Скачать или смотреть How to Find Truss Deflection Using Castigliano’s Second Theorem | Structural Analysis

Hello everyone and welcome back to Math and Engineering Made Easy!

In this lesson, we break down Carlo Alberto Castigliano’s Second Theorem and apply it step-by-step to calculate the vertical deflection of a truss joint.

We start with the fundamentals of strain energy and show how taking the partial derivative of strain energy with respect to a load gives us the displacement in the direction of that load.

🔎 In this video, you will learn:

What Castigliano's second theorem states

Why trusses are the easiest structures for energy methods

How to use a fictitious load to find vertical deflection

How to compute internal member forces

How to apply strain energy
U=F2L2EA
U=
2EA
F
2
L
​


How to correctly take partial derivatives

Why we set the fictitious load equal to zero at the end

Unit consistency (GPa, kN, mm explained clearly!)

We also briefly discuss how the approach would change for beams and frames — which are more involved due to bending moments.

If you’re studying:

Engineering Statics

Mechanics of Materials

Structural Analysis

Civil or Mechanical Engineering

This video is for you.
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