Course detail

Structural Analysis 2 (EVB)

FAST-BDA014Acad. year: 2021/2022

The course deals with static and deformation analysis of simple statically indeterminate beam structures by force and slope deflection method. Topics: Principle of virtual work. Clauses about virtual works reciprocity. Maxwell-Mohr integral. Solution of displacement and rotation of frame systems using unit dummy force method, including the influence of temperature changes. Veresčagin’s rule.
Statically indeterminate structures. Degree of static indeterminacy. Solution methods. Force method. Cantilever beam. Continuous beam solved by three-moment equation method. Planar frame by force method, selection of statically indeterminate variables, canonical equations. Influence of support settlement, effects of uniform and non-uniform temperature changes. Statically indeterminate truss girder solved by force method.
Principle of slope deflection methods. Computational model and degree of kinematic indeterminacy. Slope deflection method for planar structures. Local variables, primary vector and stiffness matrix. Beam connected by hinges, cantilever. Beam with constant cross-section. Geometric transformation, global matrix of beam. Analysis of beam systems, compilation of equations, localization. Determination of reactions and internal forces at beam. Determination of reactions of the structure and validation. Solution of rectangular frames and continuous beams. Temperature influence, support settlement. Truss girder solved by slope deflection method.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. David Lehký, Ph.D.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Not applicable.

Prerequisites

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.

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. Meaning of statics, fundamental assumptions of solution. Virtual work of internal and external forces. Lagrange’s principle of virtual works. Theorem about virtual works reciprocity. Maxwell-Mohr theorem, simplification of calculation.
2. Determination of displacement and rotation of straight and cranked beams using unit dummy force method. Veresčagin’s rule. Influence of temperature changes on deformation of beam. Calculation of deflection of truss girders.
3. Methods of solution of statically indeterminate frame structures. Assessment of static indeterminacy. Interpretation of force method.
4. Elementary statically indeterminate straight beam, effect of uniaxial loading.
5. Continuous beam, general form of three-moment equation for force and deflection load. Diagrams of internal forces.
6. Planar frame solved by force method. Selection of statically indeterminate variables, canonical equations. Effect of uniform and non-uniform temperature changes. Influence support settlement.
7. Principle of slope deflection method. Computational mode and degree of kinematic indeterminacy.
8. General slope deflection method for planar frame structures. Equilibrium conditions, parameters of deflection, bounded nodes. Scalar and matrix form.
9. Analysis of straight beam with constant cross-section: primary and secondary state.
10. Local variables, primary vector and the stiffness matrix. Beam connected by hinges, cantilever.
11. Geometric transformation, global matrix of a beam. Analysis of the frame system, compilation of the system of equations, code number and localization.
12. Completion of solution of beams – calculation of internal forces and deflections of beams. Determination of reactions and validation. Errors during the solution of frames by using slope deflection method. Another variant for assembly of equations.
13. Speciality of solution of rectangular frames and continuous girders. Temperature influences, support settlement. Truss girder solved by slope deflection method.

Work placements

Not applicable.

Aims

Not applicable.

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 BPC-EVB Bachelor's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. David Lehký, Ph.D.

Syllabus

1. Meaning of statics, fundamental assumptions of solution. Virtual work of internal and external forces. Lagrange’s principle of virtual works. Theorem about virtual works reciprocity. Maxwell-Mohr theorem, simplification of calculation. 2. Determination of displacement and rotation of straight and cranked beams using unit dummy force method. Veresčagin’s rule. Influence of temperature changes on deformation of beam. Calculation of deflection of truss girders. 3. Methods of solution of statically indeterminate frame structures. Assessment of static indeterminacy. Interpretation of force method. 4. Elementary statically indeterminate straight beam, effect of uniaxial loading. 5. Continuous beam, general form of three-moment equation for force and deflection load. Diagrams of internal forces. 6. Planar frame solved by force method. Selection of statically indeterminate variables, canonical equations. Effect of uniform and non-uniform temperature changes. Influence support settlement. 7. Principle of slope deflection method. Computational mode and degree of kinematic indeterminacy. 8. General slope deflection method for planar frame structures. Equilibrium conditions, parameters of deflection, bounded nodes. Scalar and matrix form. 9. Analysis of straight beam with constant cross-section: primary and secondary state. 10. Local variables, primary vector and the stiffness matrix. Beam connected by hinges, cantilever. 11. Geometric transformation, global matrix of a beam. Analysis of the frame system, compilation of the system of equations, code number and localization. 12. Completion of solution of beams – calculation of internal forces and deflections of beams. Determination of reactions and validation. Errors during the solution of frames by using slope deflection method. Another variant for assembly of equations. 13. Speciality of solution of rectangular frames and continuous girders. Temperature influences, support settlement. Truss girder solved by slope deflection method.

Exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Václav Sadílek, Ph.D.
Ing. Martina Sadílková Šomodíková, Ph.D.

Syllabus

1. Repetition of calculations of internal forces of planar cranked statically determinate frame structures. 2. Calculation of displacements and rotations of elementary beam structures loaded by elementary loads using unit dummy force method. 3. Calculation of displacements and rotations of more complex beam structures using unit dummy force method, effect of temperature loading. Deflection of trusses. 4. Degree of static indeterminacy. Creation of basic statically determinate system. Solution of elementary statically indeterminate beam with forced loading. Effect of axial loading. 5. Continuous beam with force and deflection loading. 6. Statically indeterminate frame with force loading. 7. Statically indeterminate frame with deflection loading. 8. Computational models of frame structures for slope deflection method, analysis of kinematic indeterminacy. 9. Solution of continuous beam with forces and deflection loading. 10. Completion of solution of continuous beam – system of equations, reactions, diagrams of internal forces. 11. Solution of complex statically indeterminate frame using slope deflection method. 12. Completion of solution of complex statically indeterminate frame – system of equations, reactions, diagrams of internal forces. Solution of statically indeterminate truss. 13. Completion of solution of truss. Credits.