1. Deflection of Beam Pairat Tanpornprasert, Ph.D. Niphon Wansophark, Ph.D Mechanical Engineering Department Faculty of Engineering Chulalonkorn University

2. Introduction A beam is defined as a structural member which cross-sectional dimensions are relatively smaller than its length A beam is defined as a structural member which cross-sectional dimensions are relatively smaller than its length A beam is subjected to loads perpendicular to its long dimension A beam is subjected to loads perpendicular to its long dimension Beam deflections are considered to be elastic deflections Beam deflections are considered to be elastic deflections

3. Introduction (con’) The design of beams is often based on deflection characteristics, rather than strength The design of beams is often based on deflection characteristics, rather than strength Beams are used in different kinds of construction Beams are used in different kinds of construction - - Machine - Bridges - Airplanes - Automotives - etc,

4. Frames

5. Machine

6. Bridge

7. Roof

8. Airplane

9. Robots Intelligence and networking

10. Motivation The deflection of machine parts must also be kept below certain tolerances to allow the machine to function properly The deflection of machine parts must also be kept below certain tolerances to allow the machine to function properly - Difficulties in parts assembly and installation - Unbalance in rotating shaft Large deflection cause or create unstable structure Large deflection cause or create unstable structure - Floor collapse - Bridge collapse

11. Motivation (con’) Precision machine needs rigid structure Precision machine needs rigid structure - Machine tool - Robotics - Measuring Instrument Allowable deflection of beams are often limited Allowable deflection of beams are often limited Stresses are also limited Stresses are also limited

12. Mississippi River Bridge Mississippi River Bridge collapsed on August 1, 2007

13. Coordinate Measuring Machine (CMM)

14. Robotics (High Rigidity)

15. Machine tool (High Rigidity)