ME 221 Statics Lecture #25 Sections 5.1 – 5.7 ME 221 Lecture 25 1 Homework #9 Chapter 5 problems: – 54, 56, 62, 64, 69, 71 & 73 • Due Wednesday, November 6 ME 221 Lecture 25 2 Last Lecture • Equilibrium in 3 Dimensions • Statically Indeterminate Reactions ME 221 Lecture 25 3 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 ME 221 x 0 y 0 z 0 M M M Lecture 25 x 0 y 0 z 0 4 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 ME 221 Lecture 25 5 Equilibrium Equations If there are more than 6 unknown forces or couples, the problem is statically indeterminate. ME 221 Lecture 25 6 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 ME 221 Lecture 25 7 Statically Indeterminate Reactions Underconstrained system Cannot maintain equilibrium Overconstrained systems More unknown forces than equations ME 221 Lecture 25 8 Equilibrium Example Problems ME 221 Lecture 25 9