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San Jose State University Department of Mechanical Engineering ME 130 Applied Engineering Analysis

San Jose State University Department of Mechanical Engineering ME 130 Applied Engineering Analysis Instructor: Tai-Ran Hsu, Ph.D. Chapter 1 Overview of Engineering Analysis. 2015 edition. Chapter Learning Objectives.

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San Jose State University Department of Mechanical Engineering ME 130 Applied Engineering Analysis

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  1. San Jose State University Department of Mechanical Engineering ME 130 Applied Engineering Analysis Instructor: Tai-Ran Hsu, Ph.D. Chapter 1 Overview of Engineering Analysis 2015 edition

  2. Chapter Learning Objectives ● To learn the concept and principles of engineering analysis, and the vital roles that engineering analysis plays in professional engineering practices ● To learn the need for the application of engineering analysis in three principal functions of professional engineering practices in: creation, problem solving and decision making. ● To illustrate the critical needs for engineers solving problems that relate to protection of properties and public safety, and also the needs for engineers making decisions in real-time situations that often involve grave consequences. ● To learn the roles that mathematics play in engineering analysis, and the ability to use mathematical modeling in problem solving and decision making in dealing with real physical situations.

  3. What is Engineering Analysis? It is a vital TOOL for practicing engineering professionals in performing their duties in: Creations Decision making Problem solving

  4. Engineers create: “Scientists DISCOVER what it was, Engineers CREATE what it is not” Engineers create “what it is not” in DESIGN to satisfy human needs and sustain high living standard for all human kind: Greatest Engineering Achievements of the 20th Century asselected by the US Academy of Engineering 1. Electrification* 11. Highways 2. Automobile* 12. Spacecraft* 3. Airplane* 13. Internet 4. Water supply and distribution 14. Imaging 5. Electronics 15. Household appliances* 6. Radio and television 16. Health technologies 7. Agriculture mechanization* 17. Petroleum and petrochemical technologies 8. Computers 18. Laser and fiber optics 9. Telephone 19. Nuclear technology* 10. Air conditioning and refrigeration* 20. High performance materials * With significant mechanical engineering involvements

  5. Engineers make DECISIONS – at all times, and often crucial ones: Decisions are required in: ● Design – Configurations of engineering systems Selection of design methodology, materials and fabrication methods Assembly, packaging and shipping ● Manufacturing – Tools and machine tools Fabrication processes Quality control and assurance ● Maintenance – Routine inspections and Procedures ● Unexpected cases with potential grave consequences – Change of customer requirements Malfunctioning of machines and equipment Defections in products Examples on Critical Decisions by Engineers on what to do if flaws or cracks appear on the surfaces of: ●Pressurized pipelines, e.g. the Alaska Pipelines and San Bruno Gas Pipeline burst or ●A jumbo jet airplane

  6. Engineers solve Problems – often in ways like fire-fighting: Problems relating to: Design fault and ambiguity Manufacturing disorder Malfunction of equipment Inferior quality in production Run-away cost control Resolving customer complaints and grievances Public grievances and mistrust

  7. All TASKS relating to: Creation Decision making Problems solving are of PHYSICALnature The required ANSWERS are of PHYSICAL naturetoo

  8. Engineering Analysis by Mathematical Modeling Engineering Problems (Physical) Mathematical Modeling Mathematical Formulation Engineering Analysis Mathematical Analysis Translate engineering problems into math formby: 1) Idealizing physical situations. 2) Identifying idealized physical situation with available math representations 3) Formulate math models, e.g., expres- sions, equations. Desirable direct approach Not Possible! Mathematical Solutions Unavoidable Approach Solution to Engineering Problems (Physical) Translation Math to Physical Situation Conclusion:Math plays a principal role as a servant to Engineering (the Master) in engineering practices

  9. Mathematical Modeling Math modeling is a practice involving the translation of physical (engineering) situations into mathematical forms, and vice versa. Tool Box for Engineering Analysis: ● Empirical formulas ● Algebraic equations and formulas from textbooks and handbooks ● Differential and integral equations with appropriate conditions fit to the specific problems ● Numerical solutions, e.g., by finite element method (FEM) or finite difference method (FDM). Many mathematical formulas and expressions are available in handbooks, e.g.: “Mark’s Standard Handbook for Mechanical Engineers,” 10th edition, Edited by Eugene A. Avallone and Theodore Baumeister III, McGraw-Hill, New York, 1996, ISBN 0-07-004997-1

  10. Example of Engineering Analysis by Empirical Formula Estimate pressure drop in fluid flow in pipes: Fluids flow in pipeline requires pressure supplied either by pumps, fans or gravitation. Pressure drop ∆P is The basis for selecting a powerful enough pump for the intended fluid flow in a pipeline. Unfortunately, it is too complicated to be computed. But engineers must have this information to design the pipe flow. Following empirical formula is often used: P2 Pump P1 Pipe flow where ρ = mass density of the fluid, v = average velocity of the fluid flow, L = length of the pipe, D = diameter of the pipe, and f = friction factor from Moody chart The friction factor f with the values available from the Moody chart is derived from experiments. where f = Moody friction factor , v = average velocity of fluid flow, D = diameter of the pipe, Rb = radius of the pipe bend, and kb = the bend loss coefficient. Numerical values of the bend loss coefficient kb are available in a handbook: The estimated pressure drop ∆P is then used to design the pump or fan to drive the fluid through a pipeline.

