Course detail
Fundamentals of Structural Mechanics
FAST-BD001Acad. year: 2018/2019
Students will be able to solve reactions and internal forces of the plane statically determinate structures, of plane beams with straight and broken axis, to solve three-hinged broken beam with and without a bar, the planar composed beam systems and plane truss systems, to determine the position of centroid and the second order moments of cross-section.
Language of instruction
Czech
Number of ECTS credits
5
Mode of study
Not applicable.
Department
Institute of Structural Mechanics (STM)
Learning outcomes of the course unit
Students get the basic knowledge of structural mechanics needed for the further study of civil engineering branch and of the following specializations.
Students will be able to solve reactions and internal forces of the plane statically determinate structures, of plane beams with straight and broken axis, to solve three-hinged broken beam with and without a bar, the planar composed beam systems and plane truss systems, to find centroid and second order moments of cross-section.
Students will be able to solve reactions and internal forces of the plane statically determinate structures, of plane beams with straight and broken axis, to solve three-hinged broken beam with and without a bar, the planar composed beam systems and plane truss systems, to find centroid and second order moments of cross-section.
Prerequisites
The basic secondary s school knowledge from mathematics and physics.
Co-requisites
Linear algebra, foundations of matrix calculus, solving of linear algebraic equations systems, foundations of vector calculus, analytical geometry, first derivative of function, indefinite integral, definite integral.
Planned learning activities and teaching methods
The subject is taught by lectures and exercises. Lectures involve the theoretical explanation of delivered matter. The theory is applied at solution of examples of real structures in exercises.
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Assesment methods and criteria linked to learning outcomes
The subject is finished by abridged examination and final examination. For abridged exam the student should pass all written tests in exercises and elaborate correctly all given homework. The abridged exam is the necessary condition for final examination entrance.
The final examination consists of written and oral parts. The written examination may contain both examples and the theoretical questions. The positive result in written examination allows the student to pass to oral part.
The final examination consists of written and oral parts. The written examination may contain both examples and the theoretical questions. The positive result in written examination allows the student to pass to oral part.
Course curriculum
1.Basic terms and axioms of statics. Concurrent system of forces in plane. System of parallel forces in plane.
2. General system of forces in plane. Static models of plane structures, constrains and supports, types of loading, reactions.
3. Components of internal forces in a straight bar with plane loading, diagrams of internal forces and moments.
4. Differential relations between loads, shear forces and bending moments, differential conditions of equilibrium.
5. Plane beams and frames with rectangular broken centre line, calculation of reactions in constraints, diagrams of internal forces.
6. Plane skew beam, continuous load of skew beam, plane beam with broken centre line and skew bars, reactions and diagrams of internal forces and moments.
7. Static analysis of plane systems of bodies composed of mass points and of rigid plates, static and kinematic determination. General method of solution of plane systems.
8. Three-hinged broken beam without and with a tie bar, Gerber’s beam, reactions and internal forces diagrams.
9. Quadratic and deviation moments of inertia, Steiner’s theorem, principal axes of inertia of cross-sections, radius of inertia.
10. Plane bar systems, static and kinematic determination. Calculation of axial forces. The off-joints loads.
11. Space systems of forces. Constraints and reactions of rigid body in space, calculation of reactions in constraints.
12. Straight bar with space loading, space cantilever beam with rectangular broken centre line, reactions and diagrams of internal forces and moments.
13. Space beam with broken centre line, reactions, diagrams of internal forces and moments.
2. General system of forces in plane. Static models of plane structures, constrains and supports, types of loading, reactions.
3. Components of internal forces in a straight bar with plane loading, diagrams of internal forces and moments.
4. Differential relations between loads, shear forces and bending moments, differential conditions of equilibrium.
5. Plane beams and frames with rectangular broken centre line, calculation of reactions in constraints, diagrams of internal forces.
6. Plane skew beam, continuous load of skew beam, plane beam with broken centre line and skew bars, reactions and diagrams of internal forces and moments.
7. Static analysis of plane systems of bodies composed of mass points and of rigid plates, static and kinematic determination. General method of solution of plane systems.
8. Three-hinged broken beam without and with a tie bar, Gerber’s beam, reactions and internal forces diagrams.
9. Quadratic and deviation moments of inertia, Steiner’s theorem, principal axes of inertia of cross-sections, radius of inertia.
10. Plane bar systems, static and kinematic determination. Calculation of axial forces. The off-joints loads.
11. Space systems of forces. Constraints and reactions of rigid body in space, calculation of reactions in constraints.
12. Straight bar with space loading, space cantilever beam with rectangular broken centre line, reactions and diagrams of internal forces and moments.
13. Space beam with broken centre line, reactions, diagrams of internal forces and moments.
Work placements
Not applicable.
Aims
The students will be acquainting with: (i) Reactions and internal forces of the plane static determinate structures, (ii) centroid and second order moments of cross-section.
