Practice Total energy stored in the beam - 2.5 | 30. Castigliano’s First Theorem | Solid Mechanics
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Total energy stored in the beam

2.5 - Total energy stored in the beam

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define Castigliano’s theorem.

💡 Hint: Think about displacement in relation to energy.

Question 2 Easy

What is axial energy in beams?

💡 Hint: Consider how force affects length.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What principle does Castigliano’s theorem describe?

Displacement in structures
Stress concentration
Fatigue analysis

💡 Hint: Consider how external loads relate to internal deformations.

Question 2

True or False: Shear energy only pertains to loading perpendicular to the longitudinal axis.

True
False

💡 Hint: Think about stress direction relative to beam length.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

A simply supported beam with a span of 5m is subjected to a central load of 30 kN. Calculate the total energy stored in the beam if the bending moment at the center is known to be 75 Nm, with E = 210 GPa and I = 0.0001 m^4.

💡 Hint: Apply the bending energy formula carefully.

Challenge 2 Hard

If a beam is fixed at one end with a torsional force applied, find the energy stored due to torsion and shear combined, given T = 100 Nm, L = 4 m, E = 200 GPa, and G = 80 GPa.

💡 Hint: Remember the formulas for each energy type mentioned!

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