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Truss Analysis and Exam Preparation

Learn truss analysis using Method of Joints & Matrix Notation, topic coverage for the final exam, and solve typical problems. Trusses composed of slender straight pieces connected by frictionless pins. Final exam topics include Vectors, Rigid Bodies, Equilibrium, Internal Forces.

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Truss Analysis and Exam Preparation

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  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

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