Course Details
Structural Analysis 1
Academic Year 2026/27
BDA003 course is part of 3 study plans
BPA-SI Summer Semester 2nd year
BKC-SI Summer Semester 2nd year
BPC-SI / VS Summer Semester 2nd year
Moving load of static quantity of statically determinate beam structures. Solution using influence lines, analytical and kinematic method (Müller-Breslau principle). Evaluation of influence lines and determination of extreme values.
Principle of virtual work. Maxwell–Betti reciprocal work theorem. Maxwell-Mohr equation. Solution of displacement and rotation of beam systems using unit dummy force method, including the influence of temperature changes and support settlements. Veresčagin’s rule.
Statically indeterminate structures. Degree of static indeterminacy. Force method (Method of consistent deformations, Flexibility method). Simple statically indeterminate beam. Continuous beam solved by three-moment equation method.
Planar frame analyzed using the force method. Selection of statically indeterminate variables. Canonical equations. Effect of support settlement; effects of uniform and non-uniform temperature changes. Use of geometric symmetry.
Structures with variable cross-sections.
Credits
4 credits
Language of instruction
Czech, English
Semester
Course Guarantor
Institute
Forms and criteria of assessment
Entry Knowledge
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.
Aims
Explanation of the aspects of moving loads on structures and an introduction to the use of influence lines for their analysis.
Explanation the principle of virtual work and theorem of reciprocity of virtual work. The calculation of displacements and rotations using the unit dummy force method.
Introduction to the force method and its application in the analysis of statically indeterminate beam structures. Students will use this method to solve for simple statically indeterminate beams, continuous beams, plane frames, and plane arches, including the effects of support settlement and temperature changes.
Basic Literature
KADLČÁK, Jaroslav a Jiří KYTÝR. Statika stavebních konstrukcí II. Brno: Nakladatelství VUTIUM, 2007. ISBN 978-80-214-3428-8. (cs)
UDOEYO, Felix F. Structural Analysis. Philadelphia: Temple University Press, 2020. Dostupné z: https://temple.manifoldapp.org/read/structural-analysis/section/e1234718-83ed-42b0-b774-658813d8b813. (en)
Recommended Reading
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.
Offered to foreign students
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
Syllabus
- 1. Introduction, course content. Moving loads. Influence lines of static quantities of statically determinate structures. Static and kinematic methods of solution. Gerber beam.
- 2. Evaluation of influence lines and determination of extremes. Criteria for deriving maximum moments.
- 3. Virtual work of external and internal forces. Lagrange's and Castigliano's principle of virtual works. Reciprocity theorems for virtual works. Maxwell-Mohr equation.
- 4. Determination of displacement and rotation of beams and frames by the unit dummy forces method. Effect of normal and shear internal forces. Vereshchagin's rule. Effect of temperature change and support shifts on displacements.
- 5. Calculation of displacement of trusses for force loads, temperature changes and support shifts. Assessment of static indeterminacy of structures.
- 6. Methods of solution of statically indeterminate structures. Description of the force method. Simple statically indeterminate beam, effect of axial load.
- 7. Continuous beams, solved by the force method (three moment equation method) for force loads, temperature changes and support shifts.
- 8. Open and closed plane frames solved by the force method. Choice of statically indeterminate quantities, canonical equations. Effects of uniform and non-uniform temperature change on the frame. Effect of support shift.
- 9. Statically indeterminate plane truss loaded by forces temperature changes and support shifts solved by the force method.
- 10. Use of geometric symmetry of the frame, decomposition of the general load, restraints on the symmetry axes.
- 11. Solution of statically indeterminate structures with variable cross-sections. Redistribution of internal forces.
- 12. Displacement and rotation of statically indeterminate structures. Curved beams. Plane statically indeterminate arch.
Exercise
13 weeks, 2 hours/week, compulsory
Syllabus
- 1. Repetition of internal force calculation on plane statically determinate structures.
- 2. Moving loads. Application of the kinematic method to a beam with overhanging and a Gerber beam.
- 3. Determination of reactions and internal forces on statically determinate structures by evaluating the influence lines.
- 4. Calculation of displacements and rotations by the unit dummy force method on simple beams. Integration and application of Vereshchagin's rule.
- 5. Calculation of displacement and rotation by the unit dummy force method on more complex structures with more complex type of loading.
- 6. Effect of temperature change and support shift on the displacement of beams. Calculation of displacement of trusses.
- 7. Degree of static indeterminacy. Creation of a basic statically determinate system.
- 8. Solution of simple statically indeterminate beams under force loading.
- 9. Solution of simple statically indeterminate beams under temperature loading and support shifts.
- 10. Solution of more complex statically indeterminate structures under force loading.
- 11. Solution of more complex statically indeterminate structures under force loading, temperature change and support shifts.
- 12. Solution of statically indeterminate plane truss.