Practice Total Energy Stored In The Beam (2.5) - Castigliano’s First Theorem

Practice: Total energy stored in the beam

Lesson 2.5Castigliano’s First Theorem

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9 questions

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6 sample questions

Question 1.
Define Castigliano’s theorem.
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Think about displacement in relation to energy.
Question 2.
What is axial energy in beams?
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Consider how force affects length.
3Question 3.
What principle does Castigliano’s theorem describe?
- Displacement in structures
- Stress concentration
- Fatigue analysis
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Consider how external loads relate to internal deformations.
4Question 4.
True or False: Shear energy only pertains to loading perpendicular to the longitudinal axis.
- True
- False
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Think about stress direction relative to beam length.
Question 5.
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.
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Apply the bending energy formula carefully.
Question 6.
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.
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Remember the formulas for each energy type mentioned!

5 more questions in this section. Enroll free to practise them all.