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) the forces which hold together the members forming a structure (Chapter 6)

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

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

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

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

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

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

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

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

Multi-force member: Free-body diagram of the portions JD and AJ D Newton’s third law: the internal forces on AJ are equivalent to an equal and opposite force-couple system. -F J V -M J M -V F Cx C Cy B FBE F: axial force V: shearing force M:bending moment at J Ax A Ay

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

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