Course detail

Structural Analysis 2

FAST-BDA007Acad. 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.

Language of instruction

Czech, English

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. Ing. Jan Eliáš, Ph.D.

Department

Institute of Structural Mechanics (STM)

Offered to foreign students

Of all faculties

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 comprehends its basic procedures and assumptions. The student is able to build computational models for both the general and simplified direct stiffness method and to use them to solve statically indeterminate frame/truss structures. The student also understands the function of haunches (cross-section variation) and the significance of influence lines for analyzing the effect of moving loads.

Professional Skills

The student can calculate kinematic and static quantities (displacements, rotations, and internal forces) in statically indeterminate structures using both the general and simplified direct displacement method, for planar frame as well as truss systems — including the effects of support settlement/flexibility and temperature changes.

Professional Competencies

The student is competent to work with structural analysis software for solving bar structures, understands the algorithms used in the software, and is able to perform a basic check/verification of the results.

Study aids

Russell Hibbeler. Structural Analysis, Pearson 2017, ISBN 978-0134610672

Prerequisites and corequisites

Not applicable.

Basic literature

Jaroslav Kadlčák, Jiří Kytýr. Statika stavebních konstrukcí II, 2009, VUTIUM, ISBN:978-80-214-3428-8 (CS)
Kytýr Jiří, Roman Gratza, Jan Plášek, Tomáš Ridoško, Jan Ekr. Statika II - Řešené příklady, CERM, ISBN 978-80-7204-946-2 (CS)

Recommended reading

Jiří Benda. Energetické principy a variační metody ve stavební mechanice, vlastním nákladem autora, Brno 2002 (CS)
Russell Hibbeler. Structural Analysis, Pearson 2017, ISBN 978-0134610672 (EN)

Classification of course in study plans

  • Programme BPA-SI Bachelor's 3 year of study, winter semester, compulsory
  • Programme BKC-SI Bachelor's 3 year of study, winter semester, compulsory

  • Programme BPC-SI Bachelor's

    specialization S , 3 year of study, winter semester, compulsory
    specialization K , 3 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 hours, optionally

Teacher / Lecturer

Ing. Zbyněk Vlk, Ph.D.
prof. Ing. David Lehký, Ph.D.
prof. Ing. Jan Eliáš, Ph.D.
doc. Ing. Petr Frantík, Ph.D.

Syllabus

  • 1. Introduction, content and outline of the subject. Meaning of deflection method, creation and development of this method, variants of deflection method. Calculation model and degree of kinematic indeterminacy.
  • 2. General deflection method for planar frame structures. Equilibrium of conditions, parameters of deflection, bounded nodes. Scalar and matrix form.
  • 3. Analysis of straight bar with variable cross-section: primary and secondary state.
  • 4. Local values, primary vector and the stiffness matrix. Bar connected by joints, cantilever.
  • 5. Bar with constant cross-section. Geometric transformation, global matrix of bar.
  • 6. Analysis of the frame system, compilation of the system of equations, code number and localization.
  • 7. Completion of solution of bars – calculation of internal forces and deflection at bars. Determination of reactions and controlling of the solution. Errors during the solution of frames by using deflection method. Another variant for assembly of equations.
  • 8. Speciality of solution of rectangular frames and continuous girders. Temperature influences, shift of supports.
  • 9. Truss girder is solved by using deflection method.
  • 10. Bar with variable cross-section, height linear ramping, determination of deflection coefficients (analytic solution, numerical integration)
  • 11. Solution of spatial frames solved by general deflection method.
  • 12. Calculation model for simplified deflection method in scalar form.
  • 13. End moments, internal forces. Joint and storey equation.

Exercise

26 hours, compulsory

Teacher / Lecturer

Ing. Jan Mašek, Ph.D.
Ing. Martina Sadílková Šomodíková, Ph.D.
Ing. Václav Sadílek, Ph.D.
doc. Ing. Hana Šimonová, Ph.D.
Ing. Zbyněk Vlk, Ph.D.
prof. Ing. David Lehký, Ph.D.
Ing. Dita Vořechovská, Ph.D.
doc. Ing. Lukáš Novák, Ph.D.
Ing. Michal Jedlička
Ing. Ondřej Holiš
Ing. Jan Raisinger

Syllabus

  • 1. Revision of solution of elementary statically indeterminate systems using deflection method. Diagrams of internal forces. Analysis of statically and kinematic determinacy of frame systems.
  • 2. Calculation models of frame structures for deflection method, analysis of kinematic indeterminacy. Solution of cranked statically determinate girder with forces loading using general deflection method.
  • 3. Completion of solution of cranked statically determinate girder with force loading, ending forces, diagram of internal forces and reactions.
  • 4. Solution of continuous girder with force loading using general deflection method.
  • 5. Solution of more complicated statically indeterminate frames using general deflection method.
  • 6. Completion of solution of more complicated frames – equation system, ending forces, diagram of internal forces and reactions. Control test 1.
  • 7. Solution of girders with forces and deflection loading.
  • 8. Complexion solution of statically indeterminate frame using deflection method.
  • 9. Completion of solution of complexion frame – equation system, ended forces, diagram of internal forces and reactions. Control test 2.
  • 10. Truss system solved by general deflection method.
  • 11. Completion of solution of truss system. Correction test. Credits.
  • 12. RFEM-SCIA: Introduction to environment of system, input of new project, units, materials and cross-sections. Input and calculation of continuous girder including cantilever. Loading forms and its combinations.
  • 13. RFEM-SCIA: planar frame – chessboard loads, temperature loads and shift of supports, evaluation of results.