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ENGI 1313 Mechanics I

ENGI 1313 Mechanics I . Lecture 30: Examples on Method of Sections. Lecture 30 Objective. to illustrate the method of sections by example. Example 30-01.

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ENGI 1313 Mechanics I

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  1. ENGI 1313 Mechanics I Lecture 30: Examples on Method of Sections

  2. Lecture 30 Objective • to illustrate the method of sections by example

  3. Example 30-01 • The Howe bridge truss is subjected to the loading shown. Determine the force in members DE, EH, and HG, and state if the members are in tension or compression.

  4. Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG • Cut Along Section? • Truss chords • ED • EH • GH • What Section to Use? • Right • Calculate Support Reaction Forces? • Yes, at G

  5. Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG • Support Reaction G • What equilibrium equation? Gy

  6. Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG • Draw Section FBD • Assume all truss member forces are in tension Gy 40kN FED FEH FGH Gy

  7. Example 30-01 (cont.) Determine the force in truss members DE, EH, and HG • Equilibrium Equation? Gy 40kN FED FEH FGH Gy

  8. Example 30-02 • Determine the force in members OE, LE, and LK of the Baltimore truss and state if the members are in tension or compression.

  9. Example 30-02 (cont.) Determine the force in truss members OE, LE, and LK • Where to Start? • What are the key truss joints (nodes)? • Joint E • Joint L • Any particular characteristics? • 5 unknowns @ E • Zero-force @ L

  10. FLM FLK L FLE Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) • Joint FBD at L

  11. Ax E Ay Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) • Section Cut? • Draw FBD • Examine FBD • Known? • Unknown? • To Be Determined? FML FOE FDE

  12. Ax E Ay Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) • Next Step? • Reduce unknowns • Find what support reaction? • Ay • What equilibrium equation? Ax Ay FML FOE FDE

  13. Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) • Support Reaction Ay Ax Ay

  14. Ax E Ay = 6.375kN Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) • Next Step? • Find FML • What equilibrium equation? FML FOE FDE

  15. Ax E Ay = 6.375kN Determine the force in truss members OE, LE, and LK Example 30-02 (cont.) • Next Step? • Find FOE • What equilibrium equation? FML FOE FDE

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

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