Mechanic of Rigid Body – Materials Strength

Instructors: Panayiotis Charitidis
Course Code: TMC335
Semester: 4ο
Weekly teaching hours: 4
Prerequisites: Mathematics I & II (Trigonometric functions, vector analysis, deferential and integral calculus)
Course offered to Erasmus students: No

Course URL: TMC335/

Learning Outcomes: 

Learning Outcomes Please describe the learning outcomes of the course: Knowledge, skills and abilities acquired after the successful completion of the course.
Basic Knowledge of Solid Mechanics – Statics and Strength of Materials

General Skills:

This course introduces students to the fundamental principles and methods of structural mechanics. Topics covered include: static equilibrium, force resultants, support conditions, analysis of determinate planar structures (beams, trusses, frames), stresses and strains in structural elements, states of stress (shear, bending, torsion), statically indeterminate systems, displacements and deformations, introduction to matrix methods, elastic stability, and approximate methods. Design exercises are used to encourage creative student initiative and systems thinking. Students are expected to have: An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
 An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
 The student (as a non-specialist) knows the application possibilities and the limitations of the developed models.
 An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
 The student can calculate or design simple practical constructions, taking into account the boundary conditions (e.g. allowable material properties and deformations, type and applying of loads).

Solid Mechanics – Statics
1. Introduction to Statics
 Mechanics – Basic Concepts
 Scalar and Vectors (conventions for equations and diagrams, working with vectors)
 Newton’ s Law
2. Statics of Particle and Rigid Bodies
 Coplanar Forces and Moments
 Forces in Space
 Equilibrium of a Particle
 Equilibrium of a Rigid Body in a Plane
 Forces and Moments in Space
 Equilibrium of a Rigid Body in a Space
3. Center of Mass and Centroids – Area Moments of Inertia
 Center of Mass (determine the center of gravity, center of mass vs. center of gravity)
 Centroids of Lines, Areas, and Volumes
 Rectangular and Polar Moments of Inertia
 Radius of Gyration
 Transfer of Axes
 Rotation of Axes
4. Structures
 Structural Elements
 Joints between Structural Elements
 Plane Trusses (simple trusses, truss connections and supports)
 Method of Joints (internal and external redundancy special conditions)
 Method of Sections (illustration of the method and additional considerations)
 Frames (pin joined frames, interconnected rigid bodies with multiforce members, force representation and free body diagram)
5. Beams – External and Internal Effects
 Type of Beams and Distributed Loads
 Force flow in a member

 Diagrams for the normal force, shear force and bending moment (sign conventions for the N, V, and M diagrams)
 Deformation symbols for shear forces and bending moments
Strength of Materials
6. Introduction
 Normal Stress (σ) and Direct Strain (ε)
 Shear Stress (τ) and Shear Strain (γ)
 Mechanical Properties of Materials (proportional limit, elastic limit, elastic and plastic ranges)
 Ductile and Brittle Material Behaviour
 Temperature Stresses
 Stress concentrations – Stress Concentration Factor
 Allowable Working Stress – Factor of Safety
7. Tension and Compression
 Internal Effects of Forces (axially loaded bar, normal stress, test specimen, normal strain, stress – strain curve)
 Allowable stress – Safety Factor
8. Shear
 Internal Effects of Forces (shear test, shear strain)
 Σύνθλιψη άντυγας οπών,
 Allowable Working Stress – Safety Factor
9. Stress State – Strain State
 Sign Conventions
 Rotate Axes
 Elastic Materials – Hooke’s Law
 Relation Between E, G and v
 Principal Stresses – Principal Planes
 Maximum Shearing Stress
 Mohr’s Circle of Stress
 Strains in an Inclined Direction
10. Thin – Walled Pressure Vessels
 Internal and External Pressure (hoop or circumferential stress, longitudinal stress, change in dimensions)
 Cylindrical Pressure Vessels
 Spherical Pressure Vessels
11. Torsion
 Simple Torsion Theory
 Polar Second Moment of Area, Section of Modulus
 Torsional Rigidity
 Torsion 0f Hollow Shafts
 Torsion of Thin – Walled Tubes
 Principal Stresses
 Combined Torsion and Axial Loading

12. Bending
 Bending Theory – Pure Plane Bending
 Neutral Axis, Section of Modulus, Second Moment of Area
 Bending Moments and Shearing Forces
 Sign Conventions for Bending Moments and Shearing Forces
 Maximum Normal Stresses – Limitations
 Shearing Force and Bending Moment Diagrams
13. Columns – Stability
 Types of Columns
 Eccentric Loading
 Axial Loaded Compression Members
 Buckling – Stability
 Critical Buckling Load
 Euler’ s Theory – Assumptions
 Yield Stress and Buckling Stress, Effective Length and Bracing
Examples – Finite Element Analysis using Comsol Multiphysics, Abaqus and Ansys

1. “Statics and Strength of Materials (Theory – Methodology – Solved Problems “, Α. Polyzakis
2. “Statics and Strength of Materials”, P. Vouthounis
3. “Strength of Materials”, Th. Kermanidis
4. “Engineering Mechanics of Deformable Solids Ι”, P. Vouthounis
5. “Strength of Materials”, Ε. Ε. Gdoutos
6. “Strength of Materials”, Ε. Papamichos and Ν. Ch. Charalampakis
7. “Statics”, Ε. Ε. Gdoutos
8. “Strength of Materials: An Introduction to the Analysis of Stress and Strain”, J. Case and A. H. Chilver
9. “Mechanics of Materials (2nd ed.)”, F. Beer and E. R Johnston, Jr. 10. “Engineering Mechanics: Statics (5th ed.)”, J. L. Meriam and Kraige L. G
11. ” Statics and Strength of Materials: Foundations for Structural Design “, B. Onouye
12. ” Vector Mechanics for Engineers: Statics and Dynamics (9th ed.)”, F. P. Beer, E. R. Johnston, Jr, D. F. Mazurek, P. J. Cornwell and E. R. Eisenberg
13. ” Strength of Materials (2nd ed.)”, R. Subramanian
14. ” Statics and Strength of Materials: Foundations for Structural Design (7th ed.)”, H. Morrow and R. Kokernak
15. “Mechanics of Materials (10th ed.)”, R.C. Hibbeler
16. “Statics and Strength of Materials”, R.C. Hibbeler
17. “Strength of Materials (7th ed.)”, W. Nash and M. C. Potter
18. “Applied Strength of Materials (6th ed.)”, R. L. Mott and J. A. Untener
19. ” Applied Strength of Materials for Engineering Technology (20th ed.)”, B. Dupen

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