  11. Examples of Using Algebraic equations and formulas from textbooks and handbooks in Engineering Analysis • Determine the dynamic force induced by changing velocity of moving solid using the Newton’s Law: Induced force (F) = Mass of the moving solid (M) x Acceleration (a) or Deceleration (-a) 2) Determine the induced stress to a solid bar by applied force using the Hooke’s Law: Induced stress (σ = F/A) = E x Induced strain (ϵ = ∆L/L) where F = applied force, A = cross-sectional area, E = Young’s modulus (material property) ∆L = elongation or contraction of the bar, L = original length of the bar • Determine the velocity of fluid flow in a pipe (nozzle) with variable cross-sections • using continuity law: A1 A2 V1 V2

  12. Examples of using Differential and Integral Equations in Engineering Analysis • Differential Equations in Engineering Analysis: Determine the rate of solvent A with lighter concentration diffuses into solvent B with heavier concentration: where C(x,t) = concentration of A at depth x and time t, D = diffusivity of diffusion of A to B 2) Integral Equation in Engineering Analysis: Solve for function f(x) in the equation: Solution:

  13. Numerical Solutions for Engineering Analysis Numerical solution methods are techniques by which the mathematical problems that are associated with engineering analysis cannot be solved by analytical methods, such as by the above methods in the “tool box.” Numerical techniques have greatly expanded the types of problems that engineers can handle in: (1) Solving nonlinear polynomial equations, (2) Graphic expressions of functions, (3) differential equations by “finite difference methods” and (4) Problems with complicated geometry, loading and boundary conditions, such as by the “finite element methods.” Example: To determine the stress induced in the plate with the following loading condition: w F F F d D Plain solid plate: EASY Plate with a small hole of diameter d is a much, much harder case Numerical solution by Finite element method: Principal tasks in numerical methods for engineering analysis is to develop algorithms that involve arithmetic and logical operations so that digital computers can perform such operations.

  14. The Four Stages in General Engineering Analysis Engineers are expected to perform “Engineering analysis” on a variety of different cases in their careers. There is no set rules or procedure to follow for such analyses. Below are the 4 stages that one may follow in his (her) engineering analysis. Stage 1:Identification of the physical problem – specification of the problem: To ensure knowing what the analysis is for on: ● Intended application(s) ● Possible geometry and size (dimensions) ● Materials for all components ● Loading: range in normal and overloading; nature of loading ● Other constraints and conditions, e.g., space, cost, government regulations Stage 2:Idealization of actual physical situations for subsequent mathematical analysis: Often, the engineer needs to make assumptions and hypotheses on the physical conditions of the problem, so that he (she) can handle the analysis by his (her) capability with the “tools” available to him or her. Stage 3:Mathematical modeling and analysis: by whatever means he (she) believes applicable e.g., solution methods from handbooks, computer software, company handbooks or own derived formula and equations, including differential equations, etc.. Stage 4:Interpretation of results – a tricky but important part of engineering analyis. To translate the results of math modeling with numbers, charts, graphs to physical sense applicable to the problem on hands

  15. Examples on Engineering Analysis with the 4 Stages in General Engineering Analysis Example 1Design of a Simple Coat Hanger: Stage 1: The problem (usually supplied by customs): To design a coat hanger that will have sufficient strength to hang up to 6 pounds for an overcoat. A design synthesis resulted in the following conditions: Geometry and dimensions as shown: Material: plastic with allowable tensile strength @ 500 psi from a materials handbook ¼” dia rods 23.23o 17” Stage 2:Idealization of actual physical situations for subsequent available mathematical modeling and analysis: This is a “beam bending” problem. The solution on the strength of the hanger appears available in “mechanics of materials.” But the required geometry shown above is too complicated to be handled by available formula in textbooks or design handbooks. Need to make the following idealizations in order to use available formula in the handbooks ● On geometry: Idealizes (How realistic is this?) (?) ● On loading condition: P – uniform distributed load of the coat = 0.3243 lb/in (?) ● On boundary (end) conditions: P Rigidly held ends (how realistic is this?)

