# Mechanics οf Deformable Solids

## Course Description:

Introduction to the Mechanics of Deformable Bodies. Stress and Strain tensors. Constitutive relations of isotropic materials. Elastic constants. Equilibrium, kinematics, compatibility. Linear Elastic analysis of Beams. Technical theories of linear elasticity to analyze flexural, shear and combined loading problems.

### Prerequisite Knowledge

Mechanics of Rigid Body, Differential Equations, Linear Algebra

### Course Units

# Title Description Hours
1 Definition of stress. Stress vector. Stress tensor. Definition of stress. Stress vector. Stress tensor. 3
2 Stresses on inclined planes during axial loading of an elastic beam. Stresses on inclined planes during axial loading of an elastic beam. 3
3 Strains. Axial deformations. Thermal strains. Strains. Axial deformations. Thermal strains 3
4 Constitutive relations of isotropic materials in 1D. Hook’s Law Poisson Ratio. Constitutive relations of isotropic materials in 1D. Hook’s Law Poisson Ratio 3
6 Shear stress and shear strain. Shear Modulus. Strain tensor. Bulk Modulus. Generalized Hook’s Law. Shear stress and shear strain. Shear Modulus. Strain tensor. Bulk Modulus. Generalized Hook’s Law. 3
7 Stress Transformation. Plane stress. Normal and shear stresses. Principle Stresses and directions. Mohr Circle. Equations of Equilibrium. Stress Transformation. Plane stress. Normal and shear stresses. Principle Stresses and directions. Mohr Circle. Equations of Equilibrium. 3
8 Strains, rotations, Strain Transformation. Principle Strains. Strain rosettes. Compatibility Equations Strains, rotations, Strain Transformation. Principal Strains. Strain rosettes. Compatibility Equations. 3
10 Pure Bending of elastic beams with symmetric cross section. Stresses, strains, curvature. Moments of Inertia of cross sections. Pure Bending of elastic beams with symmetric cross section. Stresses, strains, curvature. Moments of Inertia of cross sections. 3
12 Shear Stresses in Beams (Shear Stresses due to Bending). Shear Flow, Beams under Combined Axial, Bending, Torsional Loading Shear Stresses in Beams (Shear Stresses due to Bending). Shear Flow, Beams under Combined Axial, Bending, Torsional Loading 3
13 Deflections of Beams. Analysis of simple indeterminate structures Deflections of Beams. Analysis of simple indeterminate structures 3

### Learning Objectives

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

• Calculate the stress state (normal and shear stresses)at every point within a symmetric cross section of a structural member when under axial and/or bending and/or shear and/or torsion loads.
• Estimate principle stresses and max shear stress as well as the planes they appear
• Calculate the deflection shape/line in simple beam structures due to flexural loading, and invoke compatibility conditions to analyze simple indeterminate structures.

### 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 Ι, 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. Αντοχή των υλικών, Ε. Παπαμίχος και Ν. Χαραλαμπάκης, ISBN: 960-418-048-7, 2004
5. J. M. Gere, Mechanics of Materials, McGraw Hill
6. Roy R. Craig Jr., Mechanics of Materials, 2nd edition, John Wiley & Sons, 1999.
7. E. Popov, Engineering Mechanics of Solids, Prentice Hall, 1990.

## Lecture Time - Place:

• Monday, 09:45 – 12:30,
Rooms:
• ΖΚτ. Αντ. Υλ., ΖΚτ. Αντ. Υλ. 201
• ΖΚτ. Αντ. Υλ., ΖΚτ. Αντ. Υλ. 202

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