Course detail

Structural Analysis 2

FAST-BD004Acad. year: 2022/2023

Principle of deflection methods and its variant. Calculation model and degree of kinematic indeterminacy. Deflection method for planar structures. Analysis of straight bar with variable cross-section. Local values, primary vector and stiffness matrix. Bar connected by joints, cantilever. Bar with constant cross-section. Geometric transformation, global matrix of bar. Analysis of bar systems, compilation of equations, localization. Determination of ended forces and diagram of components of internal forces at bars. Determination of reactions and controlling of solution. Another variants for building equations up.
Solution of rectangular frames and continuous girders. Temperature influences, shift of supports. Truss girder is solved by deflection method. Bar with variable cross-section with height linear ramping, determination of deflection coefficient. Solution of spatial frames using deflection method. Calculation model for simplified deflection method.

Language of instruction

Czech

Number of ECTS credits

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 structural analysis of the statically indeterminate planar bar systems by the stiffness method, namely plane frames and plane trusses, including the temperature effects and shifts of the supports.

Prerequisites

Static analysis of planar statically determinate truss systems, straight and cranked girders. Principle of virtual work and theorem of virtual work reciprocity and calculation of deflection of frame systems by using method of unit forces. Solution of planar frame structures using force method.

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. Introduction, content and outline of the subject. Meaning of deflection method, creation and development of this method, variants of deflection method. Calculation model and degree of kinematic indeterminacy.
2. General deflection method for planar frame structures. Equilibrium of conditions, parameters of deflection, bounded nodes. Scalar and matrix form.
3. Analysis of straight bar with variable cross-section: primary and secondary state.
4. Local values, primary vector and the stiffness matrix. Bar connected by joints, cantilever.
5. Bar with constant cross-section. Geometric transformation, global matrix of bar.
6. Analysis of the frame system, compilation of the system of equations, code number and localization.
7. Completion of solution of bars – calculation of internal forces and deflection at bars. Determination of reactions and controlling of the solution. Errors during the solution of frames by using deflection method. Another variant for assembly of equations.
8. Speciality of solution of rectangular frames and continuous girders. Temperature influences, shift of supports.
9. Truss girder is solved by using deflection method.
10. Bar with variable cross-section, height linear ramping, determination of deflection coefficients (analytic solution, numerical integration)
11. Solution of spatial frames solved by general deflection method.
12. Calculation model for simplified deflection method in scalar form.
13. End moments, internal forces. Joint and storey equation.

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

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B-P-C-SI Bachelor's

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

  • Programme B-K-C-SI Bachelor's

    branch S , 3 year of study, winter semester, compulsory
    branch K , 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. Introduction, content and outline of the subject. Meaning of deflection method, creation and development of this method, variants of deflection method. Calculation model and degree of kinematic indeterminacy. 2. General deflection method for planar frame structures. Equilibrium of conditions, parameters of deflection, bounded nodes. Scalar and matrix form. 3. Analysis of straight bar with variable cross-section: primary and secondary state. 4. Local values, primary vector and the stiffness matrix. Bar connected by joints, cantilever. 5. Bar with constant cross-section. Geometric transformation, global matrix of bar. 6. Analysis of the frame system, compilation of the system of equations, code number and localization. 7. Completion of solution of bars – calculation of internal forces and deflection at bars. Determination of reactions and controlling of the solution. Errors during the solution of frames by using deflection method. Another variant for assembly of equations. 8. Speciality of solution of rectangular frames and continuous girders. Temperature influences, shift of supports. 9. Truss girder is solved by using deflection method. 10. Bar with variable cross-section, height linear ramping, determination of deflection coefficients (analytic solution, numerical integration) 11. Solution of spatial frames solved by general deflection method. 12. Calculation model for simplified deflection method in scalar form. 13. End moments, internal forces. Joint and storey equation.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Kytýr, CSc.

Syllabus

1. Revision of solution of elementary statically indeterminate systems using deflection method. Diagrams of internal forces. Analysis of statically and kinematic determinacy of frame systems. 2. Calculation models of frame structures for deflection method, analysis of kinematic indeterminacy. Solution of cranked statically determinate girder with forces loading using general deflection method. 3. Completion of solution of cranked statically determinate girder with force loading, ending forces, diagram of internal forces and reactions. 4. Solution of continuous girder with force loading using general deflection method. 5. Solution of more complicated statically indeterminate frames using general deflection method. 6. Completion of solution of more complicated frames – equation system, ending forces, diagram of internal forces and reactions. Control test 1. 7. Solution of girders with forces and deflection loading. 8. Complexion solution of statically indeterminate frame using deflection method. 9. Completion of solution of complexion frame – equation system, ended forces, diagram of internal forces and reactions. Control test 2. 10. Truss system solved by general deflection method. 11. Completion of solution of truss system. Correction test. Credits. 12. RFEM-SCIA: Introduction to environment of system, input of new project, units, materials and cross-sections. Input and calculation of continuous girder including cantilever. Loading forms and its combinations. 13. RFEM-SCIA: planar frame – chessboard loads, temperature loads and shift of supports, evaluation of results.