  16. Stage 3: Mathematical modeling and analysis: Derive or search for suitable mathematical formulations to obtain solution on the specific engineering problem. ●In this case of coat hanger design, the solution required is: “Will the assumed geometry and size of the hanger withstand the specified maximum weight of the coat up to 6 lbs?” – a physical statement ●The required solution is to keep the maximum stress in coat hanger induced by the expected maximum load (the weight of the coat) BELOW the allowable limit (the maximum tensile strength) of the hanger material (500 psi), as given (another physical statement) ● With the “idealization” in Stage 2, the maximum stress in the hanger can be computed from the formula on “simple beam theory” available from “mechanics of materials” (e.g., CE 112) textbook or a handbook for mechanical engineers Case of coat hanger Available case in textbook Distributed load, PCos(23.23o) = 0.298 lb/in Distributed load, P Maximum stress, σm = MmC/I 23.23o where Mm=max. bending moment, C radius of frame rod, I = area moment of inertia of the frame rod 9.25”

  17. Results of Stage 3 (mathematical) analysis: We may compute the following: The area moment of inertia of the frame rod, The maximum bending moment, The radius of the frame rod, C = 0.125” The maximum bending stress, occurs at both ends of the frame rod

  18. Stage 4:Interpretation of results – a tricky but very important task: ● Result from analysis in Stage 3 normally is in the form of NUMBERS, such as σm = 2078.8 psi as in the present case of a coat hanger design. ● Require ways to interpret these numbers into physical senses, e.g. in the current case: “Can the coat hanger with the assumed geometry and dimensions carry a 6-lb coat?” ●There are VARIOUS ways available for such translation: A) For the case of structure-relateddesign ONLY, one would use the following criterion: The max. stress, σm < σa where σa = allowable stress = Maximum tensile strength from handbooks/Safety Factor (SF) ● The SF in an analysis relates to “the extent engineers can make use of the strength of the material” ● There are a number of factors determining the SF in a structure design; ● The value of SF is set by designers based on the degree of sophistication of the analysis – the less “idealization” made in Stage 2: e.g., low value of SF for more sophisticated analyses with fewer idealization and assumptions made in the analysis. Physically it means less material is needed ● The value of SF also relates to possible potential consequence of the case in the analysis B) For the case of coat hanger design, the σm = 2078 psi > σa = 500 psi (given) with SF = 1. Physically, it means the coat hanger with the set geometry and dimensions CANNOT carry a 6-pound coat. The engineer will either adjust the assumed dimensions of the hanger, or reduce the weight of garment for the hanger to carry, following the following general design procedure.

  19. Stage 4 Interpretation of Results in GENERAL –General procedure in engineering design Stage 1: Understand the physical problem Stage 2: Idealization for math modeling Stage 3: Math modeling & analysis Stage 4: Interpretation of results No safety factors are involved in this situation if no structure In involved in the design

  20. Example 2Design of a Bridge across a Narrow Creek: Stage 1: Description of the Physical Conditions: The required short bridge is specifically designed to handle limited local traffic over a narrow creek. The span of the bridge is 20 feet, and the maximum load for the bridge is 20 tons (or 40000 pounds). The simplified geometry and dimensions of the bridge are illustrated in: Engineers decide to use two(2) I-beams made of steel For the support of the bridge structures based on the two reasons: (1) the bridge is built across narrow creek and is Mainly subject to bending loads. I-beams are best suited for carrying this type of loads, and (2) the primary concern for this structure is “public safety.” Steel is common structure material with reliable strength, and I-beams are widely available with moderate cost. However, design engineers need to find the adequate size of these beams from suppliers with STANDARD dimensions. Their first trial is to use the I-beams with the following dimensions set by the supplier (you may find these dimensions from handbooks): H1=12”, H2=10.92”, b1=5” and b2=0.35”. Also: Max. tensile strength= 75,000 psi and max. shear strength=25,000 psi (handbooks)

  21. Example 2Design of a Bridge across a Narrow Creek-cont’d: Stage 2:Idealizations of physical situation in order to use “Simple Beam theory” for mathematical analysis: Because the primary design consideration of the structure is its capability of taking on bending loads. Engineers realize that “simple beam theory” that they learned in “strength of materials” class (e.g., SJSU CE 112 course) would be easy to use. But the formula that they learned in these courses only deal with the following simple cases: P w lb/length Simply-supported: ● ● ● ● w lb/length Rigidly held support: None of the available conditions in the real situations resembles the above simplified situations. Therefore there are needs by design engineers to idealize the real situations in order for them to make use of the available formula in textbooks or reference books developed for simple-beam bending as show above.

