Lab #2 Report due TODAY

1. Lab #2 Report due TODAY • Individual Data Processing and Individual Write Up • Lab #2 Report is due TODAY by midnight • Answer Multiple Choice Questions ONLINE TODAY by midnight • Answer Student Survey ONLINE TODAY by midnight • Submit the Lab Report #2 in the drawer labeled “MECE204-Strength Lab” under M. E. Mail Folders

2. Torsion Testing • Circular Cross-section Only • Determine Material Properties in Torsion • Draw Shear Stress-Strain Curve • Ductile or Brittle Failure ? • ASTM E-143 Test Method • Compare results from Tensile, Poisson’s & Torsion Test • Become familiar with Tinius Olsen Torsion Tester (10,000 in-lb capacity)

3. Sign Convention

4. Assumptions Perfectly linear-elastic behavior Circular x-section (solid or hollow) Small rotations Constant length Constant diameter

5. No deformation A highly deformable member A circular x-section A grid of parallel circles and longitudinal lines on the outer surface

6. After Deformation Two torques are applied Circles remain circles Longitudinal lines become twisted All angles are equal End x-section remains flat

7. Angle of Twist A prismatic circular member Fixed at x = 0 Other end is FREE Loaded by a torque at the free end Angle (x) - angle of twist It depends on x: /x=constant

8. Shear Strain After Before

9. Shear Strain Distribution max = c  max - occurs on the outer surface  = (/c)  max Result valid also for circular tubes within the material Valid for plastic deformation also 9

10. Shear Strain Distribution

11. Shear Strain & Angle of Twist  =  *  / L max =  * D / 2 / L

12. Shear Stress Distribution - Elastic Deformation only • X-section: linear distribution • Complimentary stresses in action • Shear stress occur on axial planes (normal to the x-section 12

13. Shear Stress & Torque- Linear Elastic Deformation Only  = T *  / J max = T * D / 2 / J

14. Modulus of Rupture tmax,psi gmax, rad Shear Stress-Strain Curve Slope = Dt/Dg = Shear Modulus, G Figure 3.2 Typical shear stress-strain diagram from a Torsion Test

15. Linear Elastic Region – Shear Modulus

16. Failure Surface – Tensile Testing

17. Failure Surface – Torsion Test

18. Brittle Failure – Torsion Test

19.  n t N V P Stresses on an Inclined Plane in an Axially Loaded Member • Seek for equilibrium after cutting along the oblique plane x

20. Maximum Stress – Uniaxial Tension

21. Comparing Tensile vs. Torsion Results

22. Measuring Angle of Twist T=(R-R0)-(L-L0)

23. Torsion Data Sheet

24. Computing the Slip Angle

25. Manually Recorded Data slip= H-(LH/LT)T T=(R-R0)-(L-L0) cor = H - slip R0 L0

26. Shear Strain and Stress =Radians(cor)*D/2/LH =16T//D3

27. Integrating Computer Data slip= constant cor=H - slip

28. Selecting Computer Data Head Angle = 30.00 deg When Protractors taken OFF Max Torque = 1931 in-lb

29. Entire Stress Strain Curve

30. Elastic Curve

31. Proportional Limit =G*

32. Proportional Limit Plot columns H, I, & J

33. Key Ideas - Torsion • Shear strain formula is valid in both elastic & plastic region • Torque formula is valid in linear elastic region ONLY • Thus, shear stress formula is valid until proportional limit • After proportional limit, shear stress formula overestimates stress.

34. Torsion Results

35. Comparing Tensile vs. Torsion Results

36. Comparing Lab 1, 2, & 3Experimental Results

37. Lab #2 Report due TODAY • Individual Data Processing and Individual Write Up • Lab #2 Report is due TODAY by midnight • Answer Multiple Choice Questions ONLINE TODAY by midnight • Answer Student Survey ONLINE TODAY by midnight • Submit the Lab Report #2 in the drawer labeled “MECE204-Strength Lab” under M. E. Mail Folders