  • C. E. Greene (1842–1903): Moment-area method.
  • H. Müller-Breslau (1851–1925): Influence lines principle.
  • G. A. Maney (1888–1947): Slope-deflection method (precursor to matrix stiffness method).
  • Hardy Cross (1885–1959): Moment-distribution method (1924).

Impact of Computers:

  • 1950s: Computers revolutionized structural analysis.
  • Enabled solving large equation systems quickly.

Role in Structural Engineering

  • Structural analysis is integral to structural engineering projects, predicting performance.

Structural Engineering Project Phases:

  1. Planning Phase
  2. Preliminary Structural Design
  3. Estimation of Loads
  4. Structural Analysis
  5. Safety and Serviceability checks
  6. Revised Structural Design (if needed)

Classification of Structures

  • Tension Structures: Subjected to pure tension (e.g., cables in suspension bridges).
    • Shape changes with load.
  • Compression Structures: Develop compressive stresses (e.g., columns, arches).
    • Susceptible to buckling.
  • Trusses: Straight members with hinged connections, uniform tension/compression.
  • Shear Structures: Reinforced concrete shear walls, resist lateral movement.
  • Bending Structures: Develop bending stresses (e.g., beams, rigid frames).
    • Beams loaded perpendicular to the longitudinal axis.
    • Rigid frames have members connected by rigid or hinged connections; subject to bending moment, shear & axial forces.

Analytical Models

  • Simplified representation of real structure for analysis.
  • Simplifies analysis while representing key behavioral characteristics.
Considerations for Analytical Models:
  • Plane vs. Space Structure: Plane structures are simpler to analyze.
  • Line Diagram: Represents structure with lines coinciding with centroidal axes.
  • Connections: Rigid (transmit forces and moments) vs. Hinged (transmit forces only).
  • Supports: Fixed, hinged, or roller supports.