ME221Lecture #311 ME 221 Statics Lecture #31 Sections 6.6 – 6.7

ME221Lecture #312 Homework #11 Chapter 6 problems: –2, 3, 6 & 7 – Method of Joints –32, 36, 47 & 53 – Method of Sections –68 & 75 Due Wednesday, November 19

ME221Lecture #313 Exam #3 Results Scores posted on Angel Solution posted on Angel See syllabus for regrade policy

ME221Lecture #314 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.

ME221Lecture #315 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

ME221Lecture #316 Using Matrix Notation = Using manual calculations Look for joints with 2 unknowns

ME221Lecture #317 Example 1.2 m 1.2 m 6 kN 3 kN E B A CD 0.9 m

ME221Lecture #318 6 kN 3 kN E B A C D

ME221Lecture # m 12 kN 12 kN 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

ME221Lecture # 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

ME221Lecture #3111 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

ME221Lecture # 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