Beam & Frame Analysis using the Direct Stiffness Method in Python

Build a sophisticated structural analysis software tool that models beams and frames using Python.

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Welcome and Setup

1. Introduction and course overview

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2. Our approach to Python

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3. Getting started with Jupyter Notebooks

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Support and Lecture Q&A (Please read!)

The Beam Element Stiffness Matrix

4. Section overview

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5. Finite element equations - quick review

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6. Stiffness matrix for a beam element - part 1

7. Stiffness matrix for a beam element - part 2

8. Transforming from local to global coordinates

Beam/Frame Analysis Step-by-Step

9. Section overview

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9.1 Section 3 - Direct Stiffness Method Step by Step - Slides

10. Analysis procedure overview

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11. Calculating element stiffness matrices

12. Building the primary stiffness matrix

13. Reducing to the structure stiffness matrix

14. Solving for unknown displacements

15. Solving for reactions

16. Finding axial forces, shears and moments

Implementing Beam/Frame Analysis in Python

17. Section overview

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17.1 Jupyter Notebook (zip)

18. Element stiffness matrices

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19. Whole structure stiffness matrix

20. Solving for displacements and reactions

21. Evaluating bending moments and shear forces

22. Visualising displacements

Mid-course check-in

Generalising our Code

23. Section overview

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23.1 Jupyter Notebook (zip)

24. Element stiffness matrices

25. The structure stiffness matrix

26. Solving for displacements and reactions

27. Solving for axial forces, moments and shears

28. Graphical and text output

Building Better Visualisations

29. Section overview

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29.1 Jupyter Notebook (zip)

30. Adding nodal annotations to deflection

31. Plotting an axial force diagram

32. Planning the bending moment diagram

33. Building the bending moment diagram

34. Building the shear force diagram

34.1 Jupyter Notebook (zip)

35. Adding UI widgets for plot adjustments

35.1 Jupyter Notebook (zip)

36. Label and widget refactor

Pins, Inter-Nodal Loading and Flexible Supports

37. Section overview

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37.1 Section 7 - Pinned Beam Elements - Slides

38. Beam elements pinned at one end

38.1 Jupyter Notebook (zip)

39. Capturing pin locations

40. Pinned stiffness matrices

41. Pinned structure stiffness matrix

42. Solving for pinned member actions

43. Dealing with inter-nodal loading

43.1 Jupyter Notebook (zip)

44. Recording inter-nodal loading

45. Removing Equivalent Nodal Actions

46. Inter-nodal loading with pins

46.1 Jupyter Notebook (zip)

47. Flexible supports

Test Questions

48. Section overview

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49. Installing Nbextensions (optional)

50. Test Question #1

50.1 Jupyter Notebooks (zip)

51. Test Question #2

51.1 Jupyter Notebooks (zip)

52. Test Question #3

52.1 Jupyter Notebooks (zip)

53. Test Question #4

53.1 Jupyter Notebooks (zip)

54. Test Question #5

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54.1 Jupyter Notebooks (zip)

55. Course wrap up and Certificate of Completion

Course Updates

This section is reserved for 'post-release' updates to the course...for those good ideas and suggestions that come in from students taking the course.

So far, we have expanded to consider,

the combination of beam (bending, shear and axial force) and bar (axial force) elements.
allowing unique cross-sectional areas which is particularly helpful when modelling a combination of beam and bar elements.

56. Combining beam and axially loaded bar elements

57. Varying element cross-sectional areas

57.1 Jupyter Notebooks (zip)