Course detail

Structural Mechanics 1

FAST-BDA015Acad. year: 2022/2023

The course is focused on the interpretation of basic concepts of structural mechanics and elasticity of beam structures. Topics: introduction to structural mechanics. Coplanar and non-coplanar force systems. Structural form and idealisation, loading, supports and reactions. Types of internal forces, differential equilibrium relationship, internal forces diagrams. Statically determinate plane beams – simply supported, cantilever, inclined, bent and curved beams. Frame structures with internal pins and trusses. Statically determinate beams with 3D loads and bent beams in 3D. Geometric properties of cross-sections. Basic concepts and assumptions of the linear elasticity and strength theory. Stress, displacement, deformation. Simple stresses in Civil Engineering – tension, compression, shear, bending, and torsional stress. Stability and elastic buckling of axially loaded compression members. Combined bending and direct stress.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. Ing. Hana Šimonová, Ph.D.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

The students will be able to solve reactions and internal forces of the plane statically determinate structures, to design centroid and second order moments of gross-section, solve simple and compound stresses to and compute strain in a section, to find materials and dimensions, to calculate deformation within bend.

Prerequisites

Basic knowledge of mathematics and physics from secondary school is required.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Methods of teaching depend on the type of course unit as specified in article 7 of the Study and Examination Rules of BUT. Education runs in the form of lectures and practical classes. The character of the lectures is based on the explanation of basic principles, problems and methodology. In the practical classes, selected main topics are practised using examples.

Assesment methods and criteria linked to learning outcomes

The course is finished by credit and final examination. The credit is a necessary condition for final examination entrance. To gain credit, the students should pass two control tests during the semester. The active presence in practical classes is checked. A written exam consists of the part, in which the example is elaborated, and the theoretical part. To pass the exam successfully, both parts should be accomplished.

Course curriculum

  1. Introduction to structural mechanics. Basic concepts, principles and axioms. Coplanar and non-coplanar force systems.
  2. Basic types of statically determinate beams. Structural form and idealisation, loading, supports and reactions. Static and kinematic determinacy of structures. Calculation of support reactions.
  3. Types of internal forces. Beam equilibrium differential equations. Internal forces diagrams.
  4. Statically determinate plane beams – simply supported, cantilever.
  5. Statically determinate plane bent beams.
  6. Statically determinate plane inclined beams.
  7. Frame structures with internal pins.
  8. Trusses and curved beams. Statically determinate beams with 3D loads, and bent beams in 3D.
  9. Geometric properties of cross-sections. The parallel axis theorem. The radius of gyration and ellipse of second-order moments of the cross-section.
  10. Basic concepts and assumptions of the linear elasticity and strength theory. Stress, displacement, deformation. Simple stresses in Civil Engineering – direct tension and compression.
  11. Simple stresses in Civil Engineering – shear and bending. Transverse shear stress. Shear stress in thin-walled members. Shear centre.
  12. Torsional stress. Stability and elastic buckling of axially loaded compression members
  13. Combined bending and direct stress.

Work placements

Not applicable.

Aims

Students will be acquainted with reactions and internal forces of statically determinate plane beams and frames, and geometric properties of cross-sections (centroid, second moments of area). They also will be acquainted with basic concepts and assumptions of the linear elasticity and strength theory, such as stress, displacement, and deformations and looked into dimensioning of structures.

Specification of controlled education, way of implementation and compensation for absences

The definition of monitored instruction and the method of its implementation is annually updated by the guarantor of the course

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Kadlčák, J., Kytýr, J. Statika stavebních konstrukcí I. Základy stavební mechaniky. Staticky určité prutové konstrukce. Učebnice. Nakladatelství VUTIUM v Brně, 2001, 2010. (CS)
Šmiřák, S. Pružnost a plasticita I pro distanční studium. Skripta. Akademické nakladatelství s. r. o. Brno, 1995, 1999. (CS)

Recommended reading

Cueto E., Gonzales, D. An Introduction to Structural Mechanics for Architects. Springer, 2018. (EN)
Hulse, R. Cain, J. Structural mechanics. Red Globe Press, 2000. (EN)
Hulse, R. Cain, J. Structural mechanics: Worked examples. Palgrave Macmillan, 2009. (EN)
Jíra, A., Jandeková, D., Hlobilová, A., Janouchová, E., Zrůbek, A. Sbírka příkladů stavební mechaniky. České vysoké učení technické v Praze, 2021. (CS)
Jíra, A., Jandeková, D., Novotná, E., Řehounek, L, Prošek, Z, Štěpánek, J., Voříšek, J. Sbírka příkladů z Pružnosti a Pevnosti. ČVUT v Praze, 2022. (CS)
Křiváková, J. Stavební mechanika 1. Moduly AD01-MO1 až AD01-MO7. Studijní opory. VUT, FAST, Brno, 2011. (CS)

Classification of course in study plans

  • Programme BPC-APS Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Hana Šimonová, Ph.D.

Syllabus

  1. Introduction to structural mechanics. Basic concepts, principles and axioms. Coplanar and non-coplanar force systems.
  2. Basic types of statically determinate beams. Structural form and idealisation, loading, supports and reactions. Static and kinematic determinacy of structures. Calculation of support reactions.
  3. Types of internal forces. Beam equilibrium differential equations. Internal forces diagrams.
  4. Statically determinate plane beams – simply supported, cantilever.
  5. Statically determinate plane bent beams.
  6. Statically determinate plane inclined beams.
  7. Frame structures with internal pins.
  8. Trusses and curved beams. Statically determinate beams with 3D loads, and bent beams in 3D.
  9. Geometric properties of cross-sections. The parallel axis theorem. The radius of gyration and ellipse of second-order moments of the cross-section.
  10. Basic concepts and assumptions of the linear elasticity and strength theory. Stress, displacement, deformation. Simple stresses in Civil Engineering – direct tension and compression.
  11. Simple stresses in Civil Engineering – shear and bending. Transverse shear stress. Shear stress in thin-walled members. Shear centre.
  12. Torsional stress. Stability and elastic buckling of axially loaded compression members
  13. Combined bending and direct stress.

Exercise

13 hod., compulsory

Teacher / Lecturer

doc. Ing. Hana Šimonová, Ph.D.

Syllabus

  1. Coplanar force systems. Conditions of equilibrium.
  2. Statically determinate plane beams – simply supported, cantilever – support reactions.
  3. Statically determinate plane beams – simply supported, cantilever – internal forces diagrams.
  4. Statically determinate plane beams – bent and inclined beams. Frame structures with internal pins.
  5. Gerber beams. Trusses – method of joint and method of section.
  6. Geometric properties of cross-sections. Dimensioning of members – bending stress.
  7. Credit