Course Details

Academic Year 2026/27

BDA105 course is part of 2 study plans

​ BPC-SIS / S / S-KSS Summer Semester 3rd year

​ BPC-SIS / K Summer Semester 2nd year

  • 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.

Credits

5 credits

Language of instruction

Czech

Semester

summer

Course Guarantor

prof. Ing. Jan Eliáš, Ph.D.

Institute

Institute of Structural Mechanics

Forms and criteria of assessment

course-unit credit and examination

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.

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.

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)

Prerequisites

  • 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.

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/299004

Lecture

13 weeks, 2 hours/week, elective

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

13 weeks, 2 hours/week, compulsory

Self-study

26 weeks, 1 hours/week

Individual preparation for an ending of the course

52 weeks, 1 hours/week