Course Details
Fundamentals of Structural Mechanics
Academic Year 2023/24
BD001 course is part of 3 study plans
B-K-C-SI (N) / VS Summer Semester 1st year
B-P-C-MI (N) / MI Summer Semester 1st year
B-P-C-SI (N) / VS Summer Semester 1st year
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.
Course Guarantor
Institute
Objective
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.
Knowledge
The 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 tie, the planar composed beam systems and plane trusses systems, to design centroid and second order moments of gross-section.
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.
Prerequisites
The basic secondary s school knowledge from mathematics and physics.
Language of instruction
Czech
Credits
5 credits
Semester
summer
Forms and criteria of assessment
course-unit credit and examination
Specification of controlled instruction, the form of instruction, and the form of compensation of the absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
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.
Exercise
13 weeks, 3 hours/week, compulsory
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.