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Point and Distributed Loading

Point and Distributed Loading. Tip deflection errors and sensitivity results. Point Loading Cases. b. a. F 2. F 1. Sensor 2. Sensor 1. Tip Deflection. x 1. x 2. Case 1: a = L/2, b = L. F1 > 0, F2 > F1. Case 2: a = L/2, b = L. F1 > 0, F1 > F2.

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Point and Distributed Loading

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  1. Point and Distributed Loading Tip deflection errors and sensitivity results.

  2. Point Loading Cases b a F2 F1 Sensor 2 Sensor 1 Tip Deflection x1 x2 Case 1: a = L/2, b = L. F1 > 0, F2 > F1. Case 2: a = L/2, b = L. F1 > 0, F1 > F2. Case 3: a = L/2, b = L. F1 < 0, F2 > abs(F1).

  3. Deflection Errors at Tip

  4. Sensitivity of Deflection Errors with Respect to x1

  5. Sensitivity of Deflection Errors with Respect to x2

  6. Deflection and Curvatures when x1 = 25, x2 = 82.

  7. Conclusions: • Opposing loads lead to the same results as loads in the same direction (if magnitude is the same.) • If the load at the inflection point is larger than the load at the end, the range of deflection error and sensitivities are greater. • For all cases when a = L/2, the lowest deflection error at the tip is when x1 = 45 and x2 = 125.

  8. Distributed Loading Cases b a q Sensor 1 Sensor 2 Tip Deflection x1 x2 Case 1: a = L/2, b = L - a

  9. Case 1: q = 10e-3*9.81/75 Deflection Error at Tip Sensitivity w/Respect to x1 Sensitivity w/Respect to x2 When x1 = 25, x2 = 82:

  10. Conclusions: • For Case 1, deflection error at tip when x1 = 25, x2= 82 is 0.0574. • The best region for sensor placement seems to be when x1 = 28, x2 is in the range [122:138]. However, this is sensitive to x1. • If one sensor is at L/2 (start of loading), the position of the second sensor is not important in improving the accuracy of the curvature readings (hence the displacement error).

  11. Two Distributed Loads b a q2 q1 Sensor 2 Sensor 1 Tip Deflection x1 x2

  12. One Distributed Load and End Point Load b a q F Sensor 1 Sensor 2 Tip Deflection x1 x2

  13. Three Loading Types • Given two point loads, distributed loads were found such that the curvature at x = 0 and x = L/2 was the same. • The distributed loading caused regions of similar deflection errors.

  14. Deflection Error at TipF1 = 2 grams, F2 = 5 grams

  15. Sensitivity in x1 positionF1 = 2 grams, F2 = 5 grams

  16. Sensitivity in x2 positionF1 = 2 grams, F2 = 5 grams

  17. Deflection and Curvature when x1 = 20, x2 = 80.F1 = 2 grams, F2 = 5 grams

  18. More Extreme Case • F1 and F2 are in opposite directions, and

  19. Deflection Error at TipF1 = -5 grams, F2 = 2 grams

  20. Sensitivity in x1 positionF1 = -5 grams, F2 = 2 grams

  21. Sensitivity in x2 positionF1 = -5 grams, F2 = 2 grams

  22. Deflection and Curvature when x1 = 20, x2 = 80.F1 = -5 grams, F2 = 2 grams

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