Course detail

Structural Mechanics

FAST-BD05Acad. year: 2013/2014

Moving load, influence lines of the deflection and static quantities of the static determinate structures, evaluation of the influence lines and determination of its extremes; the kinematical method of solution; the influence lines of the deflection and static quantities of the static indeterminate bar structures; structures with bars of varying cross-section; elastic and eccentric connection of bars within the frame structures; the analysis of thin-walled bars, cross-section characteristics and the shear centre, solution of the thin-walled bars with opened cross-section, normal and shear stress; differential equation of restrained torsion of opened cross-section shape, evaluation of the characteristic quantities of the torsion, analysis of the thin-walled sections of a closed cross-section, linear stability of the frame structures, Euler’s critical force and the shapes of buckled structure; elasto-plastic analysis of a bar, the basis of a limit state analysis, the plastic limit load carrying capacity of a cross-section, the plastic limit load carrying capacity of a frame structure, the failure limit states.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Zbyněk Keršner, CSc.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Students handle basics of the structural analysis of solution of plane trusses of loading mobile load. Evaluation of the influence lines and determination of its extremes. Structures with bars of varying cross-section. Elastic and eccentric connection of bars within the frame structures. The analysis of linear stability of the frame structures, Euler’s critical force and the shapes of buckled structure. The principle of solution of the thin-walled bars with opened cross-section, equation of restrained warping torsion of opened cross-section shape. Introduction to the elastic-plastic analysis of a bar. The plastic limit load carrying capacity of a frame structure. The limit failure states.

Prerequisites

Structural analysis of axial forces in statically determinate trusses, simple built-in beam, plane frame; the principle of virtual work and theorem of reciprocity of virtual work, the calculation of deformations by the method of unit forces; 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; basic cases and complex cases of the load of the beam, design of the beams in the case of the composed (complex) load; the stability and the bucking strength of the compressed bars, Euler’s solution, the critical force and the critical stress, the theory of the material strength and failure, the stress and strain state in a point of the body, the principal stress at the planar stress problem.

Co-requisites

Force and deformation methods for solving statically indeterminate beams, frames.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Methods of teaching are lectures and exercises. Individual consultations complement teaching. Study activities of students includes entering his own independent work. Attendance at lectures is recommended. Participation in other classes is required and controlled.

Assesment methods and criteria linked to learning outcomes

The subject is completed by credit and final examination. For credit the student should pass all written tests in selected exercises. The credit is the necessary condition for final examination entrance. The final examination consists of written and oral parts. The written examination part includes both examples and theory. The positive result in written examination allows the student to pass to oral part.

Course curriculum

1.Moving load. Influence lines of the deflection and static quantities of the static determinate structures.
2.Evaluation of the influence lines and determination of its extremes. The kinematical method of solution.
3.The influence lines of the deflection and static quantities of the static indeterminate bar structures.
4.Structures with bars of varying cross-section.Elastic and eccentric connection of bars within the frame structures.
5.The analysis of thin-walled bars. Cross-section characteristics and the shear centre.
6.Solution of the thin-walled bars with opened cross-section. Normal and shear stress.
7.Differential equation of restrained warping torsion of opened cross-section shape.
8.Evaluation of the characteristic quantities of the warping.
9.Analysis of the thin-walled sections of a closed cross-section.
10.Linear stability of the frame structures. Euler’s critical force and the shapes of buckled structure.
11.Elasto-plastic analysis of a bar. The basis of a limit state analysis.
12.The limit plastic load carrying capacity of a cross-section.The limit plastic load carrying capacity of a frame structure.
13.The limit failure states.

Work placements

Not applicable.

Aims

Introduction to the structural analysis of solution of plane trusses of loading mobile load. Evaluation of the influence lines and determination of its extremes.
Structures with bars of varying cross-section. Elastic and eccentric connection of bars within the frame structures. The analysis of linear stability of the frame structures, Euler’s critical force and the shapes of buckled structure.
The principle of solution of the thin-walled bars with opened cross-section, equation of restrained warping torsion of opened cross-section shape.
Introduction to the elasto-plastic analysis of a bar. The plastic limit load carrying capacity of a frame structure. The limit failure states.

Specification of controlled education, way of implementation and compensation for absences

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Kadlčák, J., Kytýr, J.: Statika stavebních konstrukcí II. Brno: VUTIUM, 2001. ISBN 978-80-214-3428-8. (CS)
Kadlčák, J., Kytýr, J.: Statika stavebních konstrukcí I. Brno: VUTIUM, 2010. ISBN 978-80-214-3419-6. (CS)

Recommended reading

Servít, R., Doležalová, E., Crha, M.: Teorie pružnosti a plasticity I. SNTL/ALFA Praha, 1981. (CS)
Servít, R., Drahoňovský, Z., Šejnoha, J., Kufner, V.: Teorie pružnosti a plasticity II. STNL/ALFA Praha, 1984. (CS)
Bedford, A., Fowler, W. L.: Statics - Engineering Mechanics. Addison-Wesley Publisnihg Comp., Inc., 1995. (EN)
Bittnar, Z., Šejnoha, J.: Numerical Methods in Structural Mechanics. Asce Press, Thomas Telford Pub., 1996. (EN)

Classification of course in study plans

  • Programme B-P-E-SI Bachelor's

    branch K , 4. year of study, summer semester, compulsory

  • Programme B-P-C-SI Bachelor's

    branch K , 4. year of study, summer semester, compulsory

  • Programme B-K-C-SI Bachelor's

    branch K , 4. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

prof. Ing. Zbyněk Keršner, CSc.

Syllabus

1. Moving load. Influence lines of the deflection and static quantities of the static determinate structures.
2. Evaluation of the influence lines and determination of its extremes. The kinematical method of solution.
3. The influence lines of the deflection and static quantities of the static indeterminate bar structures.
4. Structures with bars of varying cross-section.Elastic and eccentric connection of bars within the frame structures.
5. The analysis of thin-walled bars. Cross-section characteristics and the shear centre.
6. Solution of the thin-walled bars with opened cross-section. Normal and shear stress.
7. Differential equation of restrained torsion of opened cross-section shape.
8. Evaluation of the characteristic quantities of the torsion.
9. Analysis of the thin-walled sections of a closed cross-section.
10. Linear stability of the frame structures. Euler’s critical force and the shapes of buckled structure.
11. Elasto-plastic analysis of a bar. The basis of a limit state analysis.
12. The limit plastic load carrying capacity of a cross-section.The limit plastic load carrying capacity of a frame structure.
13. The limit failure states.

Exercise

26 hours, compulsory

Teacher / Lecturer

prof. Ing. Zbyněk Keršner, CSc.

Syllabus

1. Introduction, influence lines of simply supported beam and cantilever beam. Static and kinematic method.
2. Influence lines of beam with overhanging parts and Gerber beam.
3. Numerical analysis of system of forces with fixed mutual distances moving on the beam.
4. Extreme bending moments caused by system of forced at selected cross-section and under selected force. Winkler’s and force criterion.
5. Extreme bending moment on the beam caused by system of forced. Šolín’s criterion.
6. Influence lines of continuous beams.
7. Deformations of beams with haunches. Analytical and numerical integration.
8. Statically indeterminate beams with haunches. Analytical and numerical integration, tables.
9. Continuous beams with haunches. Test.
10. Ultimate plastic capacity of cross-section. Plastic reserve of cross-section.
11. Ultimate plastic load-bearing capacity of structures. Kinematic and static method.
12. Ultimate plastic load-bearing capacity of structures. Incremental method.
13. Finishing of exercises, discussion, correction test, credits.