PowerPoint PresentationHomework #8Homework #9Quiz #5Last LectureTodayEquilibrium EquationsSlide 8Slide 9Solving Equilibrium EquationsStatically Indeterminate ReactionsSlide 12ME 221 Lecture 23 1ME 221 StaticsLecture #23Sections 5.6 & 5.7ME 221 Lecture 23 2Homework #8•Chapter 9 problems:–42, 43, 50 & 55•Chapter 5 problems:–11, 13, 16, 20, 24 & 25•Due TodayME 221 Lecture 23 3Homework #9Chapter 5 problems:–53, 54, 56, 62, 64, 69, 71 & 73•Due Friday, October 31ME 221 Lecture 23 4Quiz #5TodayME 221 Lecture 23 5Last Lecture•Equilibrium equations•Free body diagrams•2- & 3-force members•Modeling supportsME 221 Lecture 23 6Today•Equilibrium in 3 Dimensions•Statically Indeterminate ReactionsME 221 Lecture 23 7Equilibrium EquationsWe have examined 2-dimensional systems and analyzed their equilibrium conditions using the following:~ ~0 and 0F M  The equilibrium conditions we used may be expressed as:0 00 00 0x xy yz zF MF MF M      ME 221 Lecture 23 8Equilibrium EquationsFor 3-dimensional systems, we use the same equilibrium equations, except we write them in vector form:The moment equation may also be written as:  0M & 0F oWhere the couple C is the sum of all applied couples on the body 0C )F x r(ME 221 Lecture 23 9Equilibrium EquationsIf there are more than 6 unknown forces or couples, the problem is statically indeterminate.ME 221 Lecture 23 10Solving Equilibrium EquationsDraw a proper free body diagramWrite each force and couple as a vectorDraw position vectors from the origin to the line of action of each force Write the vector equations of static equilibrium – 6 equations, 6 unknownsME 221 Lecture 23 11Statically Indeterminate ReactionsUnderconstrained systemCannot maintain equilibriumOverconstrained systemsMore unknown forces than equationsME 221 Lecture 23 12Quiz