ME 221 Statics Lecture #25 Sections 7.1 – 7.4

1. ME 221 StaticsLecture #25Sections 7.1 – 7.4 Lecture 25

2. Homework #9 Chapter 5 problems: • 53, 54, 56, 62, 64, 69, 71 & 73 • Due Friday, October 31 Lecture 25

3. Homework #10 Chapter 7 problems: • 2, 5, 6, 8, 19, 21, 24, 26 & 35 • Due Friday, November 7 Lecture 25

4. Chapter 7:Internal Forces in Structures • Review internal/external forces • How to find internal forces • Sample problems Lecture 25

5. External/Internal Forces • External forces arise from contact or gravitational attraction • Point and distributed loading • Weight • Internal forces are forces arising to hold bodies together • Internal stress is a form of an internal force Lecture 25

6. c c b b a a 100 lb Exposing Internal Forces • To analyze the stress at a given location in a part, we need to know the forces at that particular section. At any given section a-a, b-b, or c-c, there is an internal force arising from the 100 lb external force. Lecture 25

7. Mz=0 Ay=100 lb Ax=0 Mz Fy a a Fx 100 lb 100 lb 100 lb Method for Finding Internal Forces • Determine reaction forces • Use equilibrium equations • Section and solve second equilibrium problem to find internal forces Lecture 25

8. General Internal Forces • In general, there is a force and moment component for each coordinate direction at a given section • 6 possible unknowns Sample problems: Lecture 25

9. l P y x h z O Example: Determine the internal forces and moments in the bar built into the foundation as shown in the figure. Lecture 25

10. (l-x) l P P y x x h z O Horizontal Portion Lecture 25

11. l l P P y (h-y) x h y z O Vertical Portion Lecture 25

12. Shear and Bending Diagrams(Secs. 7.3, 7.4) • Topic is also called transversely loaded beams • Beam classifications and boundary conditions • Internal forces and the components’ specific rolls • Relation between shear and bending • Generation of shear and bending diagrams • Sample problems Lecture 25

13. Simple Overhanging Cantilever Types of Beams by Supports • Transversely loaded beams have several standard configurations • Determinate beams have the same number of reactions as nontrivial equilibrium eqns. Determinate Indeterminate Lecture 25

14. P Vz • Axial is along beam Vy • Shearing forces are transverse components • Moment components • Torsion along beam T Mz • Bending for transverse components My Internal Force Component Rolls • Force components Lecture 25

15. Shear and Moment Diagrams -Sectioning Method -Integration -Singularity Functions Lecture 25

16. What is expected for shear and bending diagrams? 1. Show FBD and statics for each section 2. Determine equation for V(x) and M(x) 3. Draw shear and bending diagrams indicating linear or parabolic 4. Label end points of diagram as well as every region endpoint Lecture 25

17. Shear and Moment Diagrams using SectioningMethod 1. Find reaction forces Generate a shear / bending diagram as follows: 2. Take a section on each side of an applied force or moment and inside a distributed load (take a new section whenever there is a change in the load or shape of the beam) - draw a FBD and sum forces / moments 3. Repeat 2 along the length of the beam. w(x) distributed load V(x) shear force M(x) moment Lecture 25

18. M V M V Sign Convention Positive Shear and Positive Moment Lecture 25

19. M M Effect of External Forces Positive Shear Positive Moment Lecture 25

20. 125 lb 125 lb 20 lb/in 9 in. 12 in. 12 in. 12in. V M x x +ve -ve tension up Tension down Lecture 25

21. Lecture 25