"Mechanics is one ofthe branches ofphysics in which the number ofprinciples is at once very few and very rich in useful consequences. On the other hand, there are few sciences which have required so much thought-the conquest of a few axioms has taken more than 2000 years. "-Rene Dugas, A History 0/ Mechanics Introductory courses in engineering mechanics (statics and dynamics) are generally found very early in engineering curricula. As such, they should provide the student with a thorough background in the basic fundamentals that form the foundation for subsequent work in engi­ neering analysis and design. Consequently, our primary goal in writing Statics for Engineers and Dynamics for Engineers has been to develop the fundamental principles of engineering mechanics in a manner that the student can readily comprehend. With this comprehension, the student thus acquires the tools that would enable him/her to think through the solution ofmany types ofengineering problems using logic and sound judgment based upon fundamental principles. Approach We have made every effort to present the material in a concise but clear manner. Each subject is presented in one or more sections fol­ lowed by one or more examples, the solutions for which are presented in a detailed fashion with frequent reference to the basic underlying principles. A set of problems is provided for use in homework assign­ ments.

"Mechanics is one ofthe branches ofphysics in which the number ofprinciples is at once very few and very rich in useful consequences. On the other hand, there are few sciences which have required so much thought-the conquest of a few axioms has taken more than 2000 years. "-Rene Dugas, A History 0/ Mechanics Introductory courses in engineering mechanics (statics and dynamics) are generally found very early in engineering curricula. As such, they should provide the student with a thorough background in the basic fundamentals that form the foundation for subsequent work in engi­ neering analysis and design. Consequently, our primary goal in writing Statics for Engineers and Dynamics for Engineers has been to develop the fundamental principles of engineering mechanics in a manner that the student can readily comprehend. With this comprehension, the student thus acquires the tools that would enable him/her to think through the solution ofmany types ofengineering problems using logic and sound judgment based upon fundamental principles. Approach We have made every effort to present the material in a concise but clear manner. Each subject is presented in one or more sections fol­ lowed by one or more examples, the solutions for which are presented in a detailed fashion with frequent reference to the basic underlying principles. A set of problems is provided for use in homework assign­ ments.

4. 2 Solid Circular Shafts-Angle of Twist and Shearing Stresses 159 4. 3 Hollow Circular Shafts-Angle of Twist and Shearing Stresses 166 4. 4 Principal Stresses and Strains Associated with Torsion 173 4. 5 Analytical and Experimental Solutions for Torsion of Members of Noncircular Cross Sections 179 4. 6 Shearing Stress-Strain Properties 188 *4. 7 Computer Applications 195 5 Stresses in Beams 198 5. 1 Introduction 198 5. 2 Review of Properties of Areas 198 5. 3 Flexural Stresses due to Symmetric Bending of Beams 211 5. 4 Shear Stresses in Symmetrically Loaded Beams 230 *5. 5 Flexural Stresses due to Unsymmetric Bending of Beams 248 *5. 6 Computer Applications 258 Deflections of Beams 265 I 6. 1 Introduction 265 6. 2 Moment-Curvature Relationship 266 6. 3 Beam Deflections-Two Successive Integrations 268 6. 4 Derivatives of the Elastic Curve Equation and Their Physical Significance 280 6. 5 Beam Deflections-The Method of Superposition 290 6. 6 Construction of Moment Diagrams by Cantilever Parts 299 6. 7 Beam Deflections-The Area-Moment Method 302 *6. 8 Beam Deflections-Singularity Functions 319 *6. 9 Beam Deflections-Castigliano''s Second Theorem 324 *6. 10 Computer Applications 332 7 Combined Stresses and Theories of Failure 336 7. 1 Introduction 336 7. 2 Axial and Torsional Stresses 336 Axial and Flexural Stresses 342 7. 3 Torsional and Flexural Stresses 352 7. 4 7. 5 Torsional, Flexural, and Axial Stresses 358 *7. 6 Theories of Failure 365 Computer Applications 378 *7.

"Mechanics is one ofthe branches ofphysics in which the number ofprinciples is at once very few and very rich in useful consequences. On the other hand, there are few sciences which have required so much thought-the conquest of a few axioms has taken more than 2000 years. "-Rene Dugas, A History 0/ Mechanics Introductory courses in engineering mechanics (statics and dynamics) are generally found very early in engineering curricula. As such, they should provide the student with a thorough background in the basic fundamentals that form the foundation for subsequent work in engi­ neering analysis and design. Consequently, our primary goal in writing Statics for Engineers and Dynamics for Engineers has been to develop the fundamental principles of engineering mechanics in a manner that the student can readily comprehend. With this comprehension, the student thus acquires the tools that would enable him/her to think through the solution ofmany types ofengineering problems using logic and sound judgment based upon fundamental principles. Approach We have made every effort to present the material in a concise but clear manner. Each subject is presented in one or more sections fol­ lowed by one or more examples, the solutions for which are presented in a detailed fashion with frequent reference to the basic underlying principles. A set of problems is provided for use in homework assign­ ments.

