Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

1. Engineering 36 Chp 1Introduction Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Learning Statics • There is ONLY ONE WAY to Learn Statics Work LOTS of Problems • Work Thru, and UNDERSTAND, all Sample Problems • Work Chp Problems for Which the Book Provides Answers • Handily Located in the Back of the Book; See “ANSWERS TO SELECTED PROBLEMS”

3. Class Structure – ENGR36 • Lecture TTh 1:00-1:50p • PowerPoint Instruction-Presentation on The Interactions of Forces (Push/Pull) and Moments (Twists) on NONmoving structures • Lab – TTh 2:00-3:15p • Tu: WhiteBoard Example Solutions to Problems Similar to the LPS (HomeWork) Problems • Th: Work in Math & Science Center 3906 on the Mastering Engineering LPS Problems

4. If you can’t Make the Lab Every time... Don’t Worry • I will post my solved Examples on the ENGR36 Course WebPage • Any Student can Work at his/her own Time & Location in place of the lab AS LONG AS the LPS are Submitted to Mastering Engineering ON TIME • If a student can not make the Lab Session, I suggest forming an ENGR36 study Group outside of class times

5. Mastering Engineeringhttp://www.masteringengineering.com/

6. Mastering Engineeringhttp://www.masteringengineering.com/site/register/new-students.html Pick One, then Continue

7. Mastering Engineering: $60.50 http://www.mypearsonstore.com/bookstore/product.asp?isbn=0132915545&xid=PSED • An Access Code is provided with the TextBook Available in the BookStore • Students who purchased the book from another source can purchase Stand-Alone Mastering Engineering for $60.50

8. If you received a Course ID from your instructor, click Yes, enter your Course ID and click Continue.If you DO NOT have a Course ID, follow the instructions on the NEXT slide. CHABOTENGR36FA13

9. W12345678 Your instructor may provide specific instructions for completing this field. If so, enter the appropriate information and click Continue. If you are not sure what to enter, contact your instructor or click Skip This Step. (You can enter your Student ID later.) Use “W” Number as Student ID

10. Registering Tips Video • http://www.masteringsupport.com/videos/registration_tips/registration_tips.html

11. Engineering Product Design

12. Requirements/Goals The goal of this phase is to figure out exactly what the customer wants Specification describe exactly what the product will do and how it will perform focus on WHAT the product is supposed to do, not HOW it is supposed to do it Design Conceptual → Generate Broad Concept Solutions Preliminary → Choose 2-3 Concepts for Testing Engineering Product Design

13. Design Detailed → Select “winning” solution Sweat details → select materials, Perform engineering analyses, make Engineering DWGs, determine production and test methods Implement Make a PHYSICAL Prototype unit Test Test every item in the performance specification → Possible OutComes The product does NOT meet the spec The product meets the spec but the spec was WRONG customer CHANGED his/her mind product MEETS the spec and customer is HAPPY Engineering Product Design

14. Engineering Analysis • Goal • What EXACTLY do we want to determine? • Suggest including the UNITS for the “answer” • Given • Summarize KNOWN conditions and previously collected DATA • Assume (this HAS to be done) • Make an analytical MODEL • List Important assumptions

15. Assumption Digression • BMayer 2001 JVST Paper • See ENGR45 for More Details

16. PARTIAL Assumption List 100% Vapor Saturation at Bubble Edge Gases in bubble behave as perfect gases Bubbles are Spherical Radial Symmetry Diffusion Coefficient is Constant Assumption Digression

17. Engineering Analysis • Draw Diagram if Possible • Sketching a Diagram is critical • Take time to make a Sketch that is Clear and in Proportion (roughly to scale) • Create Math Model • Make equations based on known scientific (physics, chem) or engineering principles • Solve Math Model • Math Processors (MATLAB, Excel) helpful

18. Engineering Analysis • Check Results • Make a “Reality Check” on Results • Test with KNOWN inputs and compare to the KNOWN result • Test with a WIDE range of inputs to test “robustness”

19. Mechanics  The Physical Science Which Describes Or Predicts The Conditions Of REST Or MOTION For BODIES Under The Action Of FORCES and/or MOMENTS Some Classes of Mechanics Analysis Rigid Bodies Statics → NO Motion Dynamics → Moving in General Deformable Bodies → Forces Interact with MATERIAL Properties 3rd yr course at the University Level Fluid Mechanics → almost always deforming materials Compressible → gas Incompressible → liquids Mechanics – General

