Course detail

Structural Analysis 1

FAST-BDA003Acad. year: 2025/2026

Moving load of static quantity of statically determinate frame structures. Solution using influence lines, analytic and kinematic method. Evaluation of influence lines and determination of extreme values.
Principle of virtual work. Clauses about virtual works reciprocity. Maxwell-Mohr integral. Solution of displacement and rotation of frame systems using method of unit forces, including the influence of temperature changes. Veresčagin’s rule.
Statically indeterminate structures. Degree of static indeterminacy. Solution methods. Force method. Elementary cantilever beam. Continuous girder is solved by three-torque equation. Moving load at continuous girder. Combinations of loads.
Planar frame using by force method, option of statically indeterminate values, canonical equations. Influence of shift of supports, effects of uniform and non-uniform temperature changes at frame structure. Utilization of shape symmetry.
Planar arc is solved by force method, influence of compression of line of arc, deflection load. Statically indeterminate truss girder is solved by force method.

Language of instruction

Czech

Number of ECTS credits

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

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

Aims

Explanation the principle of virtual work and theorem of reciprocity of virtual work. The calculation of deformations by the method of unit forces.
Information about the force method of structural analysis of statically indeterminate plane frames, planar bar systems, continuous girder, including the effect of support relaxation and the temperature influence.

The student will learn the structural analysis of statically indeterminate bar structures by the force method, namely plane frames, planar bar systems, continuous girder, statically indeterminate trusses, including the effect of support relaxation and the temperature influence.

Study aids

Not applicable.

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 BPC-SI Bachelor's

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

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

Type of course unit

 

Lecture

26 hod., 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 hod., 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.