2.3 Structural Analysis

This lesson on structural analysis focuses on understanding how structures respond to loads, forces, and environmental conditions. It involves predicting internal forces and deformations to ensure safety, stability, and serviceability. The analysis of statically determinate structures uses methods like equilibrium equations and free-body diagrams. Mastering structural analysis is crucial for civil engineers to design infrastructure safely.

Structural Analysis

Structural analysis supports two main design objectives:

1. Safety: Ensuring the structureThe organisation and order of information in a text. can withstand applied loads without failure.
2. Serviceability: Ensuring acceptable performance under normal usage, such as limiting deflections or vibrations.

The maximum bending moment for a uniformly loaded simply supported beam is:

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This equation changes based on the support conditions of the beam. Some examples of different support conditions and their respective analysis equations are shown below:

Free Body Diagram	End Slope	Max Deflection	Max Bending Moment
	\(\frac{ML}{EI} \)	\(\frac{ML^{2}}{EI} \)	\(M\)
	\(\frac{\omega L^{2}}{2EI}\)	\(\frac{\omega L^{3}}{3EI}\)	\(WL\)
	\(\frac{\omega L^{3}}{6EI}\)	\(\frac{\omega L^{4}}{8EI}\)	\(\frac{\omega L^{2}}{2}\)
	\(\frac{ML}{2EI}\)	\(\frac{ML^{2}}{8EI}\)	\(M\)
	\(\frac{WL^{2}}{16EI}\)	\(\frac{WL^{3}}{48EI}\)	\(\frac{WL}{4}\)
	\(\frac{\omega L^{3}}{24EI}\)	\(\frac{5\omega L^{4}}{384EI}\)	\(\frac{\omega L^{2}}{8}\)
	\(\theta _{B}=\frac{Wac^{2}}{2LEI}  \)	\(\frac{Wac^{3}}{3LEI}\) at position c	\(\frac{Wab}{L}\) under load

Using this bending moment, we can check the beam's strength against Eurocode 3 (for steel) or Eurocode 2 (for concrete). This involves ensuring the design bending moment does not exceed the beam's resistance: