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B Synthesis Lectures on Series ISSN: 2573-3168 A K H Mechanical Engineering T I Y A R O V Solving Practical Engineering Mechanics Problems STATICS Solving Practical Sayavur I. Bakhtiyarov, New Mexico Institute of Mining and Technology Engineering mechanics is one of the fundamental branches of science that is important in S O Engineering the education of professional engineers of any major. Most of the basic engineering courses, L V I such as mechanics of materials, fluid and gas mechanics, machine design, mechatronics, N G acoustics, vibrations, etc. are based on engineering mechanics courses. In order to absorb the P R materials of engineering mechanics, it is not enough to consume just theoretical laws and A C Mechanics Problems theorems—a student also must develop an ability to solve practical problems. Therefore, it T I C is necessary to solve many problems independently. This book is a part of a four-book series A L designed to supplement the engineering mechanics courses. This series instructs and applies E N the principles required to solve practical engineering problems in the following branches of G STATICS I N mechanics: statics, kinematics, dynamics, and advanced kinetics. Each book contains between E E 6 and 8 topics on its specific branch and each topic features 30 problems to be assigned as R I N homework, tests, and/or midterm/final exams with the consent of the instructor. A solution G M of one similar sample problem from each topic is provided. E C This first book contains seven topics of statics, the branch of mechanics concerned with H A the analysis of forces acting on construction systems without an acceleration (a state of the N I static equilibrium). The book targets the undergraduate students of the sophomore/junior C S level majoring in science and engineering. The author welcomes all feedback/comments from P R O the reader. Please feel free to contact him at [email protected]. B L E M S : S Sayavur I. Bakhtiyarov T A T I C S ABOUT SYNTHESIS This volume is a printed version of a work that appears in the Synthesis Digital Library of Engineering and Computer Science. Synthesis lectures provide concise original presentations of important research and development topics, published quickly in digital and print formats. For M more information, visit our website: http://store.morganclaypool.com O R G A N & C L Synthesis Lectures on A Y PO Mechanical Engineering O store.morganclaypool.com L Solving Practical Engineering Mechanics Problems: Statics iii Synthesis Lectures on Mechanical Engineering Synthesis Lectures on Mechanical Engineering series publishes 60–150 page publications pertaining to this diverse discipline of mechanical engineering. The series presents Lectures written for an audience of researchers, industry engineers, undergraduate and graduate students. Additional Synthesis series will be developed covering key areas within mechanical engineering. Solving Practical Engineering Mechanics Problems: Statics Sayavur I. Bakhtiyarov October 2017 Resistance Spot Welding: Fundamentals and Applications for the Automotive Industry Menachem Kimchi and David H. Phillips October 2017 Unmanned Aircraft Design: Review of Fundamentals Mohammad Sadraey September 2017 Introduction to Refrigeration and Air Conditioning Systems: Theory and Applications Allan Kirkpatrick September 2017 MEMS Barometers Toward Vertical Position Detection: Background Theory, System Prototyping, and Measure- ment Analysis Dimosthenis E. Bolanakis May 2017 Vehicle Suspension System Technology and Design Avesta Goodarzi, Amir Khajepour May 2017 Engineering Finite Element Analysis Ramana M. Pidaparti May 2017 Copyright © 2018 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Solving Practical Engineering Mechanics Problems: Statics Sayavur I. Bakhtiyarov www.morganclaypool.com ISBN: 9781681731889 print ISBN: 9781681731896 ebook DOI 10.2200/S00799ED1V01Y201709MEC008 A Publication in the Morgan & Claypool Publishers series SYNTHESIS LECTURES ON MECHANICAL ENGINEERING, #8 Series ISSN: 2573-3168 Print 2573-3176 Electronic Solving Practical Engineering Mechanics Problems: Statics Sayavur I. Bakhtiyarov New Mexico Institute of Mining and Technology SYNTHESIS LECTURES ON MECHANICAL ENGINEERING #8 M &C MORGAN & CLAYPOOL PUBLISHERS vi ABSTRACT Engineering mechanics is one of the fundamental branches of science that is important in the education of professional engineers of any major. Most of the basic engineering courses, such as mechanics of materials, fluid and gas mechanics, machine design, mechatronics, acoustics, vibrations, etc. are based on engineering mechanics courses. In order to absorb the materials of engineering mechanics, it is not enough to consume just theoretical