Beam Mechanics of Materials Laboratory: Shear, Bending, and Deflection

1. Mechanics of Materials Lab Lecture 2-4 Beam Mechanics of Materials Laboratory Sec. 3-4 Jiangyu Li University of Washington Jiangyu Li, University of Washington

2. Beam Jiangyu Li, University of Washington

3. Type of Supports Beam supported on a wall Beam-to-column connection Pole anchored to a concrete pier Jiangyu Li, University of Washington

4. Types of Beams Simply supported beam Cantilever beam Simply supported beam with overhang Jiangyu Li, University of Washington

5. Shear Force & Bending Moment Jiangyu Li, University of Washington

6. Sign Convention Jiangyu Li, University of Washington

7. Shear Force & Bending Moment Diagram Negative q Negative P Positive M0 Jiangyu Li, University of Washington

8. Shear Force & Bending Moment Diagram Jiangyu Li, University of Washington

9. Shear Force and Bending Moment Diagram Jiangyu Li, University of Washington

10. Deflection in Beam Jiangyu Li, University of Washington

11. Normal Stress in Beam How to identify the neutral axis? Jiangyu Li, University of Washington

12. Normal Stress Go through centroid ! Jiangyu Li, University of Washington

13. Shear Stress Jiangyu Li, University of Washington

14. Distribution of Shear Stress Jiangyu Li, University of Washington

15. Shear Stress Jiangyu Li, University of Washington

16. Shear Stress Jiangyu Li, University of Washington

17. Deflection of Beam Jiangyu Li, University of Washington

18. Deflection of Curve Jiangyu Li, University of Washington

19. Boundary Condition Jiangyu Li, University of Washington

20. Continuity Condition Jiangyu Li, University of Washington

21. Deflection by Bending Moment Equation Jiangyu Li, University of Washington

22. Deflection by Loading Equation Jiangyu Li, University of Washington

23. Deflection by Superposition Jiangyu Li, University of Washington

24. Strain Energy of Pure Bending Jiangyu Li, University of Washington

25. Strain Energy of Bending Jiangyu Li, University of Washington

26. Strain Energy of a Beam in Shear Rectangular: 1.2 Circular: 1.11 Thin-walled tubular, round: 2.00 Box section: 1.00 Structural section: 1.00 Jiangyu Li, University of Washington

27. Strain Energy of Bending Jiangyu Li, University of Washington

28. Castigliano’s Theorem When forces act on a elastic system subject to small displacements, the displacement corresponding to any force, collinear with the force, is equal to the partial derivative of the total strain energy with respect to that force. It can also be used to find the displacement when no force is applied at that point. Jiangyu Li, University of Washington

29. Modified Castigliano’s Theorem Jiangyu Li, University of Washington

30. Application Jiangyu Li, University of Washington

31. Inclined Load Notice the sign convention: positive Mz compress upper part, negative stress; positive My extend front part, positive stress! Jiangyu Li, University of Washington

32. Inclined Load Stress Neutral axis Jiangyu Li, University of Washington

33. Assignment • Read Mechanics of Materials Lab Sec. 3 • 4.25(a,b,c), 4.26(a) posted online Jiangyu Li, University of Washington