"Mechanics is one ofthe branches ofphysics in which the number ofprinciples is at once very few and very rich in useful consequences. On the other hand, there are few sciences which have required so much thought-the conquest of a few axioms has taken more than 2000 years. "-Rene Dugas, A History 0/ Mechanics Introductory courses in engineering mechanics (statics and dynamics) are generally found very early in engineering curricula. As such, they should provide the student with a thorough background in the basic fundamentals that form the foundation for subsequent work in engi­ neering analysis and design. Consequently, our primary goal in writing Statics for Engineers and Dynamics for Engineers has been to develop the fundamental principles of engineering mechanics in a manner that the student can readily comprehend. With this comprehension, the student thus acquires the tools that would enable him/her to think through the solution ofmany types ofengineering problems using logic and sound judgment based upon fundamental principles. Approach We have made every effort to present the material in a concise but clear manner. Each subject is presented in one or more sections fol­ lowed by one or more examples, the solutions for which are presented in a detailed fashion with frequent reference to the basic underlying principles. A set of problems is provided for use in homework assign­ ments.

"Mechanics is one ofthe branches ofphysics in which the number ofprinciples is at once very few and very rich in useful consequences. On the other hand, there are few sciences which have required so much thought-the conquest of a few axioms has taken more than 2000 years. "-Rene Dugas, A History 0/ Mechanics Introductory courses in engineering mechanics (statics and dynamics) are generally found very early in engineering curricula. As such, they should provide the student with a thorough background in the basic fundamentals that form the foundation for subsequent work in engi­ neering analysis and design. Consequently, our primary goal in writing Statics for Engineers and Dynamics for Engineers has been to develop the fundamental principles of engineering mechanics in a manner that the student can readily comprehend. With this comprehension, the student thus acquires the tools that would enable him/her to think through the solution ofmany types ofengineering problems using logic and sound judgment based upon fundamental principles. Approach We have made every effort to present the material in a concise but clear manner. Each subject is presented in one or more sections fol­ lowed by one or more examples, the solutions for which are presented in a detailed fashion with frequent reference to the basic underlying principles. A set of problems is provided for use in homework assign­ ments.

4. 2 Solid Circular Shafts-Angle of Twist and Shearing Stresses 159 4. 3 Hollow Circular Shafts-Angle of Twist and Shearing Stresses 166 4. 4 Principal Stresses and Strains Associated with Torsion 173 4. 5 Analytical and Experimental Solutions for Torsion of Members of Noncircular Cross Sections 179 4. 6 Shearing Stress-Strain Properties 188 *4. 7 Computer Applications 195 5 Stresses in Beams 198 5. 1 Introduction 198 5. 2 Review of Properties of Areas 198 5. 3 Flexural Stresses due to Symmetric Bending of Beams 211 5. 4 Shear Stresses in Symmetrically Loaded Beams 230 *5. 5 Flexural Stresses due to Unsymmetric Bending of Beams 248 *5. 6 Computer Applications 258 Deflections of Beams 265 I 6. 1 Introduction 265 6. 2 Moment-Curvature Relationship 266 6. 3 Beam Deflections-Two Successive Integrations 268 6. 4 Derivatives of the Elastic Curve Equation and Their Physical Significance 280 6. 5 Beam Deflections-The Method of Superposition 290 6. 6 Construction of Moment Diagrams by Cantilever Parts 299 6. 7 Beam Deflections-The Area-Moment Method 302 *6. 8 Beam Deflections-Singularity Functions 319 *6. 9 Beam Deflections-Castigliano''s Second Theorem 324 *6. 10 Computer Applications 332 7 Combined Stresses and Theories of Failure 336 7. 1 Introduction 336 7. 2 Axial and Torsional Stresses 336 Axial and Flexural Stresses 342 7. 3 Torsional and Flexural Stresses 352 7. 4 7. 5 Torsional, Flexural, and Axial Stresses 358 *7. 6 Theories of Failure 365 Computer Applications 378 *7.

"Mechanics is one ofthe branches ofphysics in which the number ofprinciples is at once very few and very rich in useful consequences. On the other hand, there are few sciences which have required so much thought-the conquest of a few axioms has taken more than 2000 years. "-Rene Dugas, A History 0/ Mechanics Introductory courses in engineering mechanics (statics and dynamics) are generally found very early in engineering curricula. As such, they should provide the student with a thorough background in the basic fundamentals that form the foundation for subsequent work in engi­ neering analysis and design. Consequently, our primary goal in writing Statics for Engineers and Dynamics for Engineers has been to develop the fundamental principles of engineering mechanics in a manner that the student can readily comprehend. With this comprehension, the student thus acquires the tools that would enable him/her to think through the solution ofmany types ofengineering problems using logic and sound judgment based upon fundamental principles. Approach We have made every effort to present the material in a concise but clear manner. Each subject is presented in one or more sections fol­ lowed by one or more examples, the solutions for which are presented in a detailed fashion with frequent reference to the basic underlying principles. A set of problems is provided for use in homework assign­ ments.