Chapter 2 Key Elements in Engineering Analysis 4th Edition What You Are Going to Learn This is the most important single lecture in this course, really. Engineering drawing and sketching In mathematics you deal with pure numbers, in engineering you deal with variables Engineering variables have units as well as numbers How to deal with units and dimensions
Need-know-how-to-solve method Spreadsheet analysis Exploring Engineering Engineering Drawing An engineering drawing is a three-dimensional object on a two-dimensional piece of paper or computer screen by a process called projection. There are five common types of engineering drawings 1) Isometric 2) Axonometric 3) Oblique 4) Perspective
5) Orthographic Exploring Engineering 1) Isometric Drawing The three axes of the isometric drawing form 120 degrees angles with each other. Circles appear as ellipses in isometric drawings. Exploring Engineering
2) Axonometric Drawing Axonometric projection shows an image of an object as viewed from a skew direction in order to reveal more than one side in the same picture. Exploring Engineering 3) Oblique Drawing The three axes of an oblique drawing are
drawn horizontal, vertical, and at a receding angle that can vary from 30 to 60 degrees. Exploring Engineering 4) Perspective Drawing In a perspective drawing objects appear the way the human eye would see them. Parallel lines converge to a single point at the horizon.
Exploring Engineering 5) Orthographic Drawing In orthographic drawings the object appears to be inside a "glass box" with each face of the object projected onto a side of the box. Exploring Engineering Drawing Scale and The scale of a drawing is the ratio
Dimensioning of the size on the drawing to the size in reality. So if a drawing has a scale of 1:2, the drawing is the actual object size. When you add dimensions to a drawing, put in only as many dimensions necessary for a person to understand or manufacture the object. Exploring Engineering Computer Aided Design (CAD) Software
Engineering drawings are produced on computers with Computer Aided Design (CAD) software and most engineering programs include training in one or more of these computer programs. Not only can you accurately represent a threedimensional image of an object with this software, but you can also carry out complex engineering analysis for various loading conditions on the object. Exploring Engineering Engineering Sketching An engineering sketch is a free-hand drawing
used get ideas on paper quickly. Some common aids to help you sketch: Graph paper helps to maintain proportion and keep straight lines. Scraps of paper good for transferring distances Coins make good circle templates Credit cards make nice straight edges Exploring Engineering Engineering Sketching Just because a sketch is a free-hand drawing, it should still be relatively neat. However, sketching
does not require any real artistic skill. Exploring Engineering Engineering Variables Engineers typically seek answers to such questions as How hot will this get? How heavy will it be? and What's the voltage? Each of these questions involves a variable How hot temperature is the variable How heavy weight is the variable What voltage voltage is the variable
Exploring Engineering Units and Dimensions All engineers will have to understand this chapters material irrespective of sub discipline Lets start with everyones favorite superhero its Superman! Exploring Engineering Superman Engineering Hero Superman embodies many engineering concepts!
Faster speeding bullet speed and velocity More powerful mighty locomotive power Can leap tall buildings force and energy Kryptonite traps Information (or lack of it!) Exploring Engineering Superman Engineering Hero Suppose I asked you what is ? A pretty good answer is 3.14, or 3.142, or 3.141593 Suppose now I ask what is Supermans speed? Is 800 an answer?