laws and theorems—a student also must develop an ability to solve practical problems. Therefore, it is necessary to solve many problems independently. This book is a part of a four-book series designed to supplement the engineering mechanics courses. This series instructs and applies the principles required to solve practical engineering problems in the following branches of mechanics: statics, kinematics, dynamics, and advanced kinetics. Each book contains between 6 and 8 topics on its specific branch and each topic features 30 problems to be assigned as homework, tests, and/or midterm/ final exams with the consent of the instructor. A solution of one similar sample problem from each topic is provided. This first book contains seven topics of statics, the branch of mechanics concerned with the analysis of forces acting on construction systems without an acceleration (a state of the static equilibrium). The book targets the undergraduate students of the sophomore/junior level majoring in science and engineering. The author welcomes all feedback/comments from the reader. Please feel free to contact him at [email protected]. KEYWORDS force, moment, torque, gravity, equilibrium, center of gravity vii Contents .................................................... . . . . . . . . . Acknowledgments ix ........................................................... . . . . . . . . . 1 Topic S-1 1 1.1 Determination of the Reaction Forces of Supports for Rigid Body . . . . . . . . . . . . . . . . . . . . . 1 1.2 Sample Problem ............................................................ 15 1.3 Solution .................................................................. 16 ........................................................... . . . . . . . . . 2 Topic S-2 19 2.1 Application of the Method of Joints to Find Unknown Forces in a Plane (2D) Truss Structure ............................................................. 19 2.2 Sample Problem ............................................................ 32 2.3 Solution .................................................................. 32 2.3.1 Determining Reaction Forces by Analytical Method . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.2 Determining the Forces in the Truss Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ........................................................... . . . . . . . . . 3 Topic S-3 37 3.1 Determination of Reaction Forces of Supports for Composite Stud . . . . . . . . . . . . . . . . . . . . 37 3.2 Sample Problem ............................................................ 45 3.3 Solution .................................................................. 45 ........................................................... . . . . . . . . . 4 Topic S-4 49 4.1 Determination of Reaction Forces of Supports for Composite Construction (System of Two Bodies) ...................................................... 49 4.2 Sample Problem ............................................................ 62 4.3 Solution .................................................................. 62 ........................................................... . . . . . . . . . 5 Topic S-5 67 5.1 Determination of Reaction Forces of Supports for Composite Construction (System of Three Bodies) ..................................................... 67 5.2 Sample Problem ............................................................ 81 5.3 Solution .................................................................. 81 ........................................................... . . . . . . . . . 6 Topic S-6 85 6.1 Determination of reaction forces of rods supporting rectangular plate . . . . . . . . . . . . . . . . . . 85 6.2 Sample Problem ........................................................... 100 6.3 Solution ................................................................. 101 ........................................................... . . . . . . . . 7 Topic S-7 105 7.1 Determination of Center of Gravity ........................................... 105 7.2 Sample Problem ........................................................... 121 7.3 Solution ................................................................. 122 .................................................... . . . . . . . . Author Biography 125 ix Acknowledgments The author acknowledges that this work is essentially a translation and a revision of selected problems provided by Professor A. A. Yablonski (Collection of Problems for Course Projects in Theoretical Mechanics, 2nd ed., Vischaya Shkola Publishers, 1972, in Russian). The author intended to introduce this unique work to western academia, which is the product of material covered by him in many classes over a period of four decades in a number of universities and colleges.