Beam & Frame Analysis using the Direct Stiffness Method in Python
by
Dr Seán Carroll
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10. Analysis procedure overview
Beam & Frame Analysis using the Direct Stiffness Method in Python
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Beam/Frame Analysis Step-by-Step
Beam & Frame Analysis using the Direct Stiffness Method in Python
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Table of contents
Beam & Frame Analysis using the Direct Stiffness Method in Python
by
Dr Seán Carroll
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Welcome and Setup
Welcome and Setup
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1. Introduction and course overview
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1. Introduction and course overview
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2. Our approach to Python
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2. Our approach to Python
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3. Getting started with Jupyter Notebooks
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3. Getting started with Jupyter Notebooks
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The Beam Element Stiffness Matrix
The Beam Element Stiffness Matrix
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4. Section overview
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4. Section overview
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5. Finite element equations - quick review
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5. Finite element equations - quick review
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6. Stiffness matrix for a beam element - part 1
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6. Stiffness matrix for a beam element - part 1
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7. Stiffness matrix for a beam element - part 2
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7. Stiffness matrix for a beam element - part 2
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8. Transforming from local to global coordinates
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8. Transforming from local to global coordinates
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Beam/Frame Analysis Step-by-Step
Beam/Frame Analysis Step-by-Step
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9. Section overview
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9. Section overview
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Section 3 - Direct Stiffness Method Step by Step - Slides
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Section 3 - Direct Stiffness Method Step by Step - Slides
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10. Analysis procedure overview
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10. Analysis procedure overview
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11. Calculating element stiffness matrices
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11. Calculating element stiffness matrices
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12. Building the primary stiffness matrix
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12. Building the primary stiffness matrix
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13. Reducing to the structure stiffness matrix
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13. Reducing to the structure stiffness matrix
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14. Solving for unknown displacements
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14. Solving for unknown displacements
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15. Solving for reactions
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15. Solving for reactions
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16. Finding axial forces, shears and moments
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16. Finding axial forces, shears and moments
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Implementing Beam/Frame Analysis in Python
Implementing Beam/Frame Analysis in Python
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17. Section overview
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17. Section overview
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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18. Element stiffness matrices
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18. Element stiffness matrices
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19. Whole structure stiffness matrix
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19. Whole structure stiffness matrix
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20. Solving for displacements and reactions
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20. Solving for displacements and reactions
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21. Evaluating bending moments and shear forces
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21. Evaluating bending moments and shear forces
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22. Visualising displacements
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22. Visualising displacements
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Generalising our Code
Generalising our Code
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23. Section overview
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23. Section overview
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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24. Element stiffness matrices
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24. Element stiffness matrices
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25. The structure stiffness matrix
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25. The structure stiffness matrix
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26. Solving for displacements and reactions
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26. Solving for displacements and reactions
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27. Solving for axial forces, moments and shears
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27. Solving for axial forces, moments and shears
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28. Graphical and text output
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28. Graphical and text output
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Building Better Visualisations
Building Better Visualisations
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29. Section overview
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29. Section overview
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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30. Adding nodal annotations to deflection
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30. Adding nodal annotations to deflection
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31. Plotting an axial force diagram
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31. Plotting an axial force diagram
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32. Planning the bending moment diagram
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32. Planning the bending moment diagram
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33. Building the bending moment diagram
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33. Building the bending moment diagram
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34. Building the shear force diagram
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34. Building the shear force diagram
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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35. Adding UI widgets for plot adjustments
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35. Adding UI widgets for plot adjustments
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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36. Label and widget refactor
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36. Label and widget refactor
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Pins, Inter-Nodal Loading and Flexible Supports
Pins, Inter-Nodal Loading and Flexible Supports
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37. Section overview
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37. Section overview
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Section 7 - Pinned Beam Elements - Slides
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Section 7 - Pinned Beam Elements - Slides
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38. Beam elements pinned at one end
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38. Beam elements pinned at one end
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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39. Capturing pin locations
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39. Capturing pin locations
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40. Pinned stiffness matrices
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40. Pinned stiffness matrices
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41. Pinned structure stiffness matrix
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41. Pinned structure stiffness matrix
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42. Solving for pinned member actions
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42. Solving for pinned member actions
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43. Dealing with inter-nodal loading
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43. Dealing with inter-nodal loading
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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44. Recording inter-nodal loading
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44. Recording inter-nodal loading
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45. Removing Equivalent Nodal Actions
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45. Removing Equivalent Nodal Actions
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46. Inter-nodal loading with pins
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46. Inter-nodal loading with pins
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Jupyter Notebook (zip)
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Jupyter Notebook (zip)
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47. Flexible supports
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47. Flexible supports
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Test Questions
Test Questions
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48. Section overview
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48. Section overview
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49. Installing Nbextensions (optional)
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49. Installing Nbextensions (optional)
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Jupyter Notebooks (zip)
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Jupyter Notebooks (zip)
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50. Test Question #1
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50. Test Question #1
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51. Test Question #2
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51. Test Question #2
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52. Test Question #3
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52. Test Question #3
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53. Test Question #4
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53. Test Question #4
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54. Test Question #5
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54. Test Question #5
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55. Course wrap up and Certificate of Completion
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55. Course wrap up and Certificate of Completion
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Course Updates
Course Updates
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Jupyter Notebooks (zip)
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Jupyter Notebooks (zip)
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56. Combining beam and axially loaded bar elements
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56. Combining beam and axially loaded bar elements
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57. Varying element cross-sectional areas
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57. Varying element cross-sectional areas
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