No! Not unless we add something - i.e., 800 meter/second The units, m/s, really adds some new information ... had we said 800 inches/hr Superman would be called Supermolasses! Exploring Engineering Variables Velocity (speed) Energy Numbers
Units 800 meters per second (m/s) 1790 miles per hour (mph) 9.81104 newton-meters (N-m) 7.23104 foot-pounds force (ft-lbf) Power 2000 horsepower (hp)
1491 kilowatts (kW) Information Need enough to bits dodge kryptonite! bytes Exploring Engineering Units and Dimensions Did you see that we converted from one set of units to another as in m/s to furlongs/fortnight? Unit conversions can be tricky particularly for new units whose magnitude is unfamiliar
Whats the volume of a 1 ft cube in m3 if 1 m = 3.28 ft (or 3.28 [ft/m])? V = 1 ft3, V = 1/3.283 [ft3][m/ft]3 = 0.028 m3 Exploring Engineering More on Units and Dimensions Whats the acceleration of a rocket in miles per hour per second (mph/s) if you know in SI units that the acceleration is: a = 55 m/s2? 1 mile = 1609 m or 1609 [m/mile] and 1 hour = 3,600 s, or 3600 [s/hr]. Therefore, a = 55 3600/1609 [m/s2]
[s/hr][mile/m] Or, a = 123 mph/s Exploring Engineering Units and Dimensions In this course we will require the units to be manipulated in square brackets  in each problem. While easy to get the previous solutions without this method, many engineering problems are much harder than this & need this apparently clumsy methodology. Computerized unit conversions are available in free software on the Internet (for example at:
http://joshmadison.com/software/convert-for-windows Exploring Engineering More Conversion Examples These use conversion factors you can paste from Convert.exe Convert 800 m/s to miles per hour (mph) 800 [m/s][3.28 ft/m][1/5280 miles/ft][3600 s/hr] 800 x 2.236 = 1789 [mph] Convert 2,000 horsepower (hp) to kW 2,000 [hp][0.7457 kW/hp] = 1492 kW
Convert 9.81 x 104 Nmm to ftmlbf 9.81 x 104 [Nmm][1/4.448 lbf/N][3.28 ft/m] 9.81 x 104 x 0.737 = 7.234 x 104 ft m lbf Exploring Engineering Comparing SI and Engineering English Unit Systems Unit Force System SI
Mass newton kilogram (kgm/sm/s2) (kg) Length Time gc = ma/F meter (m)
second (s) 1 second (s) 32.174 lbmm/sft/lbfm/ss2 English pound
pound foot force (lbf) mass (lbm) (ft) Note: In the SI system gc = 1 kgm/(Ns2) = 1 (dimensionless) Numbers Are engineering numbers the same as every day numbers? NO! Why Not? Because engineers need more precise definitions Please use you calculators. What is 10/6?
Is it really 1.666667? Exploring Engineering Significant Figures Suppose the numbers 20, 20., 20.0, 20.00, 20.000, 20.0000 are distances in meters. Are they all the same? The naked 20 infers the division on the ruler you used to make the measurement (Maybe you were far away and used a nearby flagpole to estimate the height of a pine tree.). Thus only 1 figure is significant. But if you measured 20. (notice the period representing the place marker) your resolution improved to two significant
figures. In effect you used a 1 m ruler. If you measured 20.0 m you now measured to 0.1 m and if you measured 20.0000 m your ruler your scale was good to 0.0000 m and all 6 figures were significant Exploring Engineering Significant Figures If 10 and 6 are not integers, what is 10/6? Not 1.666667 because both the numerator and denominator are only known each to 1 significant number. Thus 10/6 = 2 (because its correct to 1 sig fig!)
Exploring Engineering Significant Figures The sum or difference of two values should contain no significant figures further to the right of the decimal place than occurs in the least precise number in the operation. The product or quotient should contain no more significant figures than are contained by the term with the least number of significant figures used in the operation. When the discarded part of the number is 0, 1, 2, 3, or 4, the next remaining digit should not be changed. When the discarded part of the number is 5, 6, 7, 8, or 9, then the next
remaining digit should be increased by 1. Exploring Engineering Significant Figures Suppose you subtract 201.12 from 509.1 519.1 (4 sig figs) 499.22 (5 sig. figs) = 19.88 = 19.9 (3 sig figs) Add 201.144 and 1.05 201.144 + 1.05 =202.194 = 202.19 (Why?) Exploring Engineering
Significant Figures Take the numbers 13,000, 13,000., 13,000.0 Sig figs are 2, 5 & 6 respectively Using exponents can be easier: 1.3 104, 1.3000 104, & 1.30000 104 respectively Subtract 0.42 10-2 from 0.380 3.80 10-1 - 0.42 10-2 = 3.80 10-1 - 0.042 10-1 = 3.758 10-1 = 3.8 10-1 (2 sig figs) Exploring Engineering
An Effective Problem Solving Technique A formal technique to help you solve problems - Need-Know-How-Solve method breaks the problem done into four constituent parts that are easier to formulate than overall problem. Exploring Engineering Problem Solving
Engineers of all disciplines are often challenged with unfamiliar problems By breaking them down into a systematic methodology, many impossible problems can be solved By systematizing your approach, you will leave an auditing trail for all those who later work on the same project. As a huge bonus, the suggested method really helps in getting a good grade! Exploring Engineering
Need-Know-How-Solve Method Need: The 1st step is obvious: read the problem very carefully. Look for what is being sought. Dont try to solve it now. Just write down what you are seeking. Know: Look at what you have been given (or look it up in available resources if not explicit in the statement of the problem). Again, dont try to solve it now. Just write down what you know as the 2nd step. Exploring Engineering
How: The 3rd step formulates your intended approach. It may be trivial (e.g., how many apples for $1?) or it may be an equation (e.g., E = mc2) or it the need for a spreadsheet analysis etc. Still dont try to solve it now. Solve: The 4th and last step does what your instincts told you (incorrectly) to try as step 1: go ahead and get to a solution. Exploring Engineering Example
Need: Stress in cable Know: Force, F is 0.5 ton = 1,000 lbf = 4450 N (Convert) and diameter is inch How: Stress F/A, where A = R2 = D2/4 Solve: A = 3.14 (0.5 0.0254)2/4 [inch m/in]2 = 5.07 10-4 m2 Hence = F/A = 4450/5.07 10-4 [N]/[m2] = 8.8 106 N/m2 Exploring Engineering Cable
Stress is defined as the force/area. Calculate the stress in SI units in an inch diameter cable supporting a 0.5 ton truck engine. 0.5 ton tons engine Need-Know-How-Solve Method On a single lane highway, you measure that there are 3140 cars/hr passing under a bridge. What is the separation between cars in seconds?
