MECHANICS OF SOLIDS IM LECTURE HOURS PER WEEK STATICS IM0232 DIFERENTIAL EQUAQTIONS

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1 COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE MECHANICS OF SOLIDS IM LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 96 HOURS OF INDEPENDENT WORK STATICS IM0232 DIFERENTIAL EQUAQTIONS JUSTIFICATION The study of the mechanics of deformable solids is of great importance in the field of engineering, because it provides the fundamental criteria for stress-strain analysis of mechanical systems, which are the pillars of design, failure analysis and evaluation of mechanical structures. INTRODUCTION Engineers have to calculate the mechanical behavior of machines elements, load bearing structures, and most products, before they build the prototypes. Internal forces and associated changes in geometry of the designed elements and products depends on the properties of the selected material, the strength of which will determine whether the components fail by breaking in service, and the stiffness of which will determine whether the amount of deformation they suffer is acceptable. Solid mechanics deals with the basic principles and the methods used to choose the suitable material for different applications using a model that make reasonable assumptions in order to simplify the real components far enough to permit it to be analyzed without an excessive amount of labor, but without at the same time simplifying it so far as to make the results of the analysis unreliable for design and other proposes. Although the course considers the developing of all necessary models in a rational and logical manner, it focuses in the process of analysis of actual engineering structures and machine components. The ability to solve problems can be reached by practical experience of solving particular problems and the systematic study of underlying principles. 1

2 It is expected that students participating in this course have completed a course of static and basic courses in calculus and physics. AIMS OF THE COURSE To develop skills to model engineering problems and make idealizations (simplifications) that allows obtaining approximate solutions at low cost. To determine the state of stress and strain of a mechanical system subjected to the action of external loads. To identify the types of mechanical elements, shapes, and the relationship with the types of loads. To perform calculations that allow selecting the materials and appropriate geometries shapes according load types. To evaluate the strength, stiffness and mechanical stability of a system under loading. To encourage the use of commercial structural elements and highlight its importance in mechanical design. GENERAL CONTENTS Introduction Geometric Properties of an Area Stress Introduction to Structural design Strain Mechanical Properties of Materials Axial Load Torsion Bending Transverse Shear Combined Loadings Stress Transformation Strain Transformation Theories of Failure Design of Beams and Shafts Deflection of Beams and Shafts Buckling of Columns 2

3 METODOLOGY Teacher exposure topics. Work in the classroom by students with the guidance of Professor or monitor for the solution of the workshops and the suggested exercises for the week. Work outside the classroom by the student solving the problems suggested for the week. EVALUATION First partial exam: 20% Written examination. (Week 5) Second partial exam: 25% Written examination. (Week 10) Third partial exam: 25% Written examination. (Week 15) Final exam: 30% Written examination. Scheduled by the registry office REFERENCES Books TEXT GUIDE BEER & Johnston Jr.. Mechanics of Materials. Mc. Graw Hill. Sixth Edition. Mexico Other texts Hibbeler, R. C. Mechanics of Materials. Prentice Hall. 6 edition. Mexico, MOTT, Robert L. Mexico, Applied Strength of Materials. Prentice Hall. Fifth edition. 3

4 WEEKLY SYLLABUS AND STUDENT WORK Week Topic Introduction: Brief introduction to the historical Development Equilibrium of a Deformable Body: - External Loads - Support Reactions - Equations of Equilibriu - Internal Resultant Loadings. Geometric Properties of an Area (1): Area Centroid of an Area Moment of Inertia for an Area - Parallel-Axis Theorem for an Area - Composite Areas Product of Inertia for an Area - Parallel-Axis Theorem Geometric Properties of an Area (2): Moments of Inertia for an Area about Inclined Axes - Principal Moments of Inertia Mohr s Circle for Moments of Inertia Stress: - Normal Stress - Shear Stress - General State of Stress Average Normal Stress in an Axially Loaded Bar - Average Normal Stress Distribution - Maximum Average Normal Stress Average Shear Stress - Shear Stress Equilibrium Introduction to Structural design: Allowable Stress Design of Simple Connections Strain Deformation - Normal Strain - Shear Strain - Small Strain Analysis Mechanical Properties of Materials (1): The Tension and Compression Test Readings & excercises 3 to 15. Exercises: F1 5, 1 3, 1 15, to to to 37. Exercises: F1-11, 1 38, 1 51, to 52. Exercises: 1 80, 1 89, 1 102, to 73 and 81 to 96. Exercises: F3 11, 2 to 3, 2 to 14, 3 to 9, 3 to 15 4

