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Spreadsheet Tools for Engineers Using Excel

Spreadsheet Tools for Engineers Using Excel. CIVE 1331 Fall 2008 Hanadi Rifai. Chapter 1. Engineering Analysis and Spreadsheets. Engineering Analysis and Spreadsheets.

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Spreadsheet Tools for Engineers Using Excel

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  1. Spreadsheet Tools for EngineersUsing Excel CIVE 1331 Fall 2008 Hanadi Rifai

  2. Chapter 1. Engineering Analysis and Spreadsheets

  3. Engineering Analysis and Spreadsheets • Engineering analysis is a systematic process for analyzing and understanding problems that arise in the various field of engineering • To carry out this process, we use problem solving techniques • Spreadsheet programs can be used to solve the problem once you have defined it and set it up properly

  4. Spreadsheets allow you to: • Import, export, store, process, and sort data • Display data graphically • Analyze data statistically • Fit algebraic equations through datasets • Solve single and simultaneous algebraic equations • Solve optimization problems

  5. Examples Book Example 1.1

  6. General Problem Solving Techniques • Think about the problem before you solve it • Draw a sketch to visualize it • Understand the overall purpose of the problem and its key points • Ask yourself: what information is known? And what information must be determined? • Ask yourself: what fundamental engineering principles apply?

  7. General Problem Solving Techniques – Cont’d • Think about how you will solve the problem • Develop your solution in an orderly and logical manner • Think about the solution: does it make sense? • Make sure solution is clear and complete Problem solving is a skill that takes time and practice

  8. Engineering Fundamentals • Equilibrium (e.g., force, flux or chemical equilibrium) • Conservation laws (mass, energy) • Rate phenomena

  9. Mathematical Solution Procedures • Data Analysis • Curve-fitting • Interpolation • Solving single algebraic equations • Solving simultaneous algebraic equations • Evaluating integrals • Engineering economic analysis • Optimization techniques

  10. Chapter 2. Creating an Excel Worksheet

  11. Spreadsheet Basics • basically a table containing numeric or alphanumeric values • Individual elements are called cells • Cells can contain a number or text • A cellreference is its column heading and row number, e.g., B3 • Tabular collection of cells is called a worksheet • Cells contain numbers resulting from formulas

  12. Definitions • Ribbon: upper portion of the window • Title Bar: top line • Office Button: replaced the File Menu • Ribbon Tabs: below title bar, replaced menu headings • Worksheet Tabs: beneath worksheet • Scroll bars: horizontal and vertical • Status bar: bottom line

  13. Skills to learn in Excel • Moving around the worksheet • Entering data • 2, -6, 3.33, 2.55e-12, -7.08e+6, 0.0, 0.004 • $25, 50%, 5/24/2006, 7:20 PM, 19:20:00 • Entering strings or label (text) • Correcting errors • Using formulas and functions • Naming a cell or worksheet • Saving, retrieving and printing worksheets

  14. Operators in Excel • Arithmetic: +, -, *, /, ^, % • String: & • Comparison: >, >=, <, <=, =, <> • Operator precedence: • 1 percentage (%) • 2 exponentiation (^) • 3 Multip/division (* and /) • 4 Add/subtract (+ and -) • 5 concatenation (&) • 6 comparisons (>, <, …) • Operations carried out from left to right

  15. Functions in Excel • Function consists of a: • Function name • Arguments Example: SUM(C1,C2,C3) The function is the sum of cells C1,C2,C3

  16. Examples Book Examples 2.4 &2.5

  17. Chapter 3. Editing an Excel Worksheet

  18. More skills to learn in Excel • Selecting a block of cells • Clearing a block of cells • Copying to adjacent cells by dragging • Copying to nonadjacent cells • Moving a block of cells • Undoing changes

  19. Copying and Moving Formulas Relative vs. Absolute addressing A1+B1 vs. $A$1+$B$1 Moving a formula will not change cell addresses but copying does C1=A1+B1 If A1 is moved to B5 then C1=B5+B1 If an object cell is moved, the formula is changed to reflect the move

  20. Yet more skills to learn in Excel • Inserting and deleting rows and columns • Inserting or deleting cells • Adjusting column width or row height • Formatting data items • Hyperlinks • Displaying cell formulas

