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.
# | Title | Description | Hours |
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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 |
5 | Axial loading of elastic and elastoplastic beams. Loading-unloading. Permanent stresses and strains. | Axial loading of elastic and elastoplastic beams. Loading-unloading. Permanent stresses and strains. | 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 |
9 | Torsion of cylindrical beams (circular cross sections) Elastic and Elastoplastic behavior (Loading- unloading). | Torsion of cylindrical beams (circular cross sections) Elastic and Elastoplastic behavior (Loading- unloading). | 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 |
11 | Pure Bending of beams with symmetric cross section from elastoplastic material (loading-unloading) | Pure Bending of beams with symmetric cross section from elastoplastic material (loading-unloading) | 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 |
With the successful completion of the course, the students will be able to:
Teaching methods | Class presentation. Solution of example problems in the class. |
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Teaching media | Power Point presentations. Calculations using Excel and/or Matlab in a PC. |
Computer and software use | Student in specific HWs use Excel in a PC. |
Problems - Applications | Weekly/Biweekly HWs are assigned |