Course detail

Structural Mechanics 2

FAST-AD002Acad. year: 2022/2023

The division of the structures, planar bar systems. Loading of structures, evaluation of influence lines. The principle of the virtual work, the calculation of the translations and rotations of the bar systems by means of the unit forces method. Statically indeterminate structures, the degree of static indeterminacy, the force method. Continuous beam solved by the Clapeyron’s theorem. Plane frame, plane arc and statically indeterminate truss girder solved by the force method. The slope and deflection method and its variants. The computation model and the number of degrees of freedom. The analysis of a straight bar with constant cross-section, local quantities, the primary vector and the stiffness matrix. Geometrical transformation, the global stiffness matrix. The analysis of a bar system, 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. Analysis of the rectangular frames and continuous girders.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

Ing. Jarmila Křiváková, CSc.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

The students will be able to solve structural analysis of statically indeterminate plane frames, planar bar system, continuous girder and plane truss systems and grids the force method. The obtaines the information about general deformation method of statically indeterminate plane and space frames and about principles of the Finite Element Method.

Prerequisites

Linear algebra, fundaments of matrix calculus, solutions of systems of linear algebraic equations, vector calculus, analytic geometry, derivative of a function , the indefinite integral, the definite integral, applications of the integral in geometry and physics.Mechanical power, physical work, second order moments. Structural analysis of axial forces in statically determinate trusses, simple plane beams and plane frames.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. The division of the structures, fundamental assumptions of the analysis. Statics of planar bar systems. The influence of the moving load on the statically determinate structures.
2. The virtual work of the internal and external forces, the Lagrange’s principle of the virtual work and the laws of virtual works correspondence. Mohr’s integral, simplifications of the calculation. Vereschagin’s rule.
3. The enumeration of the translations and rotations of the straight and broken girders by the method of unit forces. The evaluation of the translations of the truss girders by means of the unit forces method.
4. Methods of analysis of the static indeterminate structures. The evaluation of the degree of static indeterminacy. The principle of the force method.
5. Continuous girder analysed by Clapeyron’s theorem. Force and deflection loading, utilisation of the shape symmetry.
6. The plane frame analysed by the force method. The selection of the statically indeterminate unknowns, canonical equations. The influence of shifts of the supports and the influence of the uniform and non-uniform temperature changes.
7. Plane arch analysed by the force method. The influence of the compression of the arch thrust line. Statically indeterminate truss analysed by the force method.
8. The principles of the stiffness method and its variants. Calculation model and the number of degrees of freedom. Static conditions of the equilibrium, the parameters of the deflection, constrained nodes. The matrix formulation of the stiffness method.
9. The analysis of a straight bar with constant cross-section. Variously ending bars. Local quantities, the primary vector and the stiffness matrix. The modelling of a cantilever.
10. The geometrical transformation into the global coordinate system, the global matrix of a bar. The transformation at the rectangular frames. The analysis of a bar system, the versions of assemblage of the equation system, the code number and the localization. Some particularities in the analysis of the rectangular frames and continuous girders.
11. The analysis of bars – the solution of the bar actions, the diagrams of the components of the internal forces. 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.
12. Bars with haunts, temperature changes, shifts of the supports. A truss girder solved by the stiffness method. The combinations of the loading cases, the extremes. The analysis of the spatial frames by the stiffness method.
13. Other problems and methods of the structural mechanics. Plane strain and plane stress problems, plates, shells. Examination of the response of structures subjected to excitation. Information about software products.

Work placements

Not applicable.

Aims

Loading of structures, influence of mobile load. Influence lines of static quantities exerted on a beam.
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. Structural analysis of axial forces in statically indeterminate trusses.
Introduction to the stiffness method for analysis of the statically indeterminate bar systems. Simplification to the stiffness method for analysis of planar bar systems, plane trusses. Influence of the beam haunch. Temperature effects, shifts of the supports.
Principles of the finite element method. Introduction to the structural dynamics.

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

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B-P-C-APS (N) Bachelor's

    branch APS , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Jarmila Křiváková, CSc.

Syllabus

1. The division of the structures, fundamental assumptions of the analysis. Statics of planar bar systems. The influence of the moving load on the statically determinate structures. 2. The virtual work of the internal and external forces, the Lagrange’s principle of the virtual work and the laws of virtual works correspondence. Mohr’s integral, simplifications of the calculation. Vereschagin’s rule. 3. The enumeration of the translations and rotations of the straight and broken girders by the method of unit forces. The evaluation of the translations of the truss girders by means of the unit forces method. 4. Methods of analysis of the static indeterminate structures. The evaluation of the degree of static indeterminacy. The principle of the force method. 5. Continuous girder analysed by Clapeyron’s theorem. Force and deflection loading, utilisation of the shape symmetry. 6. The plane frame analysed by the force method. The selection of the statically indeterminate unknowns, canonical equations. The influence of shifts of the supports and the influence of the uniform and non-uniform temperature changes. 7. Plane arch analysed by the force method. The influence of the compression of the arch thrust line. Statically indeterminate truss analysed by the force method. 8. The principles of the stiffness method and its variants. Calculation model and the number of degrees of freedom. Static conditions of the equilibrium, the parameters of the deflection, constrained nodes. The matrix formulation of the stiffness method. 9. The analysis of a straight bar with constant cross-section. Variously ending bars. Local quantities, the primary vector and the stiffness matrix. The modelling of a cantilever. 10. The geometrical transformation into the global coordinate system, the global matrix of a bar. The transformation at the rectangular frames. The analysis of a bar system, the versions of assemblage of the equation system, the code number and the localization. Some particularities in the analysis of the rectangular frames and continuous girders. 11. The analysis of bars – the solution of the bar actions, the diagrams of the components of the internal forces. 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. 12. Bars with haunts, temperature changes, shifts of the supports. A truss girder solved by the stiffness method. The combinations of the loading cases, the extremes. The analysis of the spatial frames by the stiffness method. 13. Other problems and methods of the structural mechanics. Plane strain and plane stress problems, plates, shells. Examination of the response of structures subjected to excitation. Information about software products.

Exercise

13 hod., compulsory

Teacher / Lecturer

Ing. Jarmila Křiváková, CSc.

Syllabus

1. Eccentric tension and compression, the position of the neutral axis, the core of the section. Design of the beams in a case of the complex load. Buckling strength and the stability of the compressed bars. Checking of the buckling bars. The principal stresses. 2. The deflection of the bent beams, Mohr’s method, Clebsch’ method, the Lagrange’s principle of the virtual work, Mohr’s integral, simplifications of the calculation. Vereschagin’s rule. 3. Analysis of plane beams by the force method. 4. Analysis of continuous girders by Clapeyron’s theorem. 5. Analysis of plane frames by the force method. 6. Analysis of plane frames by the simplified stiffness method. 7. General stiffness method.