# 18PZP-en

## Elasticity and Strength

Lectures:Assoc. Prof. Daniel Kytýř, Ph.D.

Practicals:MSc. Petr Koudelka

### Subject annotation

The course 18PZP builds upon the knowledge of assessment of internal forces and moments of simple engineering structures obtained in subject 18SAT. This knowledge is extended by introduction of design methods and assessment of deformation behavior of structures in the elastic region. To solve these problems, the mathematical apparatus acquired in the courses 11CAL1 and 11CAL2 is used. During the term, the following parts are lectured and practiced:

- tension and compression,
- bending, shear stress at bending,
- design and stress analysis of the beam,
- deformation analysis,
- torsion,
- buckling,
- joints and fittings.

### Main goals of the course

The students will gain the abilities for practical deformation analysis of simple statically indeterminate engineering structures, e.g. various types of beams and frames, including thorough understanding of the related theoretical background.

### Prerequisites

- Mathematical analysis of functions of one variable: function maxima and minima, derivation and integration of polynomial functions.
- Solution of second order differential equations.
- All 18SAT topics.

### Literature

- S. Timoshenko: Strength of Materials, Part I, Elementary Theory and Problems, D. Van Nostrand Company, 1955
- J. Case: Strength of Materials and Structures, Hodder & Stoughton Edu., 1999
- F. Beer et al.: Mechanics of Materials, McGraw-Hill, 2011
- R. Taylor: Classical Mechanics, University Science Books, 2005

### Schedule of lectures

# | Title | |
---|---|---|

1 | Organization of the course. Course motivation and overview. 18SAT summary. | 26. Sep 2019 |

2 | Basic concepts of elasticity. Normal and tangential (shear) loading. Extended Hooke’s law. | 3. Oct 2019 |

3 | Beams and rods under tensile and compression loading. | 10. Oct 2019 |

4 | Design and stress analysis of the beams subjected to bending. | 17. Oct 2019 |

5 | Bernoulli-Euler beam theory. | 24. Oct 2019 |

6 | Differential equation of bending line. Mohr’s method of beam bending line solution. | 31. Oct 2019 |

7 | Tangent (shear) stress during bending. | 7. Nov 2019 |

8 | Beams and shafts under torsion loading. | 14. Nov 2019 |

9 | Plane stress. Transformation of stress components. Mohr’s circle. | 21. Nov 2019 |

10 | Combined loading. | 28. Nov 2019 |

11 | Design and analysis of fasteners and joints. | 5. Dec 2019 |

12 | Buckling - Euler method of critical load solution. | 12. Dec 2019 |

13 | Consultations. | 19. Dec 2019 |

14 | Exam | 9. Jan 2019 |

### Schedule of practicals

# | Title | |
---|---|---|

1 | Assessment of internal forces on beams. Cross-sectional characteristics of planar shapes. | 1. Oct 2019 |

2 | Tension and compression. | 15. Oct 2019 |

3 | Design and stress analysis of the beam subjected to bending. | 29. Oct 2019 |

4 | Assessment of beam deflection curve. | 12. Nov 2019 |

5 | Torsion. | 26. Nov 2019 |

6 | Shear stress at bending. Joints and fittings. | 10. Dec 2019 |

7 | Buckling. | 7. Jan 2020 |

### Conditions for course credit assignment

**Active attendance on the practicals.** Each lesson will be opened by a short test.
Up to one point can be obtained by successfully solving the exercise of each test. Active
attendance is completed by obtaining more than 50% of total sum of the points from the
tests assigned on all practicals.

### The Exam

- Valid course credit assignment is required for registration to exam.
- The exam is composed of written and oral part.
- Satisfying the conditions for pass in the written part is mandatory prior to the oral part.
- In case of lack of fundamental knowledge presented at the oral part, the exam is ranked as F (Fail) regardless of the results of the written test.
- In case of absence on the exam, the exam is ranked as F (Fail).