# 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

### E-learning

Due to actual epidemic situation and following CTU rules both lectures andh practicals will be held online using MS Teams application in Team-Predmet-B201-18PZP-00-EN group. In case of incorrect assignment to the team, please contact your lecturer.### Schedule of lectures

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

1 | Organization of the course. Course motivation and overview. 18SAT summary. | 29. Sep 2020 |

2 | Basic concepts of elasticity. Normal and tangential (shear) loading. Extended Hooke’s law. | 6. Oct 2020 |

3 | Beams and rods under tensile and compression loading. | 13. Oct 2020 |

4 | Design and stress analysis of the beams subjected to bending. | 20. Oct 2020 |

5 | Bernoulli-Euler beam theory. | 27. Oct 2020 |

6 | Differential equation of bending line. Mohr’s method of beam bending line solution. | 3. Nov 2020 |

7 | Energetical principles (Ritz method). Tangent (shear) stress during bending. | 10. Nov 2020 |

8 | Beams and shafts under torsion loading. | 24. Nov 2020 |

9 | Design and analysis of fasteners and joints. | 1. Dec 2020 |

10 | Buckling - Euler method of critical load solution. | 8. Dec 2020 |

11 | Plane stress. Transformation of stress components. Mohr’s circle. | 15. Dec 2020 |

12 | Exam. | 5. Jan 2021 |

### Schedule of practicals

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

1 | Assessment of internal forces on beams. Cross-sectional characteristics of planar shapes. | 29. Sep 2020 |

2 | Tension and compression. | 13. Oct 2020 |

3 | Design and stress analysis of the beam subjected to bending. | 27. Oct 2020 |

4 | Assessment of beam deflection curve. | 10. Oct 2020 |

5 | Torsion. | 24. Nov 2020 |

6 | Buckling. | 8. Dec 2020 |

### Conditions for course credit assignment

- Active attendance on the practicals in contact form. Each lesson will be opened by a short test. Up to one point can be obtained by successfully solving the exercise of each test. In case of proper excuse of an absence (sent by e-mail to koudelka@fd.cvut.cz no later than at midnight the day before the lesson), the test could be written only during the next lesson of practicals.
- Opening short tests will be substituted by homework during on-line lecturing. For evaluation, the tasks must be submitted by e-mail to koudelka@fd.cvut.cz no later than on Sunday 12:00 the same week the task had been assigned. The homework will be evaluated in the range of 0.0-1.0 points (the same range as original short tests). Individuals tasks will be distributed by e-mail at the day of practicals.
- Tests and homework are the part of the evaluation and no consultations will be given before evaluation. The conditions for course credit assignment is completed by obtaining more than 3.0 points. After reaching of more than 4.5 points, final E-grade evaluation may be chosen by the student without the exam.

### 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).