# Strength of Materials

Definition/derivation of stress, tensile stress/strain diagrams, plastic deformation, ductile and brittle fracture, modulus of elasticity, yield stress, ultimate strength, Hooke’s law, Poisson ratio, thermal stresses and deformations, definition/derivation of shear stress , allowable stress / factors of safety, torsion, derivation of shear strain, torsion formula, derivation / definition of polar moment of inertia, beam bending, moments of inertia of a cross-section, centroids of areas, bending deformation of a straight, prismatic, homogeneous beam subjected to pure bending, the "flexure formula", deflections of beams and shafts, the elastic curve, displacement and slope by integration, combined loadings, state of stress caused by combined loadings, mechanical behaviour of metallic materials, creep, fatigue, fatigue with the presence of cracks / notches, hardness, impact, effect of corrosion exposure on the life cycle of a material.

**Course Objectives:**

Upon successful completion of this course, you should be able to do the following:

- Prepare appropriate free body diagrams.
- Solve problems involving static stresses and strains.
- Calculate axial deformation of a structure.
- Solve torsion shafts problems.
- Calculate beam deflections under various loading and support conditions.
- Calculate shear and bending moment stresses in beams, using shear and bending moment diagrams.

**Course Goals for the Instructor:**

- To provide all students the tools necessary to succeed in their pursuit of a deeper understanding of the principles of strength (mechanics) of materials.
- To provide all students with an atmosphere conducive to learning.
- To provide sufficient feedback, enabling students to gauge their progress towards achieving their goal in acquiring a mastery of the principles of engineering mechanics of materials.
- To facilitate student learning through the use of appropriate technology and the illustration of mechanics applications in the real world.

Grading will be determined on three exams: two mid-term exams during the semester courses and a final exam. Mid-term exams covers the first 60 % of the topics of the course (30 % each) while the final exam covers the rest 40 % of the topics. The students that fail the course will be re-examined in September at the whole topic of the course (100 %).

The course grade will be calculated as follows:

(First mid-term exam 30 %) + (Second mid-term exam 30 %) + (Final exam 40 %) = (**Total 100 %)**

Exam in September covers the whole topic of the course 100 %

- F. Beer and E. Johnston, Jr.,
*Μηχανική των Υλικών, 2*^{η}έκδοση στο*SI**, Τόμος Α και Β*, Εκδόσεις Τζιόλα, Θεσ/νίκη, 1999. - Π. Βουθούνης,
*Τεχνική μηχανική: Αντοχή των υλικών*, Αθήνα, 2005. - Θ. Κερμανίδης,
*Αντοχή υλικών*, Singular Publications, Πάτρα, 1995. - Ε. Παπαμίχος και Ν. Χαραλαμπάκης,
*Αντοχή των υλικών*, Εκδόσεις Τζιόλα, Θεσ/νίκη, 2005. - W. Nash,
*Αντοχή των υλικών*, Μτφρ. Σ. Περσίδης και Γ. Τυπάδης, Schaum's outline series, ΕΣΠΙ, Αθήνα, 1988. - Π. Βουθούνης,
*Μηχανική παραμορφωσίμου στερεού Ι - Ασκήσεις*, Αθήνα, 2002.

## Notes per week

**SYLLABUS**

*Class 1 Overview of Mechanics of Materials*

- External loads/ equivalent forces/ centroids

- Types of support reactions

- Equations of equilibrium

- Free body diagrams: internal forces

- Free body diagrams:(internal forces and support reactions)

- Shear and moment diagrams

*Class 2 Definition of stress*

- Definition/derivation of stress (3 normal and 3 shear stress)

- Definition/derivation of normal stress

- Tensile stress/strain diagrams

- Plastic deformation

- Ductile and brittle fracture

*Class 3 Tensile and compression mechanical behaviour*

- Modulus of elasticity (Young’s moduli)

- Mechanical property definitions for yield stress, ultimate strength, etc

- Hooke’s law

- Poisson ratio

-·Thermal stresses and deformations

*Class 4 Shear*

- Definition/derivation of shear stress

- Shear force/shear areas in simple connections

- Allowable Stress/Factors of Safety

*Class 5 Torsion*

- Introduction to torsion / Torsion of shafts

- Derivation of shear strain

- Torsion formula

- Derivation / Definition of polar moment of inertia

- Absolute maximum shear stress

*Class 6 Beam bending*

- General review of beams

- Axial shear and bending moment diagrams

- Moments of inertia of a cross-section

- Centroids of areas; general equations, "composite" areas, axes of symmetry

- Moments of inertia of an area (2nd moment of area): Ix, Iy, Iz = J (polar moment of inertia)

*Class 7 Beam bending*

- Graphical method for constructing shear and moment diagrams

- Review of bending deformation of a straight, prismatic, homogeneous beam subjected to pure bending

- The "flexure formula"

- Examples of beam bending

*Class 8 Beam bending*

- The "flexure formula"

- Examples of beam bending

*Class 9 Deflections of Beams and Shafts*

- The elastic curve and how to draw it

- Displacement and slope by integration

- Examples of slope and displacement using the integration Method

*Class 10 Combined Loadings*

- Review of principle of superposition (is valid if);

- The loading must be linearly related to the stress or displacement

- The loading must not significantly change the original geometry of the member

- State of stress caused by combined loadings

*Class 11 Mechanical behaviour of metallic materials*

- Creep

- Fatigue

*Class 12 Mechanical behaviour of metallic materials*

- Fatigue with the presence of cracks / notches

- Hardness

*Class 13 Mechanical behaviour of metallic materials*

- Impact

- Effect of corrosion exposure on the life cycle of a material