  21. Chapter 4. Making Logical Decisions (If-Then-Else)

  22. The IF Function • Requires 3 arguments: logical expression, value for true, value for false • =IF(C1>100, “Too Big”, “Ok”) • Nested IF functions: =IF(A3<0, “Ice”, IF(A3<100, “Water”, “Steam”))

  23. Example Book Example 4.2

  24. Chapter 5. Graphing Data

  25. Examples Book Examples 5.1&5.3

  26. Chapter 6. Analyzing Data Statistically

  27. Data Analysis - Statistics • Engineers gather data to measure variability or consistency • Example: diameters of ball bearings off an assembly line • Another example: variation in sizes among customers to determine how many items of each size to manufacture Statistical data analysis tells us about data

  28. Data Characteristics • Mean or average: expected behavior • Median: a value such that half the data values lie above and half lie below 8, 10, 12, 14, 16, 18, 22, 25, 29 5, 8, 12, 16, 18, 22, 27, 29 • Mode: value that occurs the most in a data set 10, 5, 8, 9, 3, 10, 7 Mode is 10 Median is 17

  29. More Data Characteristics • Min and Max: smallest and biggest value in a dataset • Variance: an indication of the degree of spread in the data s2 = 1/(n-1)*(xi-xm)2 where xm is mean and the summation is for all I from 1 to n • The greater the spread in the data, the larger the variance • Standard deviation: square root of the variance

  30. Example Book Example 6.1

  31. Histogram or relative frequency plot • Describes how data are distributed within their range • Cumulative distribution allows us to estimate the likelihood that a data value associated with an item drawn at random is less than or greater than a specified value

  32. How to construct a histogram • Subdivide the range of the data into a series of adjacent equally spaced intervals • 1st interval begins at smallest value • Last interval extends to or beyond the largest data value (the max) • Fixed interval width • Detemine how many values fall in each interval fi = ni/n where ni is the # of points in the ith interval

  33. Examples Book Examples 6.3, 6.5, & 6.6

  34. Chapter 7. Fitting Equations to Data

  35. Fitting Equations to Data • Statistics and Histograms analyze a set of single-value data: x1, x2, etc. • Engineers need to analyze two-value or paired (x,y) data • Different Methods: • Linear Interpolation • Fitting data with a curve

  36. Linear Interpolation y2 P2 y y2-y1 y – y1 = x – x1 x2-x1 P1 y1 x1 x x2

  37. Example Book Example 7.2

  38. Curve Fitting • Fitting a line or curve through pairs of data • Concept is to represent data with an equation (y = f(x)) • Fit does not have to be exact • Goal is to minimize the error somehow between the line and the data (error between yi and y)

  39. Error in Curve Fitting • For each data point Pi = (xi, yi), the error is the difference between yi and F(xi) or the calculated value of yi • ei = yi – f(xi) • Strategy is to pick a function f(xi) that minimizes ei

  40. Straight Line Fit • Method of Least Squares • Y = ax +b • Two unknowns: a and b have to be chosen carefully to minimize the sum of the squares of the errors • Equations 7.7 and 7.8 in book • Two equations in 2 unknowns (a, b)

  41. Examples Book Examples 7.5 & 7.6

  42. Chapter 9. Transferring Data

  43. Even more skills to learn in Excel • Importing/exporting data from text files • Transferring data from and to Word or PowerPoint • Transferring graphs to Word or PowerPoint

  44. Chapters 11. Solving Single Equations

  45. Algebraic Equations • Linear – none of the unknowns are raised to a power or appear as arguments in a trig function, a log function, a square root etc. • Nonlinear – harder to solve

  46. Finding Numerical Solutions Using Excel • Goal Seek • Solver

  47. Examples Book Examples 11.5 & 11.7

  48. Chapters 12. Solving Simultaneous Equations

  49. n-linear Equations in n unknowns a11x1 + a12x2 +a13x3+….+a1nxn = b1 a21x1 + a22x2 + a23x3+….+a2nxn = b2 …. …. …. an1x1 + an2x2 + an3x3+….+annxn = bn i = row j = column aij’s and b’s are known xi’s are unknown

  50. Matrix • Is a two dimensional array of numbers • Elements characterized by a row number and a column number • A matrix with one column is called a vector • System of equations on previous slide can be written as: AX = B

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