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Engineering 101 Linking Experiments to Models through the Bridge Design Exercise

Engineering 101 Linking Experiments to Models through the Bridge Design Exercise. Prof. Subramaniam (“ Subby ”) D. Rajan, Prof. Narayanan Neithalath and Amie Baisley Graduate Students : Kirk Vance, Matt Aguayo, Tejas Ashani , Joseph Harrington and Canio Hoffarth. What are Experiments?.

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Engineering 101 Linking Experiments to Models through the Bridge Design Exercise

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  1. Engineering 101Linking Experiments to Models through the Bridge Design Exercise Prof. Subramaniam (“Subby”) D. Rajan, Prof. Narayanan Neithalath and Amie Baisley Graduate Students: Kirk Vance, Matt Aguayo, TejasAshani, Joseph Harrington and CanioHoffarth

  2. What are Experiments? • Tests to determine the relationship between (input) variables and (output) responses • Example 1: What is the effect of dowel diameter on the weight of the bridge? • Model: The entire bridge system • Input Variable: Dowel diameter • Output Response: Weight of the bridge • Example 2: What is the effect of dowel diameter on the maximum deflection of the bridge deck? • Model: The entire bridge system • Input Variable: Dowel diameter • Output Response: Deflection of the bridge deck at various locations

  3. What are Models? • Relationship between (input) variables and (output) responses • Simple equation • Model described by one or more complex equation(s) – differential equation(s), integral equation(s), … • Example 1: What is the effect of dowel diameter on the weight of the bridge? • Example 2: What is the effect of dowel diameter on the maximum deflection of the bridge deck? • Needs a model whose solution can be described by several linear, algebraic equations

  4. What is a System? • Dictionary definitions • a set of connected things or parts forming a complex whole, in particular • a set of principles or procedures according to which something is done; an organized scheme or method • Traits of a system • has structure, its parts or components are directly or indirectly interact with each other • has behavior (where input and output are linked)

  5. Questions • Q1: Draw a diagram that shows the components of the bridge system, establishes the boundary and identifies the surroundings. • Q2: Describe the bridge system with particular attention to (a) its functionalities, (b) how the different components interact with each other and (c) how the bridge system behaves.

  6. Engineering Process or Product Design

  7. Verification and Validation • Models need to be validated and verified before they can be used with any confidence • Verification: Are you building it right? • Is the theory/principle embodied in the model implemented correctly? g = 9.81 m/s2

  8. Verification and Validation • Validation: Are you building the right thing? • Do the results from the model correlate well with experimental results?

  9. Questions • Q3: Describe what a bridge model could be, by identifying the input variables and output responses. • Q4: Identify the characteristics of each input variable. Describe how you would obtain the values of these variables. • Q5: Identify the characteristics of each output response. What is the purpose of each output response? • Q6: Give examples of engineering processes and products? • Q7: Describe the linkages between experiments and modeling.

  10. Case Study

  11. Case Study • Develop a model to predict the tip deflection (displacement) of a cantilever beam due to a tip load. Use experiments to validate the model.

  12. Case Study: Basic Steps • Use a sound scientific or engineering principle to develop the model. What parameters will be a part of this model – input and output variables? • Design experiment(s) to verify the model. • Design experiment(s) to validate the model.

  13. Case Study: Principle/Theory • Euler-Bernoulli Beam Theory (w/o derivation) v(x): vertical displacement M(x): Bending moment E(x): Young’s modulus I(x): Moment of inertia L: length of the beam Differential Equation Boundary Conditions

  14. Case Study: Cantilever Beam Integrating twice and using the BCs Boundary Conditions

  15. Case Study: The Model

  16. Case Study: Modulus of Elasticity • What is modulus of elasticity or Young’s modulus (E)? • In a one-dimensional state of stress it is constant of proportionality between the normal stress and the normal strain and has the units of stress. Stress-strain curve (ductile material)

  17. Case Study: Moment of Inertia • What is moment of inertia, I? • The second moment of area (or, moment of inertia) is a measure of a beam’s cross-sectional shape’s resistance to bending.

  18. ExperimentMeasure the width, w, and thickness, t, of a steel plate

  19. Raw Measurement Data Measurements taken at 11 different locations

  20. Raw Measurement Data Histogram Plot

  21. Statistical Analysis of Data

  22. Questions • Q8: What is sample size? • Q9: What is mean? What is another name for mean? • Q10: What is median? • Q11: What is standard deviation? • Q12: Write a few sentences on the quality of the thickness and width data for the steel plate.

  23. Normal Distribution Probability Density Function* Function whose graph is a continuous curve over a range of values that x can take. It has the units of probability rate (not probability). x is called random variable. Area under curve between x1 and x2 gives the probability that x lies in the interval x1 and x2. 6s 68-95-99.7 rule: 1, 2, 3 standard deviations from mean *Excel terminology: Probability Mass Function

  24. Cumulative Distribution Function What is the probability that a random width value is between 1.113 in and 1.114 in?

  25. Questions • Q13: Normal distribution is often called bell curve. Are there other types of distribution? • Q14: Identify and rank the effect of the random variables in the equation for tip deflection.

  26. Experiment 2Measure the tip displacement of an aluminum cantilever beam

  27. Raw Experimental Data

  28. Case Study: Model Verification

  29. Case Study: Model Validation Published Elastic Modulus of Aluminum (6016-T6) = 1.01(107) psi

  30. Forensic Engineering

  31. One-Parameter Regression Analysis • Objective: Use the model and experimental data to determine the Young’s modulus of aluminum.

  32. References • Do an internet search using these keywords – system, model, experiment, verification, validation, statistical quantities. • Engineering Statistics: http://www.itl.nist.gov/div898/handbook/ • http://www.mathsisfun.com/links/curriculum-high-school-statistics.html • http://www.stevespanglerscience.com/lab/experiments • http://en.wikipedia.org/wiki/Verification_and_validation

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