# Strength Of Materials

## Course Description:

The aims of the course are to teach students the basic topic of the subject and to develop the students analytical and problem solving abilities in the following topics : Generalized Theory of Pure Bending, Eccentric Axial Loading, Core of a Cross Section, Shear Stresses in Beams, Shear Stresses in beams of Thin-walled Cross Sections, Shear Center, Energy Methods in Structural Mechanics, Failure Criterial of Materials (Tresca, Misses, Mohr – Coulomb.)

### Prerequisite Knowledge

Mechanics of Deformable Bodies, Differential Equations

### Course Units

# Title Description Hours
1 Pure Bending in Built-up Beams (built-up cross sections) 3
2 Doubly symmetric beams with skew loads. Generalized Theory of Pure Bending 3
3 Eccentric Axial Loading. Neutral Axis, Core of a cross Section. 3
4 Eccentric Axial Loading. Neutral Axis, Core of a cross Section. 3
5 Shear Stresses in Beams (Shear Stresses due to Bending). Shear Flow. 3
6 Shear Stresses in beams of Thin-walled Cross Sections (open and closed cross sections). Shear Center of Thin-walled Open Sections
8 Introduction to Energy Methods in Structural Mechanics. Strain Energy and Complementary Energy. Conservation of Energy. 3
9 Energy Methods ( Castiglianos’ Theorems, Reciprocal Theorems) 3
10 Energy Methods (Principle of Virtual Work, Introduction to the Force Method)
11 Buckling 3
12 Failure Criterial of Materials (Tresca, Misses, Mohr – Coulomb.) 3
13 Failure Criterial of Materials (Tresca, Misses, Mohr – Coulomb.) 3

### Learning Objectives

With the successful completion of the course, the students will be able to:

• Calculate the distribution of normal and shear stresses within arbitrary –non-symmetric cross sections of structural members (e.g. beams, columns, etc.) when loaded under with axial and skew bending.
• Calculate neutral axis, as well as the core of the cross section
• Estimate the shear flow of an arbitrary open or closed thin-walled cross-section
• Determine the elastic strain energy of a structural member due to combined axial-bending-torsional loading.
• Determine displacements of linear elastic structural member using energy methods.
• Calculate the buckling load of structural members for various boundary conditions.
• Estimate/guess potential points of failure in simple structural members using failure criteria.

### Teaching Methods

 Teaching methods Class presentation. Solution of example problems in the class. Power Point presentations. Calculations using Excel and/or Matlab in a PC. Student in specific HWs use Excel in a PC. Weekly/Biweekly HWs are assigned

### Student Assessment

• Final written exam: 70%
• Mid-term exam: 20%
• Problems - Applications: 10%

### Textbooks - Bibliography

1. Τεχνική Μηχανική, ΤΟΜΟΣ 2 , Ι. Βαρδουλάκης, ISBN: 978-960-266-053-9, 1999
2. Μηχανική Παραμορφωσίμων Σωμάτων ΙΙ, Γ. Τσαμασφύρος, ISBN: 978-960-266-058-4, 1990
3. Μηχανική των Υλικών, F.P. Beer and E.R. Johnston, Jr., 6η Έκδοση, ISBN: 978-960-418-381-4, 2012
4. Mηχανική των Υλικών, R. C. Hibbeler, ISBN: 978-960-330-7372, 2012.
5. Αντοχή των υλικών, Ε. Παπαμίχος και Ν. Χαραλαμπάκης, ISBN: 960-418-048-7, 2004
6. J. M. Gere and S. P. Timoshenko, Mechanics of Materials, 3rd edition, Chapman and Hall, 1991.
7. Roy R. Craig Jr., Mechanics of Materials, 2nd edition, John Wiley & Sons, 1999.
8. E. Popov, Engineering Mechanics of Solids, Prentice Hall, 1990.

## Lecture Time - Place:

• Wednesday, 09:45 – 11:30,
Rooms:
• ΖΑμφ. Αντ. Υλ. 201
• ΖΑμφ. Αντ. Υλ. 202

© 2017 School of Civil Engineering, ΕΜΠ