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: Determine the internal forces: Examples
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. Multi-force member: Free-Body-Diagram of AD: J D E F C B W G A D A TCx Cy
FBE Ax A Ay

10. 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

11. 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

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