Course detail

Structural Mechanics 2

FAST-BDA016Acad. year: 2023/2024

The course deals with static and deformation analysis of simple statically indeterminate beam structures by force and direct stiffness method. Topics: Types of structures in civil engineering. Types of loads acting on a structure. Influence lines for statically determinate structures. Principle of virtual work and its application to calculation of deflections and rotations of statically determinate beams – unit dummy force method. Statically indeterminate structures, degree of static and kinematic indeterminacy of structures. Principle of force method for analysis of indeterminate structures. Three-moment equation method for continuous beam analysis. Force method – statically indeterminate plane frames and trusses. Principle of direct stiffness method. Computational model and degree of kinematic indeterminacy. General form of direct stiffness method – matrix form, analysis of straight beam with constant cross-section, continuous beam and frame. Slope deflection method – end moments and forces, analysis of continuous beam and frame analysis.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

doc. Ing. Hana Šimonová, Ph.D.

Department

Institute of Structural Mechanics (STM)

Entry knowledge

Linear algebra, fundamentals of matrix calculus, solutions of systems of linear algebraic equations, vector calculus, analytic geometry, derivative of a function, indefinite and definite integral, applications of the integral. Determination of reactions and internal forces of statically determinate plane beams and frames.

Rules for evaluation and completion of the course

The course is finished by credit and final examination. The credit is a necessary condition for final examination entrance. To gain credit, the students should pass two control tests during the semester. The active presence in practical classes is checked. A written exam consists of the part, in which the example is elaborated, and the theoretical part. To pass the exam successfully, both parts should be accomplished.


The definition of monitored instruction and the method of its implementation is annually updated by the guarantor of the course.

Aims

Students will be acquainted with influence lines for statically determinate structures. Principle of virtual work and its application to calculation of deflections and rotations of statically determinate beams (unit dummy force method) will be clarified. Students will learn how to solve statically indeterminate beam structures by force method and direct stiffness method. The solution of statically indeterminate structures will be performed on two-sided fixed beam, continuous beam, planar frame, and truss girder. The force load, the effect of temperature changes and the support settlement are considered.


Students will be able to solve influence lines for statically determinate structures, calculate deflections and rotations of statically determinate beams using unit dummy force method and solve statically indeterminate planar beam structures by force method and direct stiffness method.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Kadlčák, J., Kytýr, J. Statika stavebních konstrukcí II. Staticky neurčité prutové konstrukce. Učebnice. Nakladatelství VUTIUM v Brně, 2004. (CS)
Kytýr, J., Gratza, R., Plášek, J., Ekr, J., Ridoško, T. Statika I – Řešené příklady. Akademické nakladatelství CERM, Brno, 2014. (CS)
Kytýr, J., Gratza, R., Plášek, J., Ridoško, T., Ekr, J. Statika II – Řešené příklady. Akademické nakladatelství CERM, Brno, 2016. (CS)

Recommended reading

Cueto E., Gonzales, D. An Introduction to Structural Mechanics for Architects. Springer, 2018. (EN)
Hulse, R. Cain, J. Structural mechanics. Red Globe Press, 2000. (EN)
Jíra, A., Jandeková, D., Novotná, E., Hájková, P., Řehounek, L., Štěpánek, J., Voříšek, J. Sbírka příkladů stavební mechaniky – princip virtuálních sil, silová metoda, deformační metoda. ČVUT v Praze, Praha, 2021. (CS)
Křiváková, J. Stavební mechanika 2. Moduly AD01-MO1 až AD01-MO3. Studijní opory. VUT, FAST, Brno, 2011. (CS)

Classification of course in study plans

  • Programme BPC-APS Bachelor's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Hana Šimonová, Ph.D.

Syllabus

  1. Types of structures in civil engineering. Types of loads acting on a structure. Influence lines for statically determinate structures.
  2. Principle of virtual work, Lagrange’s equations. Maxwell–Betti reciprocal work theorem. Maxwell–Mohr’s integral. Vereshchagin’s rule.
  3. Deflections and rotations of statically determinate straight beams, frames and trusses – unit dummy force method.
  4. Methods for analysis of statically indeterminate structures, degree of static and kinematic indeterminacy of structures. Principle of force method.
  5. Three-moment equation method for continuous beam analysis. Force and deflection load. Utilisation of symmetry of beam shape.
  6. Force method – statically indeterminate plane frames. Selection of statically indeterminate variables. Effect of temperature changes and support settlement.
  7. Force method – statically indeterminate truss.
  8. Principle of direct stiffness method. Computational model and degree of kinematic indeterminacy
  9. General form of direct stiffness method – matrix form, analysis of straight beam with constant cross-section. Load vector and stiffness matrix.
  10. Slope deflection method – end moments and forces. Analysis of continuous beam.
  11. Slope deflection method – plane frame analysis.
  12. Direct stiffness method – continuous beam analysis.
  13. Direct stiffness method – plane frame analysis.

Exercise

13 hod., compulsory

Teacher / Lecturer

doc. Ing. Hana Šimonová, Ph.D.

Syllabus

  1. Influence lines for statically determinate structures.
  2. Deflections and rotations of statically determinate straight beams, frames and trusses – unit dummy force method. Vereshchagin’s rule.
  3. Force method – statically indeterminate straight beams.
  4. Three-moment equation method – continuous beam analysis. Force method – statically indeterminate plane frame.
  5. Force method – statically indeterminate plane frame. Degree of kinematic indeterminacy.
  6. Slope deflection method – plane frame analysis.
  7. Credit