Need: Spacing in time between cars Know: 3140 cars/hr How: Dimensional analysis based on  units Solve: If 3140 cars/hr, time in s = 3600/3140 [s/hr][hr/car] = 1.15 s/car (to 3 significant figures) Exploring Engineering More If, in the previous example, the cars are traveling at 69 mph, what is their separation in m? In car lengths? Does this meet 1 car length per 10 mph spacing? Need: Spacing between cars
Know: 3140 cars/hr, interval = 1.15 s and v = 69 mph How:  method. V = 69 mph = 30.8 m/s. Assume average car is 4 m long. Solve: Since t = 1.15 s/car and V = 30.8 m/s, distance/car = 30.8 1.15 = 35.3 m of which 4 m. is car length. Spacing = 31 m or 31/4 [m/car][car/m] = 7.8 ~ 8 (car lengths), which is greater than the recommended 7 car lengths. Exploring Engineering Need-Know-How-Solve Method Summary: 1) Engage the mind before the pencil!
2) Delay solution until you have all in the facts. 3) Allow for a traceable solution for other members of an team (warts and all!). 4) As a practical matter, you can get most of the grade for the same wrong answer if you follow this methodology! E.g, write just the answer as 84.7 and may get you 0 grade but not for a clear development to a solution that said T = 8670/10 = 84.7! You would still get most of the grade. Exploring Engineering
Spreadsheets Can Aid in Calculation, Visualization and Simulation Exploring Engineering Data Visualization Data is raw facts. For example a collection of numbers. Information can be gained by presenting the data in a way that makes it possible to visualize the meaning of the data.
Exploring Engineering Organizing Data Headings Labels Formatting numbers as percentages, currency, etc. Graphs can be used to display data in a way that the significance of the numeric data can be seen. Ordering the data by sorting.
Exploring Engineering Performing Computations Spreadsheets provide built in functions to perform calculations using the data. MAX MIN SUM AVERAGE STDEV Exploring Engineering
Knowledge Knowledge results from the interpretation of information. It takes a human being with expertise to interpret the information to gain knowledge. Exploring Engineering Spreadsheets Definition: A spreadsheet is software designed to manipulate and analyze numbers and formulas in rows and columns.
We will be using Microsoft Excel in this class. However there are similar programs such as Lotus 123. Exploring Engineering The Spreadsheet Exploring Engineering Cell Contents The types of cell contents: Alphanumeric text
Headings Labels Numeric Integers Floating point Equations and formulas: B1+B4/H13 Predefined Functions: discussed in slide 5. Exploring Engineering An Example We will be creating a worksheet for a
class grade sheet. The input to a spread sheet requires entering numbers in cells. In this case the input will be grades. Exploring Engineering Summary Engineering problems need precise mathematics But not more precise than can be justified Significant Figures are important in engineering calculations. Variables have units that must be consistent. The 
method is very helpful in maintaining correct units. Its highly recommended that use the Need-Know-How-toSolve method because it sets you on a path to a solution and it provides an audit trail for those who follow. More complex problems need spreadsheets to organize them Exploring Engineering
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