2. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #1 Principles of Form Synthesis I Images: www.freeimage.co.uk

3. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #2 Design Process

4. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #3 Structural Design Structural design involves two issues  Form Synthesis  Stress analysis Images: www.freeimage.co.uk

5. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #4 What we need to know for design »Forces (location, direction, magnitude) »Design life for part »Maximum allowable cost »Weight limit »Space limit »Environmental conditions »Number required »Aesthetic factors »Material selection »Kinematics »Function

6. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #5 Simple Example 1)ForcesTypes of forces are given 2)Design life for partToo early for a stress analysis 3)Maximum allowable costAssume moderate cost 4)Weight limitMedium weight but must be strong and light 5)Space limitSmall size (say 20 cm long) 6)Environmental conditionsAssume ambient environment (for material selection) 7)Number required(<100) 8)Aesthetic factorsLooks not important 9)Material selectionAssume common cold-rolled steel 10)KinematicsAssume high speed 11)FunctionConnecting link in high speed mechanism

7. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #6 Possible Solution

8. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #7 Anatomy of a Part  Body  Joints Body Joints

9. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #8 Principles Governing Form Synthesis Form the size and shape of the part so that the stress is uniform over as large an area as possible. Minimize the weight and/or volume of the part consistent with cost, manufacturing processes, and other constraints.

10. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #9 Stress Patterns  Variation of stress across a given cross section  Functions of  Position of load  Orientation of load  Shape of part  Uniform stress patterns are “Strong”  Non-uniform stress patterns are “Weak”

11. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #10 State of Stress at Point  Applies to all possible planes through point  Nomenclature: refers to the stress on the i face and in the j direction.

12. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #11 Common Stress Patterns  Uniform Tension  Uniform Compression  Bending

13. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #12 Common Stress Patterns (cont’d)  Transverse Shear

14. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #13 Common Stress Patterns (cont’d)  Torsion

15. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #14 Common Stress Patterns (cont’d)  Bending of I-beam

16. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #15 Common Stress Patterns (cont’d)  Contact stresses

17. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #16 Things Affecting Stress Patterns  Shape of part  Force orientation  Material (if stress-strain curve nonlinear)

18. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #17 Comparison of Stresses  Force = 1000 lbs  Identify stresses for various orientations of load and shape of part.

19. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #18 Tension/Compression

20. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #19 Bending

21. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #20 Transverse Shear

22. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #21 Torsion

23. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #22 Tensile vs. Shear Stresses For ductile materials, shear stresses alone are numerically twice as bad as tensile stresses

24. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #23 Maximum Shear Stress Theory General state of stress Simple tension test For pure torsion ( )

25. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #24 Comparing Stresses When comparing severity, use Or

26. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #25 Torsion of Hollow Section Use tube with outside radius of 2” but with same area as 1” diameter rod  = Tr J

27. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #26 Torsion of a Hollow Tube (cont’d)

28. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #27 Two 1” Diameter Rods in Contact

29. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #28 Getting  and   Depends on

30. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #29 Stress Calculation c  d  0.9081000 1 2 6.0666x10  8 3  0.0283

31. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #30 Comparison of Transverse Stress and Bending When are transverse shear and bending equally severe?

32. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #31 Comparison of Transverse Stress and Bending (cont’d) Therefore

33. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #32 Comparison of Transverse Stress and Bending (cont’d)

34. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #33 Comparison of Torsion and Transverse Shear  Determine the relative value of e and d for which transverse shear and torsional shear are equally serious.

35. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #34 Comparison of Torsion and Transverse Shear (cont’d) Maximum torsional stress Maximum transverse shear stress

36. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #35 Comparison of Torsion and Transverse Shear (cont’d) Because both are shear stresses, set or

37. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #36 Comparison of Tension and Bending When is tensile stress comparable to bending stress on round section

38. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #37 Comparison of Tension and Bending (cont’d) Tension stress Bending stress When the stresses are equal

39. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #38 Comparison of Tension and Bending (cont’d) Finally If e is only 10% of this (e = d/80), the stress is increased by 10% over simple tension case alone (eccentricity of 1.25%)

40. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #39 I-Beam in Bending Consider following I-beam  10 in long  Area same as 1-in diameter bar  90% of area in flanges (10% in web)  4 in high

41. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #40 I-Beam in Bending (cont’d)  Flange area = 0.9 A = 0.707 in 2 Approximate moment of inertia Area calculation for round bar in 2 in 4

42. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #41 Bending Stress Bending stress Note: Area moved to where it carries load

43. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #42 Optimum Shapes for Bending and Torsion Optimum for bending Optimum for torsion

44. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #43 Examples of Optimum Shapes

45. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #44 Summary of Stresses

46. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #45 Summary of Form Synthesis  Form synthesis and analysis is very important in design.  The engineer must use certain assumptions and information to determine the optimal design shapes with considerations for size, shape and material.  The design greatly affects the overall performance and capabilities of the design.

47. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #46 Credits  This module is intended as a supplement to design classes in mechanical engineering. It was developed at The Ohio State University under the NSF sponsored Gateway Coalition (grant EEC- 9109794). Contributing members include:  Gary Kinzel …………………………………….. Primary Author  Walter Starkey……………...Primary source of original material  Phuong Pham and Matt Detrick ……….…….. Module revisions  L. Pham …………………………………….….. Audio voice

48. Department of Mechanical Engineering, The Ohio State UniversityGATEWAY Sl. #47 Disclaimer This information is provided “as is” for general educational purposes; it can change over time and should be interpreted with regards to this particular circumstance. While much effort is made to provide complete information, Ohio State University and Gateway do not guarantee the accuracy and reliability of any information contained or displayed in the presentation. We disclaim any warranty, expressed or implied, including the warranties of fitness for a particular purpose. We do not assume any legal liability or responsibility for the accuracy, completeness, reliability, timeliness or usefulness of any information, or processes disclosed. Nor will Ohio State University or Gateway be held liable for any improper or incorrect use of the information described and/or contain herein and assumes no responsibility for anyone’s use of the information. Reference to any specific commercial product, process, or service by trade name, trademark, manufacture, or otherwise does not necessarily constitute or imply its endorsement.