Course detail

Statické modelování

FAST-BDA105Acad. year: 2026/2027

  • The essence of the direct stiffness method and its variants. Computational model and the degree of kinematic indeterminacy.
  • The direct stiffness method for planar structures.
  • Analysis of a straight member with a variable cross-section. Local quantities, the primary vector and the stiffness matrix.
  • Hinge-connected member, cantilever. Member with a constant cross-section.
  • Geometric transformation, the global member matrix.
  • Analysis of a frame system, assembling the equations, localization.
  • Determination of end forces and the distributions of internal force components along members. Determination of reactions and verification of the solution.
  • Solution of rectangular frames and continuous beams. Thermal effects, support settlement/release.
  • Truss girder solved by the displacement method.
  • Member with a variable cross-section with a linear depth haunch, determination of deformation coefficients.
  • Solution of spatial (3D) frames by the direct stiffness method.
  • Computational model for the simplified direct stiffness method.
  • Wall and plate structures, design moments.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Jan Eliáš, Ph.D.

Department

Institute of Structural Mechanics (STM)

Entry knowledge

  • Static analysis of planar statically determinate truss systems, straight and cranked girders.
  • Principle of virtual work and theorem of virtual work reciprocity and calculation of deflection of frame systems by using method of unit forces.
  • Solution of planar frame structures using force method.

Rules for evaluation and completion of the course

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Aims

Professional knowledge

The student understands the theoretical foundations of the direct stiffness method, and grasps its basic procedures and assumptions. They are able to set up computational models for both the general and the simplified direct stiffness method, and to use them to solve statically indeterminate frame structures. The student also understands the function of haunches (cross-section changes). He/she understand and can apply the principle of virtual displacements, and understand its connection to the direct stiffness method.

Professional skills

The student can compute kinematic and static quantities (displacements, rotations, and internal forces) for statically indeterminate structures using both the general and the simplified direct stiffness method, for both planar frame and truss systems — including accounting for the effect of support flexibility and temperature change.

Professional competencies

The student is competent to work with structural analysis software for solving frame structures, understands the principles of the algorithms used in the software, and can perform basic checks and verification of results. They are also able to carry out analysis of wall structures for plane strain and plane stress, as well as compute plate structures and design moments using advanced structural analysis software.

Study aids

There are no shortened study materials available for this course.

Prerequisites and corequisites

Not applicable.

Basic literature

Kadlčák, Jaroslav a Jiří Kytýr. Statika stavebních konstrukcí II. Brno: Nakladatelství VUTIUM, 2007. ISBN 978-80-214-3428-8. (CS)

Recommended reading

Kytýr, Jiří, Roman Gratza, Jan Plášek, Tomáš Ridoško a Jan Ekr. Statika II – řešené příklady. Brno: Akademické nakladatelství CERM, 2016. ISBN 978-80-7204-946-2. (CS)
Udoeyo, Felix F. Structural Analysis. Philadelphia: Temple University Press, 2020. Dostupné z: https://temple.manifoldapp.org/read/structural-analysis/section/e1234718-83ed-42b0-b774-658813d8b813. (EN)

Classification of course in study plans

  • Programme akr_BPC-SIS Bachelor's

    specialization C_K , 2 year of study, summer semester, compulsory, profile core courses
    specialization S-KSS , 3 year of study, summer semester, compulsory
    specialization B_S_akr , 3 year of study, summer semester, compulsory-optional, profile core courses

  • Programme BPC-SIS Bachelor's

    specialization _B_S_akr , 3 year of study, summer semester, compulsory-optional, profile core courses
    specialization K , 2 year of study, summer semester, compulsory, profile core courses
    specialization S , 3 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

prof. Ing. Jan Eliáš, Ph.D.

Syllabus

  • The essentials of the direct stiffness method, its origin and development, variants of the displacement method; computational model and the degree of kinematic indeterminacy.
  • The general direct displacement method for planar frame structures, equilibrium conditions, degrees of freedom, matrix formulation.
  • Local quantities, the primary vector and stiffness matrix; hinge-connected member, cantilever.
  • System analysis, code numbers and localization (mapping), calculation of displacements of a frame system.
  • End reactions, internal forces, deformation and thermal loading.
  • Geometric transformation, global stiffness matrix of a member.
  • Strong formulation of differential equations for solving Euler-Bernoulli beams; virtual work and complementary virtual work in frame structures; the principle of virtual forces and the principle of virtual displacements.
  • Strong formulation of mechanics in three-dimensional space – geometric (kinematic) equations, constitutive equations, and equilibrium equations.
  • Modeling of walls (shear walls), plane strain and plane stress.
  • Kirchhoff theory of thin plates, degrees of freedom, internal forces, boundary conditions, design moments.
  • Mindlin theory of thick plates; brief mention of plate-wall structures (shells).
  • Static solution of foundation structures, subsoil (foundation) models.
  • Weak formulation of mechanics in three-dimensional space, the Ritz method and other solution methods.

Exercise

26 hours, compulsory

Teacher / Lecturer

prof. Ing. Jan Eliáš, Ph.D.

Syllabus

  1. Opakování silové metody.
  2. Jednoduché příklady k demonstraci deformační metody, rovnice rovnováhy ve styčníku, příhradový systém a ohýbané pruty.
  3. Seznámení s jednoduchým výpočetním programem, tvorba jednoduchých prutových modelů a výpočet.
  4. Analýza přetvárné neurčitosti; řešení spojitého nosníku se silovým zatížením obecnou deformační metodou, primární vektory a matice tuhosti prutů, globální matice tuhosti konstrukce; kontrola ve výpočetním programu.
  5. Řešení spojitého nosníku – soustava rovnic, koncové síly, průběhy vnitřních sil a reakce; kontrola ve výpočetním programu.
  6. Rám obecnou deformační metodou při silovém zatížení; analýza prutů – primární vektory a lokální matice tuhosti.
  7. Geometrická transformace do globální souřadnicové soustavy; sestavení matice tuhosti konstrukce a zatěžovacího vektoru.
  8. Výpočet koncových sil; průběhy vnitřních sil, určení reakcí, kontrola výpočtu ve výpočetním programu.
  9. Příhradová soustava obecnou deformační metodou, kontrola ve výpočetním programu.
  10. Vliv deformačního zatížení na prutovou konstrukci; kontrola výsledků ze softwaru, rovnováha konstrukce a styčníků.
  11. Analýza stěn pomocí MKP softwaru, tvorba sítě konečných prvků, singularity, výpočet napětí.
  12. Analýza desek pomocí MKP softwaru, tvorba sítě konečných prvků, podepření.
  13. Práce s modely desek, dimenzační momenty, varianty desek a podepření.

Individual preparation for an ending of the course

52 hours, optionally

Teacher / Lecturer

prof. Ing. Jan Eliáš, Ph.D.

Self-study

26 hours, optionally

Teacher / Lecturer

prof. Ing. Jan Eliáš, Ph.D.