Course detail

Structural Mechanics 1

FAST-BDA015Acad. year: 2024/2025

The course is focused on the interpretation of basic concepts of structural mechanics and elasticity of beam structures. Topics: introduction to structural mechanics, plane 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, and angled beams. Frame structures with internal pins and trusses. 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

3

Mode of study

Not applicable.

Guarantor

doc. Ing. Hana Šimonová, Ph.D.

Department

Institute of Structural Mechanics (STM)

Entry knowledge

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

Rules for evaluation and completion of the course

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. The exam consists of written and oral parts, in which the practical examples and the theoretical part are elaborated. To pass the exam successfully, all parts should be accomplished.

 

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

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 look into the dimensioning of structures.

Students will be able to solve reactions and internal forces of statically determinate plane beams and frames, determine centroid and second moments of area, solve simple and combined bending and direct stresses and calculate stress in cross-section to design its dimension and material.

Study aids

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

  • Programme CZV1-AKR Lifelong learning

    specialization PBC , 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. Planar 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. Planar lattice girders. Determination of normal forces – method of joint and the method of section.
  4. Types of internal forces. Beam equilibrium differential equations. Internal forces diagrams.
  5. Statically determinate plane beams – simply supported, cantilever.
  6. Statically determinate plane angled
  7. Statically determinate plane inclined beams.
  8. Frame structures with internal pins.
  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. Concurrent system of forces in a plane. Composition and decomposition of force into orthogonal components. Resultant, equivalence, equilibrium.
  2. System of parallel forces in a plane. General system of forces in a plane. Resultant, equivalence, equilibrium.
  3. Calculation of reactions of simple straight, angled and truss beams loaded by forces, moments, and continuous loading
  4. Calculation of axial forces in members of planar lattice girders.
  5. Straight planar statically determined beams and cantilevers with simple load, reactions and diagrams of internal forces.
  6. Plane straight beams loaded with any uniform load, calculation of reactions in bonds, calculation and drawing of internal force diagrams.
  7. Plane rectangular angled beams loaded with any load, including uniformly continuous and linear, reactions and diagrams of internal forces. The first control test (calculation of the reactions of a simple planar beam).
  8. Plane inclined beams, reactions and diagrams of internal forces.
  9. Three-joint angled beam with and without rod, reactions and diagrams of internal forces.
  10. Gerber beam. Calculation of reactions and diagrams of internal forces.
  11. Centre of gravity, quadratic and deviation moments of plane compound shapes, application of Steiner's theorem.
  12. Geometric properties of compound rolled steel sections. The second control test (diagrams of internal forces of a simple planar beam).
  13. Design and assessment of bent elements – normal stresses. Credit