ME 221Lecture 251 ME 221 Statics Lecture #25 Sections 5.1 – 5.7

ME 221Lecture 252 Homework #9 Chapter 5 problems: –54, 56, 62, 64, 69, 71 & 73 Due Wednesday, November 6

ME 221Lecture 253 Last Lecture Equilibrium in 3 Dimensions Statically Indeterminate Reactions

ME 221Lecture 254 Equilibrium Equations We have examined 2-dimensional systems and analyzed their equilibrium conditions using the following: The equilibrium conditions we used may be expressed as:

ME 221Lecture 255 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 221Lecture 256 Equilibrium Equations If there are more than 6 unknown forces or couples, the problem is statically indeterminate.

ME 221Lecture 257 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 221Lecture 258 Statically Indeterminate Reactions Underconstrained system Cannot maintain equilibrium Overconstrained systems More unknown forces than equations

ME 221Lecture 259 Equilibrium Example Problems