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-K-C-SI Bachelor's
branch VS , 1 year of study, summer semester, compulsory
- Programme B-P-C-MI (N) Bachelor's
branch MI , 1 year of study, summer semester, compulsory
- Programme B-P-C-SI Bachelor's
branch VS , 1 year of study, summer semester, compulsory
- Programme B-P-E-SI Bachelor's
branch VS , 1 year of study, summer semester, compulsory
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
Syllabus
1.Basic terms and axioms of statics. Concurrent system of forces in plane. System of parallel forces in plane.
2. General system of forces in plane. Static models of plane structures, constrains and supports, types of loading, reactions.
3. Components of internal forces in a straight bar with plane loading, diagrams of internal forces and moments.
4. Differential relations between loads, shear forces and bending moments, differential conditions of equilibrium.
5. Plane beams and frames with rectangular broken centre line, calculation of reactions in constraints, diagrams of internal forces.
6. Plane skew beam, continuous load of skew beam, plane beam with broken centre line and skew bars, reactions and diagrams of internal forces and moments.
7. Static analysis of plane systems of bodies composed of mass points and of rigid plates, static and kinematic determination. General method of solution of plane systems.
8. Three-hinged broken beam without and with a tie bar, Gerber’s beam, reactions and internal forces diagrams.
9. Quadratic and deviation moments of inertia, Steiner’s theorem, principal axes of inertia of cross-sections, radius of inertia.
10. Plane bar systems, static and kinematic determination. Calculation of axial forces. The off-joints loads.
11. Space systems of forces. Constraints and reactions of rigid body in space, calculation of reactions in constraints.
12. Straight bar with space loading, space cantilever beam with rectangular broken centre line, reactions and diagrams of internal forces and moments.
13. Space beam with broken centre line, reactions, diagrams of internal forces and moments.
2. General system of forces in plane. Static models of plane structures, constrains and supports, types of loading, reactions.
3. Components of internal forces in a straight bar with plane loading, diagrams of internal forces and moments.
4. Differential relations between loads, shear forces and bending moments, differential conditions of equilibrium.
5. Plane beams and frames with rectangular broken centre line, calculation of reactions in constraints, diagrams of internal forces.
6. Plane skew beam, continuous load of skew beam, plane beam with broken centre line and skew bars, reactions and diagrams of internal forces and moments.
7. Static analysis of plane systems of bodies composed of mass points and of rigid plates, static and kinematic determination. General method of solution of plane systems.
8. Three-hinged broken beam without and with a tie bar, Gerber’s beam, reactions and internal forces diagrams.
9. Quadratic and deviation moments of inertia, Steiner’s theorem, principal axes of inertia of cross-sections, radius of inertia.
10. Plane bar systems, static and kinematic determination. Calculation of axial forces. The off-joints loads.
11. Space systems of forces. Constraints and reactions of rigid body in space, calculation of reactions in constraints.
12. Straight bar with space loading, space cantilever beam with rectangular broken centre line, reactions and diagrams of internal forces and moments.
13. Space beam with broken centre line, reactions, diagrams of internal forces and moments.
Exercise
39 hod., compulsory
Teacher / Lecturer
Syllabus
1. Moment of force to a point, pair of forces. Concurrent system of forces in plane, general system of forces in plane.
2. System of parallel forces in plane and its static centre. Static centre of plane composed shapes.
3. Beam supports and types of loads. Calculation of support reactions. Internal forces diagrams of plane beams.
4. Solution of basic types of beams: supported beams and cantilevers, straight beams with overhangs.
5. Supports reactions and internal forces diagrams of the beams with broken and curved axis.
6. Decomposition of slant continuous loads. Support reactions and internal forces diagrams of the slant beam.
7. Three-hinged broken beam (with and without a bar) and plane arches.
8. Beam with internal hinges - Gerber’s girder.
9. Centroid of planar cross-sections. Second order moments of planar cross-section, Steiner’s theorem. Mohr’s circle.
10. Planar trusses (hinged bar systems). Calculation of axial forces of trusses by method of sections, Ritter's solution.
11. Space systems of forces. General space system of forces. Constraints and reactions of rigid body in space.
12. Straight bar with space loading, space cantilever beam with rectangular broken centre line, reactions and diagrams of internal forces and moments.
13. Space beam with broken centre line, reactions and diagrams of internal forces and moments.
2. System of parallel forces in plane and its static centre. Static centre of plane composed shapes.
3. Beam supports and types of loads. Calculation of support reactions. Internal forces diagrams of plane beams.
4. Solution of basic types of beams: supported beams and cantilevers, straight beams with overhangs.
5. Supports reactions and internal forces diagrams of the beams with broken and curved axis.
6. Decomposition of slant continuous loads. Support reactions and internal forces diagrams of the slant beam.
7. Three-hinged broken beam (with and without a bar) and plane arches.
8. Beam with internal hinges - Gerber’s girder.
9. Centroid of planar cross-sections. Second order moments of planar cross-section, Steiner’s theorem. Mohr’s circle.
10. Planar trusses (hinged bar systems). Calculation of axial forces of trusses by method of sections, Ritter's solution.
11. Space systems of forces. General space system of forces. Constraints and reactions of rigid body in space.
12. Straight bar with space loading, space cantilever beam with rectangular broken centre line, reactions and diagrams of internal forces and moments.
13. Space beam with broken centre line, reactions and diagrams of internal forces and moments.