  22. Example 2Design of a Bridge across a Narrow Creek-cont’d: Stage 2:Idealizations of physical situation in order to use “Simple Beam theory” for mathematical analysis – cont’d: • Following are the idealization engineers need to make in order to use “simple-Beam theory:” • The maximum load applied to the bridge is equally carried by two identical I-beams • The weight of the beams and other materials is neglected (This is obviously a serious violation of reality! We make this idealization nonetheless in order to simplify the subsequent mathematical manipulations). • Each I-beam carries half of the total load, i.e. 20,000 lbf. • Assume that each of the 4 wheels carries equal amount of load (another questionable assumption). • By judgment, the worst condition to be considered is when the vehicle is at the mid-span position. • One end of the beam is hinged to a fixed anchor and the other rests on a roller. • The I-beams can thus be considered to be simply supported (as engineering mechanics textbooks often indicate).

  23. Example 2Design of a Bridge across a Narrow Creek-cont’d: Stage 3: Mathematical analysisUse available formula for “Simple Beam theory” for the present engineering analysis: One-side front wheel load: One-side rear wheel load: Real problem Simulated simple beam bending The maximum bending stress is: at the center of beam cross section, Where M = maximum bending moment c = half the depth of beam cross section I = area moment of inertia The maximum shearing stress is: normal stress along the longitudinal direction Numerical results: σn,max= 26,740 psi, and σs,max = 2744 psi The maximum deflection at the center span is: 0.84 – not a critical factor in this design Where V = maximum vertical shearing force b2 = width of the rib of an I-beam Q (0) = statical moment at the center of beam cross section

  24. Example 2Design of a Bridge across a Narrow Creek- (End) Stage 4: Interpretation of Results We obtained the numerical results: σn,max= 26,740 psi, and σs,max = 2744 psi from Stage 3 analysis. What do these numbers mean to us? We were given in Stage 1 that the maximum tensile strength of the steel I-beams to be: 75,000 psi, which is much higher than the numerical results we computed. So, the selected 12” I-beams should be safe enough because both σn,max and σs,max are LESS than the maximum strength of the material, or is it? It would have been all right with the above assessment. However, because of the IDEALIZATIONS that we made in Stage 2 of the analysis, the maximum induced stresses in the beam may be a lot higher than what we have computed. Yet such idealization were necessary in order for us to use simple beam theory to produce these numerical results. Some COMPENSATION for the “convenience” we get in Stage 3 analysis must be given – The Safety Factor (SF) as we introduced in the book. In this case the SF is equal to: SF = Max tensile strength/ maximum induced stress = 75000/26740 = 2.8, which is far less than 5 or 6 for this type of structures We thus conclude that the use of 12” I-beams in this design is NOT safe enough!!

  25. Bonus Quizzes on Engineering Case Studies • Quiz 1:Conduct your research and analysis on this engineering case study by response • to the following particular queries: • What really happened on the accident on “Gas Pipeline burst in San Bruno, CA in 2010?” • What are the consequences of this engineering disaster? • What was the cause of the accident relating to engineering negligence? • What were the loss of properties and human lives by this accident? • What the owner of the pipeline – PG&E has been doing in compensations to the victims • and remedial actions taken to avoid future similar occurrence? • If you were a senior engineering manager at PG&E, what would you do to prevent • the recurrence of the tragedy? • How can engineering analysis help? • Quiz 2: Crash of a DC 10 jet passenger plane over the Chicago O’Hare • airport on May 25th, 1979 as shown in the picture: • What would be your response to the similar questions as posted in Quiz 1? The owner of • the ill-fated aircraft was American Airlines.

  26. Bonus Quiz 3 • Conduct an engineering analysis on Example 2 of a bridge structure and Determine the following with the missing information and conditions by your own research: • Include the weight of the steel structure plus the weight of the concrete pavement road surface, 20 feet long x 12 feet wide and 6 inches thick. • With realistic load distributions on front and rear wheels • What differences in the numerical solutions will you get in (1) and (2), and with (1) and (2) combined? You must supply all references sources in your solutions.

  27. Chapter-End Assignment • Read the Example on Application of Engineering Analysis on a bridge on P. 9. • Conduct an engineering analysis on the above example but include the weights of the steel structure and the required concrete road surface for the bridge. Remind you that you do not always have the information and conditions given in your design analyses. You, as an engineer, needs to make reasonable and logical assumptions on these missing information based on available reference “tools” available to you. 3. Be prepared to answer the question on the significance of “Safety Factor” used in a design analysis of a structure or machine component. What are the fundamental principles for determining the numerical value of this factor? Explain why a SF = 4 is used in pressure vessel design by ASME design code, yet SF = 1.2 is used in aircraft structure design. • Be prepared to offer example of engineers making decisions and solve problems based on your personal experience.

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