PowerPoint PresentationHomework #11Exam #3 ResultsTrussesSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10Trusses: 3-D (Space Trusses)3-D Truss MethodologyME221 Lecture #31 1ME 221 StaticsLecture #31Sections 6.6 – 6.7ME221 Lecture #31 2Homework #11Chapter 6 problems:–2, 3, 6 & 7 – Method of Joints–32, 36, 47 & 53 – Method of Sections–68 & 75 •Due Wednesday, November 19ME221 Lecture #31 3Exam #3 ResultsScores posted on AngelSolution posted on AngelSee syllabus for regrade policyME221 Lecture #31 4TrussesComposed 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 #31 5Analysis 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 #31 6Using Matrix Notation100sin00000cos10000sin0sin000cos0cos01000sin00101cosCyCxByBxAyAxPPPPPPyyxBCACABCAAFFF=-1Using manual calculationsLook for joints with 2 unknownsME221 Lecture #31 7 Example 1.2 m 1.2 m6 kN3 kNEBAC D0.9 mME221 Lecture #31 86 kN3 kNEBACD4416164499151555ME221 Lecture #31 91.8 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 #31 101.8 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 #31 11Trusses: 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 #31 123-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