1 / 25

The Problem

The Problem. Sines and Cosines. sin a 1 = (-12 - 0) / (20) = -0.6 cos a 1 = (16 - 0) / (20) = 0.8 sin a 2 = (12 - 0) / (15) = 0.8 cos a 2 = (9 - 0) / (15) = 0.6 . Element Matrices [S]. 3 4 1 2. 1 2 5 6. System Stiffness Matrix.

raymond-osborne
Download Presentation

The Problem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Problem

  2. Sines and Cosines sina1 = (-12 - 0) / (20) = -0.6 cosa1 = (16 - 0) / (20) = 0.8 sina2 = (12 - 0) / (15) = 0.8 cosa2 = (9 - 0) / (15) = 0.6

  3. Element Matrices [S] 3 4 1 2 1 2 5 6

  4. System Stiffness Matrix

  5. Element Matrices [S] 3 4 1 2 1 2 5 6

  6. Summing Element Stiffnesses

  7. Summing Element Stiffnesses

  8. Two Matrix Contributions 1 2 3 4 5 6

  9. Final [K] 1 2 3 4 5 6

  10. Final Equation P=KX

  11. System Stiffness Matrices

  12. Solving the System of Equations

  13. Modify for Known Loads

  14. Modify for Boundary Conditions

  15. Modify to Ease Solution

  16. Return Symmetry

  17. Modified Equations

  18. Recap

  19. Initial Matrix

  20. Loads

  21. Boundary Conditions

  22. Symmetry

  23. Solution 10 = AE/L X1 100 = AE/L X2 0 = AE/L X3 0 = AE/L X4 0 = AE/L X5 0 = AE/L X6

  24. Force Calculation (f=sbX) {(X3i-X1i) cosai + (X4v-X2v) sinai} is simply the change in length t1 = AE/L {(10L/AE - 0)(0.8) + (100L/AE - 0)(-0.6)} + (0) t2 = AE/L {(0 - 10L/AE - 0)(0.6) + (0 - 100L/AE - 0)(0.8)} + (0) t1 = f2 = -f1 = -52 kips t2 = f4 = -f3 = -86 kips

More Related