ME221Lecture 131 ME 221 Statics Lecture #13 Sections 5.1 – 5.7 Exam #2 Review

ME221Lecture 132 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 Wednesday, June 23

ME221Lecture 133 Homework #6 Chapter 7 problems: –6, 19 & 26 Chapter 6 problems –3 & 6 –Due Monday, June 28 MatLab Group Problems –7.19, 7.26 & 6.15 –Due Monday, June 28

ME221Lecture 134 Exam #2 Monday, June 21 Details at end of lecture

ME221Lecture 135 Chapter 5 Equilibrium of Rigid Bodies

ME221Lecture 136 Last Lecture Equilibrium in 3 Dimensions Statically Indeterminate Reactions

ME221Lecture 137 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:

ME221Lecture 138 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

ME221Lecture 139 Equilibrium Equations If there are more than 6 unknown forces or couples, the problem is statically indeterminate.

ME221Lecture 1310 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

ME221Lecture 1311 Statically Indeterminate Reactions Underconstrained system Cannot maintain equilibrium Overconstrained systems More unknown forces than equations

ME221Lecture 1312 Equilibrium Example Problems

ME221Lecture 1313 Exam #2  Chapter 4 Center of mass Centroids of areas and volumes Centroids of composite bodies Distributed loads on beams

ME221Lecture 1314 Exam #2 Chapter 9: Moments of Inertia –Second Moment of Area; I xx & I yy –Polar Moments; J 0z –Parallel Axis Theorem –Composite Areas –Principal Second Moments –Product Moments; I xy –Mohr’s Circle – I max & I min

ME221Lecture 1315 Exam #2 Chapter 5: Equilibrium of Rigid Bodies –Equilibrium Equations –Supports –Free Body Diagrams –Two-Force Members –3D Equilibrium