ME 221 Statics Lecture #16 Sections 6.6 – 6.7 Final Exam Review

1. ME 221 StaticsLecture #16Sections 6.6 – 6.7Final Exam Review Lecture #16

2. Homework #6 • Chapter 7 problems: • 6, 19 & 26 • Chapter 6 problems • 3 & 6 • Due Today • MatLab Group Problems • 7.19, 7.26 & 6.15 • Due Today Lecture #16

3. Trusses Composed of slender straight pieces connected together by frictionless pins where all the loads (no moments) are applied. Each member will act as a two-force member (either in tension or compression). All the forces acting on a truss member are axial. Lecture #16

4. PBy PBx B PAY PCy PAx a b PCx Ax C A Ay Cy Analysis of Trusses Using the Method of Joints We need to solve for: (1) - Internal forces FAB, FAC, and FCA (2) - Reactions Ax, Ay and Cy Lecture #16

5. Using Matrix Notation -1 = Using manual calculations Look for joints with 2 unknowns Lecture #16

6. Example 6 kN A B 3 kN 0.9 m C D E 1.2 m 1.2 m Lecture #16

7. 6 kN A 4 B 4 5 9 15 3 kN 9 15 5 C 16 16 4 4 E D Lecture #16

8. Method of Sectioning 12 kN 12 kN A C E G I B D F H J 4 @ 2.4 m=9.6 m 1.8 m If the question is to find internal forces in selected members of the truss, then one can alternatively use the method of sectioning. Example: Determine the force in members FG and FH Lecture #16

9. 12 kN 12 kN A C E G I FGE 1.8 m FGF FHF B D F H J 12 kN 12 kN A C E G I FEG FFG FEH 1.8 m B D F H J Lecture #16

10. Trusses: 3-D (Space Trusses) • Consider all the members as two force members • Joints are ball & socket • Generally, use the method of joints • Determinate structures • Equation for determining 3j = m + r Lecture #16

11. 3-D Truss Methodology • Determine unit vectors based on structure geometry • Solve for reaction forces with entire structure • Draw FBD of joint • Sum forces at joint to determine member forces • Solve joint-by-joint or write out as a system of equations • the latter method may also include reaction forces Lecture #16

12. Example Lecture #16

13. Final Exam Wednesday, June 30, 10:20am 25% of course grade Lecture #16

14. Final Exam Topics Chapter 2: Vectors and Force Systems • Scalars & vectors • Laws of sine & cosine • Resolution of a vector into components • 3D coordinates & unit base vectors • Directional cosines • Scalar products of two vectors • 2D & 3D equilibrium problems Lecture #16

15. Final Exam Topics Chapter 3: Rigid Bodies • Calculating moments • Cross products • Moment of force about an axis • Moment of a couple • Equivalent force systems Lecture #16

16. Final Exam Topics Chapter 4: Distributed Forces • Center of mass • Centroids of areas & volumes • Centroids of composite bodies • Distributed loads on beams Lecture #16

17. Final Exam Topics Chapter 9: Moments of Inertia • Second Moment of Area; Ixx & Iyy • Polar Moments; J0z • Parallel Axis Theorem • Composite Areas • Principal Second Moments; Ixy Lecture #16

18. Final Exam Topics Chapter 5: Equilibrium of Rigid Bodies • Equilibrium Equations • Supports • Free Body Diagrams • Two-Force Members • 3D Equilibrium Lecture #16

19. Final Exam Topics Chapter 7: Internal Forces in Structures • Internal Forces • Shear Forces • Bending Moments • Shear & Bending in Beams Lecture #16

20. Final Exam Topics Chapter 6: Analysis of Structures • Planar trusses • Method of joints • Method of sections Lecture #16

21. Final Exam Format 4 to 5 Problems At least one each: Internal Forces – Chapter 7 Structures – Chapter 6 Others from previous material Lecture #16

22. Other Topics Check Angel to make sure all scores have been properly entered Pick up all old homework & quizzes Lecture #16