Course detail
Fundamentals of Structural Mechanics
FAST-BD01Acad. year: 2014/2015
Student will be study: Basic idea and principles and axioms of structural mechanics, static of the plane forces, equilibrium condition, static of the plane point and rigid plate, condition of the static and kinematic definiteness, calculation of the reactions and internal forces in the beam in systems. Student will be acquiring: To solve position of the centroid of cross-section., second order moments of cross-section, second order moments of cross-section with shift axis, Steiner sentence, second order moments of cross-section with axis under rotation, calculation of eextreme values of 2nd order moments, calculation with used Mohr’s circle, radius and ellipse of 2nd order moments of cross-section, polar moment of cross-section.
Language of instruction
Czech
Number of ECTS credits
5
Mode of study
Not applicable.
Guarantor
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. The theoretical knowledge and its application ability represent the possible base for later evaluation of loading capacity, security and reliability of structures.
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. Introduction of structural mechanics, basic principles and axioms, tasks of Structural mechanics, calculation model, load actions. Decomposition of the plane forces. Moment to point, forces pair. Bunch of plane forces, general system of forces. System of parallel forces in the plane and this static centum.
2. Supports and reactions of the plane point and plate. Beam, supports and load actions. Calculation of support reactions – application of equilibrium conditions. Internal forces diagrams (normal and shear forces, bending moments) of the plane beam.
3. Differential equilibrium conditions, solution of basic types of beams – simply supported beams and cantilevers, straight beams with overhangs
4. Decomposition of slant connected load action. Support reactions and internal forces diagrams of the slant beam.
5. Supports reactions and internal forces diagrams of the beams with broken and curved axis.
6. Static of plane systems composites from points and rigid plate and, static and kinematical definiteness, exceptional state of the support. Solution of the reactions at supports.
7. Three-hinged broken beam (with and without a tie) and arches. Planar composed systems. Beam with hinges - Gerber’s girder.
8. Cross-section characteristics: Centroid of cross-section of the planar figures. 2nd order moments of cross-section of the planar figures, Steiner’s theorem.
9. 2nd order moments for axis under rotation and eextreme values of 2nd order moments, polar moment of cross-section.
10. Mohr circles. Radius and ellipse of 2nd order moments of cross-section.
11. Planar trusses (hinged bar systems). Method of joints and method of sections, static and kinematical definiteness. Calculation of axial forces of hinged bar systems by method of joints and basic method of joints.
12. Calculation of axial forces of hinged bar systems by method of sections, Ritter solution, and no-joint load actions.
13. Static moment of force in space. Forces pair in space. Bunch of plane forces in space, general system of forces in space. Support and reaction in the space and this static centum. Internal forces in the space member, broken member in the space. Knowledge recapitulation.
2. Supports and reactions of the plane point and plate. Beam, supports and load actions. Calculation of support reactions – application of equilibrium conditions. Internal forces diagrams (normal and shear forces, bending moments) of the plane beam.
3. Differential equilibrium conditions, solution of basic types of beams – simply supported beams and cantilevers, straight beams with overhangs
4. Decomposition of slant connected load action. Support reactions and internal forces diagrams of the slant beam.
5. Supports reactions and internal forces diagrams of the beams with broken and curved axis.
6. Static of plane systems composites from points and rigid plate and, static and kinematical definiteness, exceptional state of the support. Solution of the reactions at supports.
7. Three-hinged broken beam (with and without a tie) and arches. Planar composed systems. Beam with hinges - Gerber’s girder.
8. Cross-section characteristics: Centroid of cross-section of the planar figures. 2nd order moments of cross-section of the planar figures, Steiner’s theorem.
9. 2nd order moments for axis under rotation and eextreme values of 2nd order moments, polar moment of cross-section.
10. Mohr circles. Radius and ellipse of 2nd order moments of cross-section.
11. Planar trusses (hinged bar systems). Method of joints and method of sections, static and kinematical definiteness. Calculation of axial forces of hinged bar systems by method of joints and basic method of joints.
12. Calculation of axial forces of hinged bar systems by method of sections, Ritter solution, and no-joint load actions.
13. Static moment of force in space. Forces pair in space. Bunch of plane forces in space, general system of forces in space. Support and reaction in the space and this static centum. Internal forces in the space member, broken member in the space. Knowledge recapitulation.
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
Bedford, A., Fowler, W.: Statics - Engineering Mechanics. Addison-Wesley Publishing Company, Inc., 1995. (EN)
KADČÁK, Jaroslav a KYTÝR, Jiří: Statika stavebních konstrukcí I. Brno: VUTIUM, 2010. ISBN 978-80-214-3419-6. (CS)
Meriam, J. L.: Statics and Dynamics. John Wiley & Sons, 1978. (EN)
KADČÁK, Jaroslav a KYTÝR, Jiří: Statika stavebních konstrukcí I. Brno: VUTIUM, 2010. ISBN 978-80-214-3419-6. (CS)
Meriam, J. L.: Statics and Dynamics. John Wiley & Sons, 1978. (EN)
Recommended reading
Kytýr Jiří, Keršner Zbyněk, Zídek Rostislav, Vlk Zbyněk: Základy stavební mechaniky. 2004. (CS)
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 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. Introduction of structural mechanics, basic principles and axioms, tasks of Structural mechanics, calculation model, load actions. Decomposition of the plane forces. Moment to point, forces pair. Bunch of plane forces, general system of forces. System of parallel forces in the plane and this static centum.