5 4 The Stress Strain Diagram - Conventional Stress Strain Diagram - True Stress Strain Diagram Stress Strain Behavior of Ductile and Brittle Materials Hooke s Law Strain Energy - Modulus of Resilience - Modulus of Toughness Mechanical Properties of Materials (2): Poisson s Ratio The Shear Stress Strain Diagram Relationship involving E, ν, G Failure of Materials Due to Creep and Fatigue Axial Load (1): Saint-Venant s Principle Elastic Deformation of an Axially Loaded Member Principle of Superposition Statically Indeterminate Axially Loaded Member 102 to 109. Exercises: F3-14, 3 to 29, 3 to to 142. Exercises: F4 1, 4 2, 4 35, 4 46 First Partial Exam (20%) Week Partial Feedback Axial Load (2): The Force Method of Analysis for Axially Loaded Members Thermal Stress Stress Concentrations Torsion (1): Torsional Deformation of a Circular Shaft The Torsion Formula Power Transmission Torsion (2): Angle of Twist Statically Indeterminate Torque-Loaded Members Thin-Walled Tubes Having Closed Cross Sections Stress Concentration Bending (1): Shear and Moment Diagrams Graphical Method for Constructing Shear and Moment 143 to 144, 151 to 154, 158 to 161. Exercises: 4 35, 4 67, 4 69, to 191. Exercises: F5 4, 5 3, 5 18, to 207, 214 to 217, 224 to 229, 234 to 236. Exercises: F5 11, 5 86, 5 111, to

6 7 8 9 Diagrams Exercises: F6 13, 6 6, 6 8, 6 19 Bending (2): Bending Deformation of a Straight Member The Flexure Formula Bending (3): Unsymmetric Bending - Moment Applied About Principal Axis - Moment Arbitrarily Applied - Orientation of the Neutral Axis Bending (4): Composite Beams Reinforced Concrete Beams Stress Concentrations Bending (5): Inelastic Bending - Linear Normal-Strain Distribution - Plastic Moment - Residual Stress Transverse Shear (1): Shear in Straight Members The Shear Formula - Limitations on the Use of the Shear Formula Transverse Shear (2): Shear Flow in Built-Up Members 281 to 292. Exercises: F6 17, 6 78, 6 87, to 308. Exercises: F6 21, 6 110, 6 115, to 318, 326 to 328. Exercises: 6 130, 6 138, 6 142, to 345. Exercises: 6 168, 6 183, 6 172, F7 3, 7 6, 7 12, 7 to to 382. Exercises: F7 8, 7 38, 7 42, 7 46 Second Partial Exam (25%) Week Partial Exam Feedback Transverse Shear (3): Shear Flow in Thin-Walled Members Shear Center for Open Thin-Walled Members 387 to 397. Exercises: 7 50, 6

7 Combined Loadings (1): Thin-Walled Pressure Vessels - Cylindrical Vessels - Spherical Vessels Combined Loadings (2): State of Stress Caused by Combined Loadings 7 63, 7 67, to 408. Exercises: 8 4, Stress Transformation (1): Plane-Stress Transformation General Equations of Plane-Stress Transformation Principal Stresses and Maximum In-Plane Shear Stress Stress Transformation (2): Mohr s Circle: Plane Stress Absolute Maximum Shear Stress Strain Transformation (1): Plane Strain General Equations of Plane-Strain Transformation Mohr s Circle: Plane Strain Absolute Maximum Shear Strain Strain Transformation (2): Conceptos generales de medición de presión, desplazamiento y deformación Strain gauge para deformación axial Strain Rosettes Generalized Hooke s Law Theories of Failure: Ductile Materials Brittle Materials Exercises: F8 3, 8 6, 8 20, to 451. Exercises: F9 4, 9 14, 9 22, 9 43, 461 to 467. Exercises: , F9 10, 9 70, 9 74, 9 92, to 498, 502 to 503. Exercises: 10 5, to 505, 508 to 515. Exercises: 10 25, 10 28, 10 40, 10 44, 520 to 527. Exercises: 10 68, 10 74, 10 85, Design of Beams and Shafts: 7

8 15 Basis for Beam Design Prismatic Beam Design Fully Stressed Beams Shaft Design Deflection of Beams and Shafts (1): The Elastic Curve Slope and Displacement by Integration Discontinuity Functions Slope and Displacement by the Moment-Area Method Method of Superposition Partial Exam Feedback Deflection of Beams and Shafts (2): Statically Indeterminate Beams and Shafts - Method of Integration - Moment-Area Method - Method of Superposition Buckling of Columns (1) Critical Load Ideal Column with Pin Supports Columns Having Various Types of Supports 537 to 547, 554 to 561. Exercises: F11 6, 11 6, 11 10, 11 31, to 585, 604 to 611, 619 to 623. Exercises: F12 2, 12 7, 12 18, 12 56, to 630, 633 to 637, 639 to 647. Exercises: , , to 669, 678 to 686, Exercises:F13 2, 13 4, 13 10, Third Partial Exam (25%) Week Buckling of Columns (2) Design of Columns for Concentric Loading Design of Columns for Eccentric Loading 692 to 699, 703 to 707. Exercises: 13 91, , ,