Course detail

Structural Analysis 1

FAST-BDA003Acad. year: 2026/2027

Moving load of static quantity of statically determinate beam structures. Solution using influence lines, analytical and kinematic method (Müller-Breslau principle). Evaluation of influence lines and determination of extreme values.
Principle of virtual work. Maxwell–Betti reciprocal work theorem. Maxwell-Mohr equation. Solution of displacement and rotation of beam systems using unit dummy force method, including the influence of temperature changes and support settlements. Veresčagin’s rule.
Statically indeterminate structures. Degree of static indeterminacy. Force method (Method of consistent deformations, Flexibility method). Simple statically indeterminate beam. Continuous beam solved by three-moment equation method.
Planar frame analyzed using the force method. Selection of statically indeterminate variables. Canonical equations. Effect of support settlement; effects of uniform and non-uniform temperature changes. Use of geometric symmetry.
Structures with variable cross-sections.

Language of instruction

Czech, English

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. Ing. David Lehký, Ph.D.

Department

Institute of Structural Mechanics (STM)

Offered to foreign students

Of all faculties

Entry knowledge

Linear algebra, fundaments of matrix calculus, solutions of systems of linear algebraic equations, vector calculus, analytic geometry, derivative of a function, the indefinite and definite integral, applications of the integral.

Rules for evaluation and completion of the course

The procedure for completing the course and the rules for evaluating students will be set forth in a notice issued by the course coordinator, which is updated annually.

Aims

Explanation of the aspects of moving loads on structures and an introduction to the use of influence lines for their analysis.
Explanation the principle of virtual work and theorem of reciprocity of virtual work. The calculation of displacements and rotations using the unit dummy force method.
Introduction to the force method and its application in the analysis of statically indeterminate beam structures. Students will use this method to solve for simple statically indeterminate beams, continuous beams, plane frames, and plane arches, including the effects of support settlement and temperature changes.

Study aids

Udoeyo, Felix F. Structural Analysis. Philadelphia: Temple University Press, 2020. Available from: https://temple.manifoldapp.org/read/structural-analysis/section/e1234718-83ed-42b0-b774-658813d8b813.
Kytýr, J., Gratza, R., Plášek, J., Ekr, J., Ridoško, T.: Statika I – řešené příklady. Skriptum. Akademické nakladatelství CERM, Brno, 2014.
Elektronické podklady: www.stm.fce.vutbr.cz/study/materials

Prerequisites and corequisites

Not applicable.

Basic literature

KADLČÁK, Jaroslav a Jiří KYTÝR. Statika stavebních konstrukcí I. Brno: Nakladatelství VUTIUM, 2007. ISBN 978-80-214-3419-6. (CS)
KADLČÁK, Jaroslav a Jiří KYTÝR. Statika stavebních konstrukcí II. Brno: Nakladatelství VUTIUM, 2007. ISBN 978-80-214-3428-8. (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)

Recommended reading

KYTÝR, Jiří, Roman GRATZA, Jan PLÁŠEK, Jan EKR a Tomáš RIDOŠKO. Statika I – řešené příklady. Brno: Akademické nakladatelství CERM, 2014. ISBN 978-80-7204-868-7. (CS)

Classification of course in study plans

  • Programme BPA-SI Bachelor's 2 year of study, summer semester, compulsory
  • Programme BKC-SI Bachelor's 2 year of study, summer semester, compulsory

  • Programme BPC-SI Bachelor's

    specialization VS , 2 year of study, summer semester, compulsory

  • Programme CZV1-AKR Lifelong learning

    specialization PBC , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

prof. Ing. David Lehký, Ph.D.

Syllabus

  • 1. Introduction, course content. Moving loads. Influence lines of static quantities of statically determinate structures. Static and kinematic methods of solution. Gerber beam.
  • 2. Evaluation of influence lines and determination of extremes. Criteria for deriving maximum moments.
  • 3. Virtual work of external and internal forces. Lagrange's and Castigliano's principle of virtual works. Reciprocity theorems for virtual works. Maxwell-Mohr equation.
  • 4. Determination of displacement and rotation of beams and frames by the unit dummy forces method. Effect of normal and shear internal forces. Vereshchagin's rule. Effect of temperature change and support shifts on displacements.
  • 5. Calculation of displacement of trusses for force loads, temperature changes and support shifts. Assessment of static indeterminacy of structures.
  • 6. Methods of solution of statically indeterminate structures. Description of the force method. Simple statically indeterminate beam, effect of axial load.
  • 7. Continuous beams, solved by the force method (three moment equation method) for force loads, temperature changes and support shifts.
  • 8. Open and closed plane frames solved by the force method. Choice of statically indeterminate quantities, canonical equations. Effects of uniform and non-uniform temperature change on the frame. Effect of support shift.
  • 9. Statically indeterminate plane truss loaded by forces temperature changes and support shifts solved by the force method.
  • 10. Use of geometric symmetry of the frame, decomposition of the general load, restraints on the symmetry axes.
  • 11. Solution of statically indeterminate structures with variable cross-sections. Redistribution of internal forces.
  • 12. Displacement and rotation of statically indeterminate structures. Curved beams. Plane statically indeterminate arch.

Exercise

26 hours, compulsory

Teacher / Lecturer

prof. Ing. David Lehký, Ph.D.

Syllabus

  • 1. Repetition of internal force calculation on plane statically determinate structures.
  • 2. Moving loads. Application of the kinematic method to a beam with overhanging and a Gerber beam.
  • 3. Determination of reactions and internal forces on statically determinate structures by evaluating the influence lines.
  • 4. Calculation of displacements and rotations by the unit dummy force method on simple beams. Integration and application of Vereshchagin's rule.
  • 5. Calculation of displacement and rotation by the unit dummy force method on more complex structures with more complex type of loading.
  • 6. Effect of temperature change and support shift on the displacement of beams. Calculation of displacement of trusses.
  • 7. Degree of static indeterminacy. Creation of a basic statically determinate system.
  • 8. Solution of simple statically indeterminate beams under force loading.
  • 9. Solution of simple statically indeterminate beams under temperature loading and support shifts.
  • 10. Solution of more complex statically indeterminate structures under force loading.
  • 11. Solution of more complex statically indeterminate structures under force loading, temperature change and support shifts.
  • 12. Solution of statically indeterminate plane truss.