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ENGI 1313 Mechanics I

ENGI 1313 Mechanics I . Lecture 28: Method of Joints. Lecture 28 Objective. to understand the method of joints for establishing forces in truss members. Recall 2D Rigid Body Equilibrium. Support Reactions. A x. A y. C y. Method of Joints. Joint Equilibrium FBD at a joint

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ENGI 1313 Mechanics I

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  1. ENGI 1313 Mechanics I Lecture 28: Method of Joints

  2. Lecture 28 Objective • to understand the method of joints for establishing forces in truss members

  3. Recall 2D Rigid Body Equilibrium • Support Reactions Ax Ay Cy

  4. Method of Joints • Joint Equilibrium • FBD at a joint • Particle equilibrium concepts • Solve for member forces

  5. Method of Joints (cont.) • Joint Forces • Tension pulls on joint • + convention • Compression pushes on joint • - convention • Newton’s 3rd Law • T pull on member • C push on member

  6. Method of Joints Equilibrium Equations • Two-Force Member • Coplanar and concurrent force system • What does this mean? Automatically Satisfied Necessary for Equilibrium

  7. Procedure for Method of Joints • Find Support Reactions • Typically required but not always necessary • Draw FBD at Truss Joint • Select joint with 1 known force and at most 2 unknowns • Assume forces are tensile (positive scalar) unless obvious by inspection • Apply Equations of Equilibrium • Repeat for all Joints

  8. Joint Free Body Diagrams

  9. Coordinate Axes Orientation

  10. Find Support Reactions Coordinate Axes Orientation (cont.) Resolve FCB

  11. Find Support Reactions Coordinate Axes Orientation (cont.) Resolve FCB Resolve FCD

  12. Example 28-01 • Determine the force in each member. Indicate whether the member is in tension (T) or compression (C).

  13. 500N FBC FBA Example 28-01 (cont.) • Where to Start? • Examine joints • # Known Forces? • # Unknown Forces?

  14. Example 28-01 (cont.) • Joint B

  15. Example 28-01 (cont.) • Joint C

  16. Example 28-01 (cont.) • Joint A

  17. Example 28-01 (cont.) • Support Reactions • More than 2 unknowns at each joint then determine reactions first • For this case not necessary but to show equivalence Ax Ay Cy

  18. Example 28-01 (cont.) • Results Summary

  19. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1

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