Course detail

Structural Analysis II

FAST-BD04Acad. year: 2014/2015

Loading of structures, influence of mobile load. Influence lines of static quantities of statically dependent bar structures. Kinematic method of solution. Evaluation of the influence lines and determination of the extremes. Criteria.
The principles of the slope and deflection method and its variants. The computation model and the number of degrees of freedom. The slope and deflection method for the planar structures. The analysis of a straight bar with changing cross-section. Local quantities, the primary vector and the stiffness matrix. Hinged bar, cantilever. A bar with the constant cross-section. Geometrical transformation, the global stiffness matrix. The analysis of a bar system, the assembling of the equations, the localization process. Calculation of the end forces of a bar and the diagrams of the internal forces. The solution of the reactions and the check of the equilibrium. Another version of the assembling of the system of equations.
Analysis of the rectangular frames and continuous girders. Temperature effects, shifts of the supports. A truss girder solved by the slope and deflection method. Utilisation of the symmetry. Elastically connected bar. The combinations of the loading cases, the extremes. The stability of the plane frames.
The analysis of the spatial frames by the slope and deflection method. Information on software products.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Jiří Kytýr, CSc.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

The student will learn the moving load of statically dependent bar structures. The student will also learn the structural analysis of statically indeterminate bar structures by the stiffness method, namely plane frames, planar bar systems, continuous girders, statically indeterminate trusses, influence of the temperature changes and shifts of the supports. The student will learn the basic tasks with the programme system RFEM–SCIA.

Prerequisites

Structural analysis of axial forces in statically determinate trusses, simple built-in beams, plane frames. Explanation the principle of virtual work and theorem of reciprocity of virtual work. The enumeration of the translations and rotations of the straight and broken girders by the method of unit forces. The solution of planar bar systems by the force method.

Co-requisites

Applications of the integral. Solutions of linear differential equations.

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 finished by abridged examination or final examination. For abridged exam the student should pass all written tests in exercises. The final examination consists of written and oral parts. The written examination may contain both examples and the theoretical questions. The positive result in written examination allows the student to pass to oral part.

Course curriculum

1. Moving load. Influence lines of static quantities of statically dependent bar structures.
2. Kinematic method of solution. Evaluation of the influence lines and determination of the extremes. Criteria.
3. The principles of the stiffness method, its origin and its development, the variants of this method. Calculation model and the number of degrees of freedom.
4. Static conditions of the equilibrium, the parameters of the deflection, constrained nodes. The matrix formulation of the stiffness method.
5. The analysis of a straight bar with changing cross-section. Variously ending bars. Local quantities, the primary vector and the stiffness matrix. The modelling of a cantilever.
6. A bar with a constant cross-section, fundamental deflection coefficients. The assembling of the primary vector based upon the end forces of a bar.
7. The geometrical transformation into the global coordinate system, the global matrix of a bar. The transformation at the rectangular frames.
8. The analysis of a bar system, the assemblage of the system of equations, the code number and the localization.
9. The analysis of bars – the calculation of components of the internal forces, the diagrams of the normal, shearing forces and the bending moments.
10. The solution of the reactions, the check of the equilibrium –in the nodes and for the whole structure. Errors produced in the solution of the frames by the stiffness method.
11. Another version of the assemblage of the system of equations. Some particularities in the analysis of the rectangular frames and continuous girders.
12. The analysis of the spatial frames by the stiffness method. Temperature changes, shifts of the supports.
13. A truss girder solved by the stiffness method. Slope and deflection method.

Work placements

Not applicable.

Aims

Introduction to the stiffness Method for analysis of the statically indeterminate of planar bar systems. Simplification to the stiffness method and deflection method for analysis of planar bar systems, plane trusses. Influence of the beam haunch.

