Lecture 39: Section Overview - Multi-Shell Structures | Analytical Modelling of Plate and Shell Structures: Part 2 - Shells | EngineeringSkills.com

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Section 1

Course Introduction

1. Welcome and course overview

04:18 (Preview)

2. Shell structures in the built environment (Recap) 📂

3. Undeformed shell curvature (Recap) 📂

Section 2

The Membrane Theory of Shells

4. Section Overview - Membrane Theory of Shells

02:40 (Preview)

5. Membrane theory and the membrane state of stress 📂

6. Linear displacements and meridional strain 📂

7. Linear displacements and hoop strain 📂

8. Angular displacement 📂

9. Equilibrium of the infinitesimal element 📂

10. Equilibrium in the normal direction 📂

11. Equilibrium in the vertical direction 📂

12. A recap of our system of equations 📂

13. Solving the system to find meridional, normal and angular displacements 📂

Section 3

Applying the Theory to Spherical Shells

14. Section Overview - Applying the Theory to Spherical Shells

02:28 (Preview)

15. Spherical shell under self-weight - force equations 📂

16. Spherical shell under self-weight - evaluating forces 📂

17. Spherical shell under self-weight - displacement equations 📂

18. Spherical shell under self-weight - evaluating displacements 📂

19. Spherical shell under snow loading 📂

20. Spherical shell case study - membrane stresses 📂

21. Spherical shell case study - membrane displacements 📂

22. Truncated spherical shell (Skylight) 📂

23. Truncated spherical shell - membrane forces 📂

Section 4

Liquid Retaining Shells

24. Section Overview - Liquid Retaining Shells

01:42 (Preview)

25. Evaluating normal pressure 📂

26. Spherical tank - filled to the top 📂

27. Spherical tank - membrane forces 📂

28. Partially filled spherical tank - membrane forces 📂

Section 5

Zero & Negative Gaussian Curvature Shells

29. Section Overview - Zero & Negative Gaussian Curvature Shells

02:01 (Preview)

30. Cylindrical shell membrane forces 📂

31. Cylindrical shell membrane displacements 📂

32. Conical shell 📂

33. Truncated conical shell 📂

34. Geometry of the hyperboloid of revolution - the cooling tower 📂

35. Visualising tower geometry 📂

36. Cooling tower principal curvatures 📂

37. Bridging between linear and angular coordinates 📂

38. Cooling tower membrane force distribution 📂

Section 6

Compound / Multi-Shell Structures

39. Section Overview - Multi-Shell Structures

02:18 (Preview)

40. Structure review and load path analysis 📂

41. Truncated spherical roof (Level A-B) 📂

42. Cylindrical walls (Level B-C) 📂

43. Truncated inverted cone (Level C-D) 📂

44. Spherical dome base (Level D-E) 📂

45. Complete membrane force distribution 📂

46. Course wrap-up and certificate of completion

Full Preview

39. Section Overview - Multi-Shell Structures

Compound / Multi-Shell Structures

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Analytical Modelling of Plate and Shell Structures: Part 2 - Shells

Unlocking the Fundamentals of Shell Behaviour with Analytical Modelling and Membrane Theory

After completing this course...

You will understand how to describe and characterise shell structures based on their principal curvatures.
You will understand the membrane theory of shells, one of the most fundamental models of shell behaviour.
You will have completed a wide range of analysis case studies that help to contextualise the membrane theory of shells, leaving you in a position to deploy it independently in your own work.
You will further enhance your ability to use Python and the SymPy library to work programmatically with symbolic math and bring your analyses to life.

Next Lesson

40. Structure review and load path analysis