20. Rigid-Body Analysis Considers All Bodies To Be Perfectly Stiff → NO Deformation Not Strictly True In Practical Situations as All Physical Structures Deform (However Slightly) When Subjected to Force-Loading. Rigid Body Analysis Applies When Deformations Are “Small” and so Do Not “Significantly” Affect The Conditions Of Equilibrium Or Motion i.e., Can Neglect Deformation For Equil/Motion Analysis Rigid Body ≡ A Body is Considered Rigid When The Relative Movement Between Its Parts is Negligible Rigid Body – Special Case

21. Statics Is A SubClass of Rigid Body Mechanics Analysis Statics ≡ Study Of Equilibria Of A System Without Regard To Inertia Forces Or Velocity Dependent Forces → No or Const. Motion Apply Newton’s 2nd Law Using Vector Notation Statics – Further Special Case • Consequences of Static Rigid-Body Conditions • System Accelerations Are ZERO • Force InterActs with CONFIGURATION Only • governing equations are ALGEBRAIC In Nature

22. Static Analysis is Based on Incompletely Defined, But Thoroughly Familiar Concepts SPACE ≈ The Geometric Region Occupied By Bodies Whose Positions Are Described By Linear and Angular MeasurementsRelative to a Coordinate System TIME ≈ The Measure Of TheSuccession Of Events MASS ≈ The Measure of the Body’s Inertia, Which Is Its Resistance to a Change Of Motion. Sometimes Called "Quantity Of Matter“ FORCE ≈ The Action Of One Body On Another Statics - Fundamental Concepts CartesianSpace

23. Sir Isaac Newton (1642-1727) Was the First Person To Mathematically Describe the Physical Relationship Between the Fundamentals In Newtonian Mechanics Space, Time, And Mass Are Absolute, And Independent Of Each Other Newton’s Laws Objects At Rest Will Stay At Rest, and Objects In Motion Will Stay In Motion In A Straight Line Unless Acted Upon By An Unbalanced Force (Resultant Force = 0). Newtonian Mechanics

24. Force Is Equal To Body Mass Times its Acceleration; Mathematically Newtonian Mechanics cont. • Note: for STATIC; i.e., NonMoving, systems a = 0 • For Every Action There Is Always An Opposite And Equal Reaction that is CoLinear Sir Issac Newton

25. Base units For Static Analysis Systems of Units • FORCE is the Most Important Derived Unit • Find the SI Consistent Force Unit by Applying a Unitary Acceleration, a, of 1 m/s2 • Funit = (1 kg)•(1 m/s2) = 1 N (newton) • Recall for a Weight, the Acceleration is g. One kg “weighs”: • W = mg = (1 kg)•(9.81 m/s2) = 9.81 N

26. Maintain Units Through ALL Calculations Serves as A Consistency Check Use SI Prefixes (Next Slide) to Avoid Scientific Notation But for Complex Calculations, Convert back to Non-Prefixed SI Units to Avoid Order-of Magnitude Errors Separate 3-Digit Groups with a Space, NOT a Comma YES → 45 611 m NO → 789,321 s Tips on Units

27. SI prefixes

28. In The US Customary System the Unit of FORCE  Pound (lb) F = ma and 1 lb = m•(1 ft/s2) Thus m = 1 lb•s2/ft = 1 slug Weight of 1 slug by gravity? W = mg Where g = 32.2 ft/s2 Thus Wslug = 32.2 slug•ft/s2 = 32.2 lb Summary 1 lb Is The Force Required To Give A Mass Of 1 Slug An Acceleration Of 1 ft/s² 1 lb Is The Force Required To Give A Mass Of 1/32.2 Slug An Acceleration Of 32.2 ft/s² US Units  lbs vs. slugs

29. As Noted Before Unit-Consistency Is Critical for Arriving at a Proper Answer To Convert From One Set of Units to Another use the “Cross-Out” Division Method e.g. Given a Speed, , of 60 mph; find ft/s & m/s Given From ref Bk: 1mi = 5280ft and 1hr = 3600sand 1m = 3.281ft Unit Conversion

