**Instructors:** Panayiotis Charitidis

**Course Code:** TMC335

**Semester:** 4ο

**Weekly teaching hours:** 4

**ECTS CREDITS:** 5

**Prerequisites: **Mathematics I & II (Trigonometric functions, vector analysis, deferential and integral calculus)

**Course offered to Erasmus students:** No

**Course URL: **https://eclass.duth.gr/courses/ 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).

**COURSE CONTENT:**

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

**SUGGESTED BIBLIOGRAPHY:**

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