| Course Unit Code | 228-0242/01 |
|---|
| Number of ECTS Credits Allocated | 4 ECTS credits |
|---|
| Type of Course Unit * | Compulsory |
|---|
| Level of Course Unit * | First Cycle |
|---|
| Year of Study * | Second Year |
|---|
| Semester when the Course Unit is delivered | Winter Semester |
|---|
| Mode of Delivery | Face-to-face |
|---|
| Language of Instruction | Czech |
|---|
| Prerequisites and Co-Requisites | |
|---|
| Prerequisities | Course Unit Code | Course Unit Title |
|---|
| 228-0241 | Fundamentals of Structural Mechanics for Architects |
| Name of Lecturer(s) | Personal ID | Name |
|---|
| KRE13 | prof. Ing. Martin Krejsa, Ph.D. |
| BRO12 | prof. Ing. Jiří Brožovský, Ph.D. |
| Summary |
|---|
| Subject Introduction to Elasticity and Plasticity provides students with basic information on strain and strain of generally loaded supporting elements and simple rod structures with respect to the basic strain and elastic or ideal elastic-plastic behavior of the material. The course provides basic information on the design and assessment of the reliability of load bearing structures for the needs of an architect. The training also includes the stability analysis of slender columns in compression. The course also provides information on the basic cross-sectional characteristics that are used in static calculations. Students will acquire basic knowledge of principles and methods of building mechanics, which are applied in normative regulations for design of structures. |
| Learning Outcomes of the Course Unit |
|---|
| Learning of fundamentals of building mechanics - the theory of elasticity and plasticity, focusing on the ability to design and evaluate the reliability of load bearing elements and simple beam structures with respect to stresses and deformations. |
| Course Contents |
|---|
Lectures:
1. Introduction: Flexibility and strength in civil engineering. Integration of subject matter into the theory and design of engineering structures.
2. Cross-sectional characteristics: Moments of inertia and deviating moments: the concept of quadratic moments of planar shapes, central quadratic moments of basic and compound cross-sections, quadratic moments to rotated axes, polar moment of inertia.
3. Stress: Basic concepts, default assumptions. Relationships between internal forces and stresses in the cross section.
4. Deformations and displacements in the body: Physical relationships between stress and strain, Hook\'s law, physical constants, stress-strain diagrams of building materials, deformation from temperature change.
5. Principles of design and structural reliability assessment: Ultimate limit state, strength of building materials. Loads of building structures. Limit state of serviceability. Probabilistic assesment of the reliability of the load-bearing structures.
6. Normal stress and deformation of tensioned rod (simple pressure): Basic relations and assumptions of solution. Stress and strain of axial task. Statically determined and indeterminde task. Elastic-plastic strain.
7. Torsion: Basic principles and relationships. Shear stress and strain. Statically determined and indetermined task.
8. Normal stresses in bent beams: Basic relationships and assumptions for the solution. Calculation of normal stress. Dimensioning of bent beams. Bending with consideration of the elastic-plastic behavior of the material.
9. Shear stresses in bent beams: Basic relationships and assumptions for the solution. Calculation of shear stress of selected cross-sections. Dimensioning of bent beams in shear. Calculation of shear flows and shear center. Composite beams.
10. Deformation of bent beams I.: Basic relations and assumptions of solution. Shaping beams from uneven warming. Method of direct integration of the differential equation of the bending strain curve. Clebsch method.
11. Deformation of bent beams II.: Deformation of bendt beams with variable cross section. Statically indeterminate bending tasks. Effect of shear on the strain of the bent beam.
12. Composite beam strain: Spatial bending. Excentric compression, cross section core.
13. Stability and buckling strength of rods: Euler\'s solution
14. Sample examples.
Tutorials:
1. Introduction: Determination of reactions and internal forces of selected statically and kinematically determined structures.
2. Cross-sectional characteristics: Moments of inertia and deviating moments, quadratic moments of planar shapes, compound cross-sections, polar moment of inertia.
3. Deformations and displacements in the body: Physical relationships between stress and strain, Hook\'s law, physical constants, stress-strain diagrams of building materials, deformation from temperature change.
4. Normal stress and deformation of tensioned rod (simple pressure) I: Computation of stress and strain of axial task.
5. Normal stress and deformation of tensioned rod (simple pressure) II: Statically indeterminde task.
6. Normal stress and deformation of tensioned rod (simple pressure) III: Elastic-plastic strain. Deformation of a rod with a variable normal force (self-weight) and a variable cross-sectional area.
7. Torsion: Computation of shear stress and strain. Statically determined and indetermined task. Dimensioning of beam under torsion.
8. Normal stresses in bent beams: Calculation of normal stress in bending. Dimensioning of bent beams according ultimate limit state. Neural axis, modulus of cross-section, non-symetric cross-section in bending.
9. Shear stresses in bent beams: Calculation of shear stress of selected cross-sections. Dimensioning of bent beams in shear. Composite beams.
10. Deformation of bent beams I.: Method of direct integration of the differential equation of the bending strain curve. Dimensioning of bent beams according limit state of serviceability.
11. Deformation of bent beams II.: Clebsch method.
12. Deformation of bent beams III.: Statically indeterminate bending tasks. Method of direct integration of the fourth order differential equation of the bending strain curve.
13. Stability and buckling strength of rods: Euler\'s solution of direct elastic rod. Dimensioning of slender columns under compression.
14. Credit test |
| Recommended or Required Reading |
|---|
| Required Reading: |
|---|
1. Russell C. Hibbeler, Mechanics of Materials (10th Edition), 896 pages, 2016, ISBN-13: 978-0134319650, ISBN-10: 0134319656.
2. James M. Gere, Stephen P. Timoshenko, Mechanics of Materials (4th Edition), 912 pages, 1996, ISBN-13: 978-0534934293, ISBN-10: 0534934293. |
| 1. Krejsa, Lausová, Michalcová: Pružnost a plasticita. VŠB-TU Ostrava 2011 |
| Recommended Reading: |
|---|
1. Russell C. Hibbeler, Engineering Mechanics: Statics (13th Edition), 672 pages, 2012, ISBN-13: 978-0132915540 , ISBN-10: 0132915545.
2. Russell C. Hibbeler, Structural Analysis (10th Edition), 736 pages, 2017, ISBN-13: 978-0134610672, ISBN-10: 0134610679. |
1. Šmířák: Pružnost a plasticita I, VUT Brno 1999
2. Šmířák, Hlavinková: Pružnost a plasticita I - Příklady, VUT Brno 2000 |
| Planned learning activities and teaching methods |
|---|
| Lectures, Tutorials |
| Assesment methods and criteria |
|---|
| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
|---|
| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 35 | 18 |
| Examination | Examination | 65 | 30 |