1. ME221Lecture #161 ME 221 Statics Lecture #16 Sections 6.6 – 6.7 Final Exam Review

2. ME221Lecture #162 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

3. ME221Lecture #163 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.

4. ME221Lecture #164 Analysis of Trusses Using the Method of Joints AyAy AxAx P Ax P AY P By P Bx P Cy P Cx CyCy A B C  We need to solve for: (1) - Internal forces F AB, F AC, and F CA (2) - Reactions A x, A y and C y

5. ME221Lecture #165 Using Matrix Notation = Using manual calculations Look for joints with 2 unknowns

6. ME221Lecture #166 Example 1.2 m 1.2 m 6 kN 3 kN E B A CD 0.9 m

7. ME221Lecture #167 6 kN 3 kN E B A C D 44 16 4 4 9 9 15 5 5

8. ME221Lecture #168 1.8 m 12 kN 12 kN 4 @ 2.4 m=9.6 m B D F H J A C E G I Method of Sectioning 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

9. ME221Lecture #169 1.8 m 12 kN 12 kN B D F H J A C E G I F GE F GF F HF 1.8 m 12 kN 12 kN B D F H J A C E G I F EG F FG F EH

10. ME221Lecture #1610 Trusses: 3-D (Space Trusses) Consider all the members as two force members Generally, use the method of joints Determinate structures –Equation for determining 3j = m + r –Joints are ball & socket

11. ME221Lecture #1611 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

12. ME221Lecture #1612 Example

13. ME221Lecture #1613 Final Exam Wednesday, June 30, 10:20am 25% of course grade

14. ME221Lecture #1614 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

15. ME221Lecture #1615 Final Exam Topics Chapter 3: Rigid Bodies –Calculating moments –Cross products –Moment of force about an axis –Moment of a couple –Equivalent force systems

16. ME221Lecture #1616 Final Exam Topics Chapter 4: Distributed Forces –Center of mass –Centroids of areas & volumes –Centroids of composite bodies –Distributed loads on beams

17. ME221Lecture #1617 Final Exam Topics Chapter 9: Moments of Inertia –Second Moment of Area; I xx & I yy –Polar Moments; J 0z –Parallel Axis Theorem –Composite Areas –Principal Second Moments; I xy

18. ME221Lecture #1618 Final Exam Topics Chapter 5: Equilibrium of Rigid Bodies –Equilibrium Equations –Supports –Free Body Diagrams –Two-Force Members –3D Equilibrium

19. ME221Lecture #1619 Final Exam Topics Chapter 7: Internal Forces in Structures –Internal Forces –Shear Forces –Bending Moments –Shear & Bending in Beams

20. ME221Lecture #1620 Final Exam Topics Chapter 6: Analysis of Structures –Planar trusses –Method of joints –Method of sections

21. ME221Lecture #1621 Final Exam Format 4 to 5 Problems At least one each: Internal Forces – Chapter 7 Structures – Chapter 6 Others from previous material

22. ME221Lecture #1622 Other Topics Check Angel to make sure all scores have been properly entered Pick up all old homework & quizzes