2. Supports and reactions of the plane point and plate. Beam, supports and load actions. Calculation of support reactions – application of equilibrium conditions. Internal forces diagrams (normal and shear forces, bending moments) of the plane beam.
3. Differential equilibrium conditions, solution of basic types of beams – simply supported beams and cantilevers, straight beams with overhangs
4. Decomposition of slant connected load action. Support reactions and internal forces diagrams of the slant beam.
5. Supports reactions and internal forces diagrams of the beams with broken and curved axis.
6. Static of plane systems composites from points and rigid plate and, static and kinematical definiteness, exceptional state of the support. Solution of the reactions at supports.
7. Three-hinged broken beam (with and without a tie) and arches. Planar composed systems. Beam with hinges - Gerber’s girder.
8. Cross-section characteristics: Centroid of cross-section of the planar figures. 2nd order moments of cross-section of the planar figures, Steiner’s theorem.
9. 2nd order moments for axis under rotation and eextreme values of 2nd order moments, polar moment of cross-section.
10. Mohr circles. Radius and ellipse of 2nd order moments of cross-section.
11. Planar trusses (hinged bar systems). Method of joints and method of sections, static and kinematical definiteness. Calculation of axial forces of hinged bar systems by method of joints and basic method of joints.
12. Calculation of axial forces of hinged bar systems by method of sections, Ritter solution, and no-joint load actions.
13. Static moment of force in space. Forces pair in space. Bunch of plane forces in space, general system of forces in space. Support and reaction in the space and this static centum. Internal forces in the space member, broken member in the space. Knowledge recapitulation.
2. Supports and reactions of the plane point and plate. Beam, supports and load actions. Calculation of support reactions – application of equilibrium conditions. Internal forces diagrams (normal and shear forces, bending moments) of the plane beam.
3. Differential equilibrium conditions, solution of basic types of beams – simply supported beams and cantilevers, straight beams with overhangs
4. Decomposition of slant connected load action. Support reactions and internal forces diagrams of the slant beam.
5. Supports reactions and internal forces diagrams of the beams with broken and curved axis.
6. Static of plane systems composites from points and rigid plate and, static and kinematical definiteness, exceptional state of the support. Solution of the reactions at supports.
7. Three-hinged broken beam (with and without a tie) and arches. Planar composed systems. Beam with hinges - Gerber’s girder.
8. Cross-section characteristics: Centroid of cross-section of the planar figures. 2nd order moments of cross-section of the planar figures, Steiner’s theorem.
9. 2nd order moments for axis under rotation and eextreme values of 2nd order moments, polar moment of cross-section.
10. Mohr circles. Radius and ellipse of 2nd order moments of cross-section.
11. Planar trusses (hinged bar systems). Method of joints and method of sections, static and kinematical definiteness. Calculation of axial forces of hinged bar systems by method of joints and basic method of joints.
12. Calculation of axial forces of hinged bar systems by method of sections, Ritter solution, and no-joint load actions.
13. Static moment of force in space. Forces pair in space. Bunch of plane forces in space, general system of forces in space. Support and reaction in the space and this static centum. Internal forces in the space member, broken member in the space. Knowledge recapitulation.
Exercise
26 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.
2. System of parallel forces in plane and its static center.
3. Beam supports and types of loads. Calculation of support reactions – application of equilibrium conditions. Internal forces diagrams (normal and shear forces, bending moments) of plane beams.
4. Solution of basic types of beams – simply 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. Cross-section characteristics. Centroid of planar cross-section. 2nd order moments of planar cross-section, Steiner’s theorem.
10. 2nd order moments to inclined axes and main values of 2nd order moments, polar moment of cross-section. Mohr circle. Radius and ellipse of inertia .Polar moment of cross-section.
11. Planar trusses (hinged bar systems). Method of joints and method of sections.
12. Calculation of axial forces of trusses by method of sections, Ritter's solution, and off-joint loads.
13. Concurrent system of forces in space. General system of forces in space. Supports and reactions of a rigid body in space and its static center. Internal forces in beam with space loading, broken member in space.
2. System of parallel forces in plane and its static center.
3. Beam supports and types of loads. Calculation of support reactions – application of equilibrium conditions. Internal forces diagrams (normal and shear forces, bending moments) of plane beams.
4. Solution of basic types of beams – simply 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. Cross-section characteristics. Centroid of planar cross-section. 2nd order moments of planar cross-section, Steiner’s theorem.
10. 2nd order moments to inclined axes and main values of 2nd order moments, polar moment of cross-section. Mohr circle. Radius and ellipse of inertia .Polar moment of cross-section.
11. Planar trusses (hinged bar systems). Method of joints and method of sections.
12. Calculation of axial forces of trusses by method of sections, Ritter's solution, and off-joint loads.
13. Concurrent system of forces in space. General system of forces in space. Supports and reactions of a rigid body in space and its static center. Internal forces in beam with space loading, broken member in space.