PowerPoint PresentationHomework #6TrussesSlide 4Slide 5Slide 6Slide 7Slide 8Slide 9Trusses: 3-D (Space Trusses)3-D Truss MethodologyExampleFinal ExamFinal Exam TopicsSlide 15Slide 16Slide 17Slide 18Slide 19Slide 20Final Exam FormatOther TopicsME221 Lecture #16 1ME 221 StaticsLecture #16Sections 6.6 – 6.7Final Exam ReviewME221 Lecture #16 2Homework #6•Chapter 7 problems:–6, 19 & 26•Chapter 6 problems–3 & 6–Due Today•MatLab Group Problems–7.19, 7.26 & 6.15 –Due TodayME221 Lecture #16 3TrussesComposed 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.ME221 Lecture #16 4Analysis of Trusses Using the Method of JointsAyAxPAxPAYPByPBxPCyPCxCyABC   We need to solve for:(1) - Internal forces FAB, FAC, and FCA(2) - ReactionsAx, Ay and CyME221 Lecture #16 5Using Matrix Notation100sin00000cos10000sin0sin000cos0cos01000sin00101cosCyCxByBxAyAxPPPPPPyyxBCACABCAAFFF=-1Using manual calculationsLook for joints with 2 unknownsME221 Lecture #16 6 Example 1.2 m 1.2 m6 kN3 kNEBAC D0.9 mME221 Lecture #16 76 kN3 kNEBACD4416164499151555ME221 Lecture #16 81.8 m 12 kN 12 kN4 @ 2.4 m=9.6 mB D F H J A C E G IMethod of SectioningIf 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 FHME221 Lecture #16 91.8 m 12 kN 12 kNB D F H J A C E G IFGEFGFFHF1.8 m 12 kN 12 kNB D F H J A C E G IFEGFFG FEH  000AnyptyxMFFME221 Lecture #16 10Trusses: 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 & socketME221 Lecture #16 113-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 forcesME221 Lecture #16 12ExampleME221 Lecture #16 13Final ExamWednesday, June 30, 10:20am25% of course gradeME221 Lecture #16 14Final Exam TopicsChapter 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 problemsME221 Lecture #16 15Final Exam TopicsChapter 3: Rigid Bodies–Calculating moments–Cross products–Moment of force about an axis–Moment of a couple–Equivalent force systemsME221 Lecture #16 16Final Exam TopicsChapter 4: Distributed Forces–Center of mass–Centroids of areas & volumes–Centroids of composite bodies–Distributed loads on beamsME221 Lecture #16 17Final Exam TopicsChapter 9: Moments of Inertia–Second Moment of Area; Ixx & Iyy–Polar Moments; J0z–Parallel Axis Theorem–Composite Areas–Principal Second Moments; IxyME221 Lecture #16 18Final Exam TopicsChapter 5: Equilibrium of Rigid Bodies–Equilibrium Equations–Supports–Free Body Diagrams–Two-Force Members–3D EquilibriumME221 Lecture #16 19Final Exam TopicsChapter 7: Internal Forces in Structures–Internal Forces–Shear Forces–Bending Moments–Shear & Bending in BeamsME221 Lecture #16 20Final Exam TopicsChapter 6: Analysis of Structures–Planar trusses–Method of joints–Method of sectionsME221 Lecture #16 21Final Exam Format4 to 5 ProblemsAt least one each:Internal Forces – Chapter 7Structures – Chapter 6Others from previous materialME221 Lecture #16 22Other TopicsCheck Angel to make sure all scores have been properly enteredPick up all old homework &