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

Antony Bedford, Wallace L. Fowler: Statics - Engineering Mechanics. Addison-Wesley Publishing Company, Inc., 1995. (EN)
KADLČÁK, J. - KYTÝR, J.: Statika stavebních konstrukcí I. VUTIUM Brno, 2010. ISBN 80-214-1204-6. (CS)
KADLČÁK, Jaroslav a KYTÝR, Jiří: Statika stavebních konstrukcí II. Brno: VUTIUM, 2009. ISBN 978-80-214-3428-8. (CS)
Zdeněk Bittnar, Jiří Šejnoha: Numerical Methods in Structural Mechanics. Asce Press, Thomas Telford, 1996. (EN)

Recommended reading

Sobota, J.: Statika stavebných konštrukcií 2. ALFA Bratislava, 1991. (SK)

Classification of course in study plans

  • Programme B-K-C-SI Bachelor's

    branch K , 3 year of study, winter semester, compulsory
    branch S , 3 year of study, winter semester, compulsory

  • Programme B-P-C-SI Bachelor's

    branch K , 3 year of study, winter semester, compulsory
    branch S , 3 year of study, winter semester, compulsory

  • Programme B-P-E-SI Bachelor's

    branch K , 3 year of study, winter semester, compulsory
    branch S , 3 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Jiří Kytýr, CSc.

Syllabus

1. Moving load. Influence lines of static quantities of statically dependent bar structures.
2. Kinematic method of solution. Evaluation of the influence lines and determination of the extremes. Criteria.
3. The principles of the stiffness method, its origin and its development, the variants of this method. Calculation model and the number of degrees of freedom.
4. Static conditions of the equilibrium, the parameters of the deflection, constrained nodes. The matrix formulation of the stiffness method.
5. The analysis of a straight bar with changing cross-section. Variously ending bars. Local quantities, the primary vector and the stiffness matrix. The modelling of a cantilever.
6. A bar with a constant cross-section, fundamental deflection coefficients. The assembling of the primary vector based upon the end forces of a bar.
7. The geometrical transformation into the global coordinate system, the global matrix of a bar. The transformation at the rectangular frames.
8. The analysis of a bar system, the assemblage of the system of equations, the code number and the localization.
9. The analysis of bars – the calculation of components of the internal forces, the diagrams of the normal, shearing forces and the bending moments.
10. The solution of the reactions, the check of the equilibrium –in the nodes and for the whole structure. Errors produced in the solution of the frames by the stiffness method.
11. Another version of the assemblage of the system of equations. Some particularities in the analysis of the rectangular frames and continuous girders.
12. The analysis of the spatial frames by the stiffness method. Temperature changes, shifts of the supports.
13. A truss girder solved by the stiffness method. Slope and deflection method.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Kytýr, CSc.

Syllabus

1. Conditions for performance in practice and obtaining credit. Entrance test – repetition of simple statically indeterminate systems, the internal forces. Analysis of static and kinematic determination of bar systems.
2. Influence lines of static quantities of simple beam, cantilever and Gerber’s beam.
3. Determination of the extreme effects of moving load. Winkler’s, forces and Sholin’s criterion.
4. Calculation models of bar structures for stiffness method. Analysis of the number of degrees of freedom. Calculation of continuous beam with force load by stiffness method. Primary vectors and stiffness matrices of bars. Global stiffness matrix of the structure.
5. Calculation of continuous beam – solution of the equations, the end forces, the internal forces, reactions. The first test.
6. Frame analysed by the stiffness method with a force load. Analysis of the bars – primary vectors and local stiffness matrices.
7. The geometrical transformation into the global coordinate system. The assemblage of the system of equations.
8. The analysis of bars – the calculation of the end forces, the diagrams of the normal, shearing forces and the bending moments. The solution of the reactions, the check of the equilibrium –in the nodes and for the whole structure. The second test.
9. A truss girder solved by the stiffness method.
10. Completion – a truss girder solved by the stiffness method.
11. The influence of temperature changes and shifts of the supports on a bar structure.
12. Programme system RFEM–SCIA – details. The calculation of a continuous girder with cantilever. Load and the combinations of the loading cases and the extremes.
13. RFEM–SCIA: Calculation of the plane frame. Temperature changes, shifts of the supports. Evaluation of the results. Credit.