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mechanic

University Physics with Modern Physics with Mastering Physics (11th Edition)

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Copyright © 1993-2001, Hugh Jack Engineer On a Disk Overview: This note set is part of a larger collection of materials available at http://claymore.engi- neer.gvsu.edu. You are welcome to use the material under the license provided at http://clay- more.engineer.gvsu.edu/eod/global/copyrght.html. As always any feedback you can provide will be welcomed. This section last updated: April 28, 2002 Copyright © 1993-2002, Hugh Jack email: [email protected] phone: (616) 771-6755 fax: (616) 336-7215
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page 2 1. TABLE OF CONTENTS TABLE OF CONTENTS .......................................................................................................... 2 MECHANICAL DESIGN ........................................................................................................ 9 BASIC PHILOSOPHY - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 9 TYPICAL MECHANICAL FUNCTIONS - - - - - - - - - - - - - - - - - - - - - - - - - - - - 9 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 FORCES ................................................................................................................................. 11 SOME BASIC CONCEPTS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12 VECTOR AND SCALAR FORCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 13 EQUILLIBRIUM .................................................................................................................... 38 THE BASIC EQUATIONS OF STATICS - - - - - - - - - - - - - - - - - - - - - - - - - - - - 39 FREE BODY DIAGRAMS (FBD) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 44 PRACTICE PROBLEMS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 51 MOMENTS ............................................................................................................................ 53 CALCULATING SCALAR AND VECTOR MOMENTS - - - - - - - - - - - - - - - - - 56 FORCE COUPLES TO MAKE CENTERLESS MOMENTS - - - - - - - - - - - - - - - 64 MECHANISMS ...................................................................................................................... 79 REACTIONS AND SUPPORTS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 79 EQUILLIBRIUM OF FORCES AND MOMENTS - - - - - - - - - - - - - - - - - - - - - - 82 SPECIAL CASES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 90 STATICALLY INDETERMINATE - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 91 TRUSSES AND FRAMES ..................................................................................................... 93 WHAT ARE TRUSSES? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 93 STABILITY OF TRUSSES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 99 THE METHOD OF JOINTS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 102 THE METHOD OF SECTIONS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 114 METHOD OF MEMBERS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 122 SUMMARY - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 132 DRY STATIC FRICTION .................................................................................................... 132 THE BASIC PHYSICS OF FRICTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - 132 APPLICATIONS OF FRICTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 137 FORCES ............................................................................................................................... 150 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 150 SOME BASIC CONCEPTS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 151 VECTOR VS. SCALAR QUANTITIES - - - - - - - - - - - - - - - - - - - - - - - - - - - - 152 MATH REVIEW - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 153 RECTANGULAR FORM OF VECTORS - - - - - - - - - - - - - - - - - - - - - - - - - - - 158 POLAR FORM OF VECTORS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 159 EQUILLIBRIUM .................................................................................................................. 187 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 187 THE BASIC EQUATIONS OF STATICS - - - - - - - - - - - - - - - - - - - - - - - - - - - 187 FREE BODY DIAGRAMS (FBD) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 196 PRACTICE PROBLEMS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 205 STRESS ................................................................................................................................ 208 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 208
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page 3 TYPES OF STRESS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 210 STRESS ANALYSIS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 214 STRAIN CAUSED BY AXIAL LOADS - - - - - - - - - - - - - - - - - - - - - - - - - - - 219 STRESS STRAIN CURVES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 220 ANALYSIS OF MEMBERS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 222 GENERALIZED STRESS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 225 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 229 STRESS ON OBLIQUE PLANES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 229 SHEAR STRAIN - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 232 POISSON’S RATIO - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 236 GENERALIZED HOOKES LAW - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 238 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 239 MOMENTS .......................................................................................................................... 240 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 240 CALCULATING SCALAR MOMENTS - - - - - - - - - - - - - - - - - - - - - - - - - - - 244 CALCULATING VECTOR MOMENTS - - - - - - - - - - - - - - - - - - - - - - - - - - - 247 MOMENTS ABOUT AN AXIS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 251 EQUILLIBRIUM OF MOMENTS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 256 FORCE COUPLES TO MAKE CENTERLESS MOMENTS - - - - - - - - - - - - - - 260 TORSION ............................................................................................................................. 276 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 276 THE RELATIONSHIP BETWEEN STRESS AND STRAIN IN TORSION - - - - 280 PRACTICE PROBLEMS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 285 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 286 MASS PROPERTIES ........................................................................................................... 287 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 287 CENTRE OF MASS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 290 CENTROIDS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 293 FORCES AND MOMENTS ON RIGID BODIES .............................................................. 311 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 311 REACTIONS AND SUPPORTS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 311 EQUILLIBRIUM OF FORCES AND MOMENTS - - - - - - - - - - - - - - - - - - - - - 314 SPECIAL CASES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 323 STATICALLY INDETERMINATE - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 324 TRUSSES AND FRAMES ................................................................................................... 331 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 331 WHAT ARE TRUSSES? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 331 STABILITY OF TRUSSES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 336 THE METHOD OF JOINTS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 339 THE METHOD OF SECTIONS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 352 ADDITIONAL TOPICS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 361 STRESS FAILURE .............................................................................................................. 363 FACTOR OF SAFETY - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 363 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 367 STRAIN FAILURE .............................................................................................................. 368 POISSON’S RATIO - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 369
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page 4 GENERALIZED HOOKES LAW - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 372 STRESS CONCENTRATIONS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 373 TORSION STRESS CONCENTRATIONS - - - - - - - - - - - - - - - - - - - - - - - - - - 379 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 380 METHOD OF MEMBERS ................................................................................................... 381 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 381 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 391 SUMMARY - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 391 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 391 INTERNAL FORCES IN MEMBERS ................................................................................. 392 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 392 PRACTICE PROBLEMS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 405 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 409 MOMENTS OF INERTIA ................................................................................................... 410 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 410 STRESSES IN BEAMS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 410 MOMENT CURVATURE IN BEAMS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 412 EVALUATING THE SECOND MOMENT OF INERTIA - - - - - - - - - - - - - - - 414 MOMENTS OF INERTIAS B COMPOSITE AREAS - - - - - - - - - - - - - - - - - - 415 POLAR MOMENT OF INERTIA - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 419 REVIEW OF BASIC CALCUATIONS - - - - - - - - - - - - - - - - - - - - - - - - - - - - 421 PRODUCT OF INERTIA - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 433 REFERENCES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 435 PURE BENDING ................................................................................................................. 436 INTRODUCTION - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 436 TRANSVERSE SHEAR - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 440
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