introduction to structural analysis

Introduction to Structural Analysis

Structural Analysis is the prediction of the performance of a given structure under prescribed loads and/or other external effects, such as support movements and temperature changes.

In the Philippines, the primary reference for structural design and analysis is the National Structural Code of the Philippines (NSCP) 2015, Volume 1 (Buildings, Towers, and Other Vertical Structures), published by the Association of Structural Engineers of the Philippines (ASEP).

Classification of Structures

Structures are classified based on their geometry and load transfer mechanisms:

• Beams: Horizontal members subjected to bending.
• Columns: Vertical members subjected to axial compression.
• Trusses: Assemblies of members connected at joints, subjected primarily to axial forces.
• Frames: Combinations of beams and columns rigidly connected.

Loads (Dead, Live, Wind, Earthquake)

Loads are forces or other actions that result from the weight of all building materials, occupants and their possessions, environmental effects, differential movement, and restrained dimensional changes.

According to NSCP 2015 (Chapter 2):

• Dead Loads (DL): Vertical loads due to the weight of permanent structural and non-structural components.
• Live Loads (LL): Loads produced by the use and occupancy of the building.
• Wind Loads (WL): Loads caused by wind pressure, critical for high-rise structures and in typhoon-prone areas like the Philippines.
• Earthquake Loads (E): Lateral forces resulting from ground shaking during seismic events. The Philippines is in a high seismic zone.

Basic Load Combination (LRFD): $1.2D + 1.6L + 0.5(L_r \text{ or } R)$

Idealization of Structures

Real structures are complex. For analysis, we idealize them into simpler models:

• Support Conditions: Pin, Roller, Fixed.
• Connections: Rigid (Moment-resisting) or Pinned (Truss).
• Line Diagrams: Representing members by their centerlines.

Stability and Determinacy of Beams, Trusses, and Frames

A structure must be stable to maintain its shape and position under loads. It is statically determinate if the equations of equilibrium are sufficient to determine all unknown reactions and internal forces.

• Equations of Equilibrium: $\sum F_x = 0$, $\sum F_y = 0$, $\sum M = 0$ (for 2D).
• Degree of Indeterminacy (DOI):
  • For Beams: $DOI = r - 3 - c$ (where $c$ is equations of condition).
  • For Frames: $DOI = 3m + r - 3j - c$.
  • For Trusses: $DOI = m + r - 2j$.

If $DOI = 0$ and the structure is stable, it is statically determinate. If $DOI > 0$, it is statically indeterminate.