Course Details
Structural Analysis 2
Academic Year 2026/27
BDA007 course is part of 4 study plans
BPA-SI Winter Semester 3rd year
BKC-SI Winter Semester 3rd year
BPC-SI / S Winter Semester 3rd year
BPC-SI / K Winter Semester 3rd year
- The essence of the direct stiffness method and its variants. Computational model and the degree of kinematic indeterminacy.
- The direct stiffness method for planar structures.
- Analysis of a straight member with a variable cross-section. Local quantities, the primary vector and the stiffness matrix.
- Hinge-connected member, cantilever. Member with a constant cross-section.
- Geometric transformation, the global member matrix.
- Analysis of a frame system, assembling the equations, localization.
- Determination of end forces and the distributions of internal force components along members. Determination of reactions and verification of the solution.
- Solution of rectangular frames and continuous beams. Thermal effects, support settlement/release.
- Truss girder solved by the displacement method.
- Member with a variable cross-section with a linear depth haunch, determination of deformation coefficients.
- Solution of spatial (3D) frames by the direct stiffness method.
- Computational model for the simplified direct stiffness method.
Credits
4 credits
Language of instruction
Czech, English
Semester
winter
Course Guarantor
Institute
Forms and criteria of assessment
course-unit credit and examination
Entry Knowledge
- 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.
Aims
Professional Knowledge
The student understands the theoretical foundations of the direct stiffness method, and comprehends its basic procedures and assumptions. The student is able to build computational models for both the general and simplified direct stiffness method and to use them to solve statically indeterminate frame/truss structures. The student also understands the function of haunches (cross-section variation) and the significance of influence lines for analyzing the effect of moving loads.
Professional Skills
The student can calculate kinematic and static quantities (displacements, rotations, and internal forces) in statically indeterminate structures using both the general and simplified direct displacement method, for planar frame as well as truss systems — including the effects of support settlement/flexibility and temperature changes.
Professional Competencies
The student is competent to work with structural analysis software for solving bar structures, understands the algorithms used in the software, and is able to perform a basic check/verification of the results.
Basic Literature
Jaroslav Kadlčák, Jiří Kytýr. Statika stavebních konstrukcí II, 2009, VUTIUM, ISBN:978-80-214-3428-8 (cs)
Kytýr Jiří, Roman Gratza, Jan Plášek, Tomáš Ridoško, Jan Ekr. Statika II - Řešené příklady, CERM, ISBN 978-80-7204-946-2 (cs)
Kytýr Jiří, Roman Gratza, Jan Plášek, Tomáš Ridoško, Jan Ekr. Statika II - Řešené příklady, CERM, ISBN 978-80-7204-946-2 (cs)
Recommended Reading
Jiří Benda. Energetické principy a variační metody ve stavební mechanice, vlastním nákladem autora, Brno 2002 (cs)
Russell Hibbeler. Structural Analysis, Pearson 2017, ISBN 978-0134610672 (en)
Russell Hibbeler. Structural Analysis, Pearson 2017, ISBN 978-0134610672 (en)
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.
Offered to foreign students
To offer to students of all faculties
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
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.
Lecture
13 weeks, 2 hours/week, elective
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.
Lecture
13 weeks, 2 hours/week, elective
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
13 weeks, 2 hours/week, compulsory
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.
Exercise
13 weeks, 2 hours/week, compulsory
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.
Exercise
13 weeks, 2 hours/week, compulsory
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.
Exercise
13 weeks, 2 hours/week, compulsory
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.
Exercise
13 weeks, 2 hours/week, compulsory
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.