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Internal Forces of a given member in an Engineering Structure

Internal Forces of a given member in an Engineering Structure. Chapter 7: Forces in Beams and Cables (page 354). Dr. Claudia Genovese-Martinez. So far, you have learned:. the external forces which act on a structure (Chapter 4)

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Internal Forces of a given member in an Engineering Structure

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  1. Internal Forces of a given member in an Engineering Structure Chapter 7: Forces in Beams and Cables (page 354) Dr. Claudia Genovese-Martinez

  2. So far, you have learned: • the external forces which act on a structure (Chapter 4) • the forces which hold together the members forming a structure (Chapter 6)

  3. Objective of this Chapter: • Determine the internal forces of a given member in a structure, such as: • beams • cables (Suspension bridges, transmission lines, etc.)

  4. Outline: • Analyze a: • two-force member • multi-force member • Determine the internal forces: • tension or compression • bending and shear • Examples

  5. Internal forces in members: • Let’s consider: -F F and -F: Directed along AB, opposite sense, same magnitude. B A F

  6. Internal forces in members: • Let’s cut the member AB at C -F B B -F C C A F F C -F A The new forces are equivalent to Internal Forces and must have existed in the member. F

  7. So far, we can conclude that: • In a straight two-force member: • internal forces to axial forces • In this case (tension) : • elongate under the action of internal forces B -F C C F In Compression:? -F A F

  8. Multi-force member: • Crane D D E F C C B B W G A A

  9. D E F C Multi-force member: B W G • Free-Body-Diagram of AD: A D J T Cx Cy FBE Ax A Ay

  10. Multi-force member: • Free-body diagram of the portion JD D T Force-Couple System V J M F • Equilibrium: • F and V to balance T • Couple M to balance the • moment of T about J

  11. Multi-force member: • Free-body diagram of the portions JD and AJ D T Newton’s third law: the internal forces on AJ are equivalent to an equal and opposite force-couple system. V J -F -M M J -V F Cx C Cy B FBE F: axial force V: shearing force M:bending moment at J Ax A Ay

  12. Non-straight two-force member • Internal Forces are also equivalent to a force couple system M B D F D P V P -P A C A B -V M -F D -P C

  13. Conclusion: • INTERNAL FORCES are equivalent to force couple system. • When determining INTERNAL FORCES in a member, indicate on which portion the forces are acting. • In two-force member, internal forces produce tension or compression. • In multi-force member AD, internal forces not only produce tension and compression but also shear and bending D A

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