Principles of Form Synthesis I

1. Principles of Form Synthesis I Images: www.freeimage.co.uk

2. Evaluate Preliminary Design Concepts Intermediate Design Functional Problem create Requirements Need or Conceptual Selected Synthesis Source Identification design Desire Stage Concepts Stage Constraints Stage configuration equations List ways of cost 1) Determine what accomplishing life is exactly wanted Design design noise Tentative 2) Identify all requirements elements of Optimization design 1) Be prepared for criticism Analysis Evaluation System 2) Be prepared to explain design Stage Stage Performance 3) Cite good and bad points Detail Design 4) Illustrate design and build models Design development: Final Design Make judgment on design Sell your design Production User Stage Design Process

3. Structural Design Structural design involves two issues • Form Synthesis • Stress analysis Images: www.freeimage.co.uk

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

5. Simple Example • 1) Forces Types of forces are given • Design life for part Too early for a stress analysis • 3) Maximum allowable cost Assume moderate cost • 4) Weight limit Medium weight but must be strong and light • 5) Space limit Small size (say 20 cm long) • 6) Environmental conditions Assume ambient environment (for material selection) • 7) Number required (<100) • 8) Aesthetic factors Looks not important • 9) Material selection Assume common cold-rolled steel • 10) Kinematics Assume high speed • 11) Function Connecting link in high speed mechanism

6. Possible Solution

7. Body Body Joints Anatomy of a Part • Body • Joints

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.

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”

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.

11. Common Stress Patterns • Uniform Tension • Uniform Compression • Bending

12. Common Stress Patterns (cont’d) • Transverse Shear

13. Common Stress Patterns (cont’d) • Torsion

14. Common Stress Patterns (cont’d) • Bending of I-beam

15. Common Stress Patterns (cont’d) • Contact stresses

16. Things Affecting Stress Patterns • Shape of part • Force orientation • Material (if stress-strain curve nonlinear)

17. Comparison of Stresses • Force = 1000 lbs • Identify stresses for various orientations of load and shape of part.

18. Tension/Compression

19. Bending

20. Transverse Shear

21. Torsion

22. Tensile vs. Shear Stresses For ductile materials, shear stresses alone are numerically twice as bad as tensile stresses

23. Maximum Shear Stress Theory • General state of stress • Simple tension test • For pure torsion ( )

24. Comparing Stresses When comparing severity, use Or

25.  Tr J = Torsion of Hollow Section Use tube with outside radius of 2” but with same area as 1” diameter rod

26. Torsion of a Hollow Tube (cont’d)

27. Two 1” Diameter Rods in Contact

28. Getting a and b • Depends on

29. Stress Calculation 1 - 8 c = d = 0 . 908 1000 6 . 0666 x 10 = 0 . 0283 3 2

30. Comparison of Transverse Stress and Bending When are transverse shear and bending equally severe?

31. Comparison of Transverse Stress and Bending (cont’d) Therefore

32. Comparison of Transverse Stress and Bending (cont’d)

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.

34. Comparison of Torsion and Transverse Shear (cont’d) Maximum torsional stress Maximum transverse shear stress

35. Comparison of Torsion and Transverse Shear (cont’d) Because both are shear stresses, set or

36. Comparison of Tension and Bending When is tensile stress comparable to bending stress on round section

37. Comparison of Tension and Bending (cont’d) Tension stress Bending stress When the stresses are equal

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%)

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

40. I-Beam in Bending (cont’d) • Flange area = 0.9 A = 0.707 in2 • Area calculation for round bar in2 Approximate moment of inertia in4

41. Bending Stress Bending stress Note: Area moved to where it carries load

42. Optimum Shapes for Bending and Torsion Optimum for bending Optimum for torsion

43. Examples of Optimum Shapes

44. Summary of Stresses

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.

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

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