Course detail

Fundamentals of Structural Mechanics

FAST-BD001Acad. year: 2022/2023

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.

Guarantor

prof. Ing. Jiří Kala, Ph.D.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

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.

Prerequisites

The basic secondary s school knowledge from mathematics and physics.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Literature

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

Not applicable.

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.

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.

Classification of course in study plans

  • Programme B-P-C-SI (N) Bachelor's

    branch VS , 1. year of study, summer semester, 5 credits, compulsory

  • Programme B-P-E-SI (N) Bachelor's

    branch VS , 1. year of study, summer semester, 5 credits, compulsory

  • Programme B-K-C-SI (N) Bachelor's

    branch VS , 1. year of study, summer semester, 5 credits, compulsory

  • Programme B-P-C-MI (N) Bachelor's

    branch MI , 1. year of study, summer semester, 5 credits, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

prof. Ing. Jiří Kala, Ph.D.

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

39 hours, compulsory

Teacher / Lecturer

prof. Ing. Jiří Kala, Ph.D.

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.