30. Precision is Determined by The PHYSICAL Situation, NOT the CALCULATOR In Particular, A Computed Result Can be NO MORE Precise Than The LEAST Accurate of Physically Measured (or Derived from Measured) DATA The Precision of the Calculation This Was Issue in the SlideRule Days, But Rarely Now Example: Find the Average of this Physically Reliable Data Set (13.47, 9.9, 7.803) Numerical Precision • In This Example, the Middle Value Governs Precision

31. It is Physically difficult to Make Precise and Reliably-Accurate Measurements to Better Than 1 part per 1 000 (1 ppt); or about 0.1% Most Practicing Engineers are Very Skeptical of Any Data/Calculations Presented at 1 part in 10 000 (or more) Good “Rule of Thumb” 4 Figures For Values Starting With No. 1 Called “3½” Significant Figures 3 Figures In All Other Cases Numerical Precision, cont.

32. CoOrdinate Systems • The CoOrd TriAd is Defined by Your RIGHT Hand → Rt-Hand Rule

33. Right-Hand Rule • Thumb points in the positive x direction • Index finger points in the positive y direction • Middle finger points in the positive z direction • Used to define positive rotation • Point thumb in the positive direction along the axis which is perpendicular to the plane of rotation • The fingers point in the direction of positive rotation

34. VECTOR ≡ Parameter Possessing Magnitude And Direction, Which Add AccordingTo The Parallelogram Law Vectors • Examples: Displacements, Velocities, Accelerations, FORCES • SCALAR ≡ Parameter Possessing Magnitude But Not Direction • Examples: Mass, Volume, Temperature • Vector Classifications • FIXED Or BOUND Vectors Have Well Defined Points Of Application That CanNOT Be Changed Without Affecting An Analysis

35. FREE Vectors May Be Moved In Space Without Changing Their Effect On An Analysis SLIDING Vectors May Be Applied Anywhere Along Their Line Of Action Without Affecting the Analysis EQUAL Vectors Have The Same Magnitude And Direction NEGATIVE Vector Of a Given Vector Has The Same Magnitude but The Opposite Direction Vectors cont. Equal Vectors Negative Vectors

36. Mag-Angle Vector Representations • Unit Vectors • Length of “Unit” Vectors (i, j, k) = 1 • More on Vector “DeComposition” in future lectures • Magnitude ≡ ||V||= Geometric Length • Space Angles: θx, θy, θz

37. Formal Drawing Engineering Drawings • Informal Drawing • Contains all information needed for FABRICATION or ASSEMBLY

38. Free-Body Diagrams • SPACE DIAGRAM  A Sketch Showing The Physical Conditions Of The Problem • FREE-BODY DIAGRAM  A Sketch Showing ONLY The Forces Acting On The Selected Body

39. Solving Statics Problems Often Involves Non-Right Triangle Geometry. Some Useful Relationships (See your Math Book) Suggested Review → Trig • Law of Sines • Law of CoSines • a=13, c=17, B=43° • A=31.4°, C=105.6°b=24 • a=11, b=19, C=101° • c = 23.7

40. Battle of the TriAngle • If 3 SIDE-LENGHTS areknown → Use Cos-Law to Find any angle • Solve Eqn at Right for cos(c) • If 2 SIDE-LENGTHS and theIncluded Angle are known→ Use Cos-Law to find the Opp Side-Length • Use Sin-Law for • 2-ANGLES & 1-SIDE known • 2-SIDES & NonIncluded Angle

41. Done for 1st Meeting • Please see me if you would like to ADD Static Loading

42. Engineering 36 Appendix Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

43. Force Is Equal To Body Mass Times its Acceleration; Mathematically M F -F m Newtonian Mechanics cont. • For Every Action There Is Always An Opposite And Equal Reaction • Newton’s Law of Gravitation • F  mutual force of attraction between 2 particles • G  universal constant known as the constant of gravitation • M, m  masses of the 2 particles • r  distance between the 2 particles

44. Consider An Object of mass, m, at Height, h, Above the Surface of the Earth, Which as Radius R Then the Force on the Object (e.g., Yourself) Weight • This Force Exerted by the Earth is called Weight • While g Varies Somewhat With the Elevation & Location, to a Very Good Approximation • g  9.81 m/s2  32.2 ft/s2

45. Earth Facts • D  7 926 miles (12 756 km) • M  5.98 x 1024 kg • About 2x1015 EmpireState Buildings • Density,   5 520 kg/m3 • water  1 027 kg/m3 • steel  8 000 kg/m3 • glass  5 300 kg/m3