1. Dealing with Uncertainty in Statics 1

2. Outline Uncertainty in statics Why consider uncertainty Basics of uncertainty Uncertainty analysis in statics Examples Conclusions 2

3. Uncertainty in Statics: An Example A 1.5 m 3.5 m 4 m 3

4. Where Does Uncertainty Come From? Manufacturing Imprecision - Dimensions of a structure - Material properties Environment - Loading - Temperature - Different user conditions - Wind, snow, etc. 4

5. Why Consider Uncertainty? We know the true solution We know the effect of uncertainty We can make more reliability decisions We can predict the chance of failure If we consider uncertainties in the above example, we can design better cost-effective beams with sufficient reliability against failures with respect to strength, stiffness, etc. 5

6. How Do We Model Uncertainty? A 1.5 m 3.5 m 4 m 6

7. How Do We Measure the Dispersion (Uncertainty)? 7

8. More About Standard Deviation (std) It indicates how data spread around the average It is always non-negative High std means –High dispersion –High uncertainty –High risk 8

9. Probability Distribution With more samples, we can draw a histogram. 9

10. Normal Distribution 10

11. Use Excel –NORMDIST(x,mean,std,cumulative) –Cumulative=true 11

12. Example 1 The moment (in N∙m) acting on a beam was recorded 20 times. Assume the moment is normally distributed. Questions - Mean =? Std = ? - What is the probability that the beam has a moment greater than 1192.3 N∙m? 11198.5 21192.5 31188.1 41190.2 51195.1 61198.7 71196.3 81190.7 91193.9 101192.2 111191.5 121199.2 131197.7 141194.1 151196.9 161193.0 171197.5 181194.9 191199.1 201192.6 12

13. Solution: Use Excel 13

14. More Equations 14

15. Example 2 GMGM GTGT 7 in 22 in A B 15

16. Example cont. 7 in22 in A B 16

17. If Consider Uncertainty 17

18. 18

19. Conclusions 19