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Valentin Molotnikov Antonina Molotnikova Theoretical and Applied Mechanics Theoretical and Applied Mechanics Valentin Molotnikov • Antonina Molotnikova Theoretical and Applied Mechanics ValentinMolotnikov AntoninaMolotnikova DonStateTechnicalUniversity RostovInstitutefortheDefenseof Rostov-on-Don,Russia EntrepreneurProtection Rostov-on-don,Russia ISBN978-3-031-09311-1 ISBN978-3-031-09312-8 (eBook) https://doi.org/10.1007/978-3-031-09312-8 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland DedicatedtotheblessedmemoryofBoris AnisimovichBondarenko(1923–2017)—an outstanding mathematicianandmechanic,a talentedteacherandorganizerofscience, DoctorofPhysicalandMathematical Sciences,andacademicianoftheAcademyof SciencesoftheRepublicofUzbekistan. ValentinandAntonina Abstract The textbook outlines the fundamentals of theoretical and applied mechanics, supplementedbyselectedsectionsfromthedevelopmentsofrecentdecades(drone flight, car variators, etc.). The book is designed to be studied during one to two semesters in the training of bachelors and masters in the direction of “Engi- neering.” The course includes the main sections of the disciplines “Theoretical Mechanics,” “Theory of Mechanisms and Machines,” “Strength of Materials,” “Machine Parts and Design Fundamentals,” “Interchangeability, Standardization, and Technical Measurements,” and “Introduction to CAD of based AutoCAD – AutoLISP”. Such a representative set of disciplines allows the book to be used by students of other technical and technology majors in each of these disciplines. The conciseness makes the textbook a valuable aid in conditions of limited time for the preparation of both during a semester and a session. In addition to being concise, this differs from existing textbooks in its presentation of the state of the artinmechanics,demonstrationofengineeringapplicationscomputerapplications (MathCad,COSMOSWorks,Inkscape,AutoCAD,AutoLISP,etc.),presentationof updateddataonengineeringmaterials-fromcompositestotheprospectsgraphene. There are examples of designs of units in modern machines (combine harvester “Don,”thecar“Infiniti”etc.),andalsothereisinformationaboutnationalstandards in mechanical engineering. Examples are given of both simple and complex engineeringcalculations.Attheendofeachchapterarequestionsforself-checking andmultivariateproblemsforexercises. vii Acknowledgements The authors express their gratitude to Doctor of Physical and Mathematical Sciences,memberoftheRussianNationalCommitteeofIUTAMprof.L.M.Zubov and prof. V. P. Zabrodin for selfless work on reviewing the manuscript. Special thankstooursonZaur,whoinspiredustocreatethisbookforhishelpfuladviceon book design and, as a native speaker, for taking on much of the communication with Springer. We also thank Professor V. G. Malinin, Doctor of Physical and MathematicalSciences,forhishelpintranslatingthisbookintoEnglish. ix Introduction Modern scientific and technological progress and the rapid development of high technologieshaveledtotheneedtoincludeinthecurriculaofeducationalinstitu- tions many new disciplines,theknowledge of which isbecoming mandatory fora modern specialist. Although the duration of training is limited, the modernization of curricula inevitably leads to a reduction in the number of hours allocated for thedevelopmentoffundamentalgeneraltechnicaldisciplines,includingtheoretical and applied mechanics. The desire to preserve the completeness of the course, and the rigor and clarity of the main provisions, combined with the clarity of the presentationofthematerialandthedemonstrationofitsapplicationintechnology, promptedtheauthorstowriteashortbutcompletetextbook. The concentrated presentation of the course made it necessary to exclude from consideration a number of issues traditionally presented in courses of theoretical mechanics. Some of them seem to be utilitarian (e.g., graphostatics), while others are applications of the main theorems of theoretical mechanics (fluctuations of a materialpoint)anddonotcontainfundamentallynewmaterialcomparedtowhatis studiedinschoolphysicscourses. Atthesametime,tosolvemanyproblemsofmoderntechnology,sometimesthe methodsofthetraditionalcourseoftheoreticalmechanicsarenotenough,anditis necessary to use the general methods of analytical mechanics and control theory. Inthisregard,theauthorconsidereditappropriatetomoveawayfromthetradition andincludeinthebookmaterialonbothclassicalandthelatestvariationalmethods of mechanics. And if the study of this material is still provided for only by a few educationalstandardsformaster’sprograms,thenitcanbeusedinoptionalclasses. In order not to overload the book with complex mathematical constructions, when presenting this material, the authors deliberately never discussed the most important question of the existence and uniqueness of solutions to the formulated problems. In recent decades, almost all over the world, a wave of reforms in the field of education has unfolded. As a result, most higher education institutions were transformedintouniversitiesandacademies.Thiscircumstanceobligestheauthors oftextbookstoemphasizethestyleborderingonmonographic.Howfartheauthors xi xii Introduction succeeded,thereaderscanjudge.Atthesametime,theauthorshaveretainedcertain classicalelementsofthetextbook.Forexample,attheendofeachchapter,thereare questionsforself-controlandmultivariatetasksforexercises. Thebookisbasedonlecturesgivenbytheauthorsinrecentdecadesinindustrial, military,andagriculturaluniversitiesoftheSovietUnionandRussia. TheauthorsexpresstheirgratitudetotheCandidateofTechnicalSciences,assoc. VeselovskyV.A.,whocarefullyreadthemanuscriptandmadeanumberofvaluable commentsthatweretakenintoaccountinthefinalversionofthemanuscript. Wearegratefulinadvancetoreaderswhowillsendfeedbackorsuggestionstoei- theroftheemailaddresses:[email protected]@gmail.com. Contents PartI TheoreticalMechanics 1 Statics........................................................................ 3 1.1 Introduction........................................................... 3 1.2 TheSubjectandTasksofTheoreticalMechanics .................. 5 1.3 Strength.Forcesyste................................................. 6 1.4 AxiomsofTheoreticalMechanics................................... 8 1.5 ConnectionsandTheirReactions.................................... 10 1.5.1 ClassificationofConstraints.............................. 13 1.6 ConditionsfortheEquilibriumofConvergingForces.............. 14 1.7 ASystemofParallelForces:PowerPairs........................... 14 1.8 MomentofForceRelativetothePointandAxis................... 16 1.9 BasicTheoremofStatics ............................................ 20 1.10 EquilibriumofanArbitrarySystemofForces...................... 22 1.11 SolvingProblemsontheBalanceofSystemsofForces ........... 24 1.11.1 GeneralComment......................................... 24 1.11.2 Example1 ................................................. 25 1.11.3 Example2 ................................................. 26 1.11.4 Example3 ................................................. 28 1.12 TrussCalculation..................................................... 31 1.12.1 CalculationofaTriangularCantileverTruss ............ 33 1.12.2 CalculationofaSymmetricalBridgeGirder............. 36 1.13 ComputerCalculationofTruss...................................... 37 1.14 CenterofParallelForces............................................. 39 1.15 TheCenterofGravityofaRigidBody ............................. 41 Self-TestQuestions .......................................................... 43 References.................................................................... 52 2 Kinematics................................................................... 53 2.1 WaystoSettheMovement .......................................... 53 2.2 SpeedandAccelerationofthePoint ................................ 57 xiii