ME 221 Statics Lecture #12 Sections 5.6 – 5.7 ME221 Lecture 12 1 Homework #5 • Chapter 9 problem: – 43 • Chapter 5 problems – 11, 20, 56 & 69 – Due Monday, June 21 • MatLab Group Problems – 5.22, 5.37 & 5.58 – Due Monday, June 21 ME221 Lecture 12 2 Quiz #5 Today ME221 Lecture 12 3 Exam #2 Monday, June 21 ME221 Lecture 12 4 Chapter 5 Equilibrium of Rigid Bodies ME221 Lecture 12 5 Last Lecture • • • • ME221 Equilibrium equations Free body diagrams 2- & 3-force members Modeling supports Lecture 12 6 Today • Equilibrium in 3 Dimensions • Statically Indeterminate Reactions ME221 Lecture 12 7 Equilibrium Equations We have examined 2-dimensional systems and analyzed their equilibrium conditions using the following: F 0 ~ and M 0 ~ The equilibrium conditions we used may be expressed as: F F F ME221 x 0 y 0 z 0 M M M Lecture 12 x 0 y 0 z 0 8 Equilibrium Equations For 3-dimensional systems, we use the same equilibrium equations, except we write them in vector form: The moment equation may also be written as: Where the couple C is the sum of all applied couples on the body ME221 Lecture 12 9 Equilibrium Equations If there are more than 6 unknown forces or couples, the problem is statically indeterminate. ME221 Lecture 12 10 Solving Equilibrium Equations Draw a proper free body diagram Write each force and couple as a vector Draw position vectors from the origin to the line of action of each force Write the vector equations of static equilibrium – 6 equations, 6 unknowns ME221 Lecture 12 11 Statically Indeterminate Reactions Underconstrained system Cannot maintain equilibrium Overconstrained systems More unknown forces than equations ME221 Lecture 12 12 Example ME221 Lecture 12 13 Quiz #5 ME221 Lecture 12 14