Course detail

Structural Mechanics I

FAST-0D1Acad. year: 2020/2021

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 second order moments, calculation with used Mohr’s circle, radius and ellipse of second order moments of cross-section, polar moment of cross-section.

Language of instruction

Czech

Number of ECTS credits

6

Guarantor

prof. Ing. Zdeněk Kala, Ph.D.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Not applicable.

Prerequisites

The basic secondary s school knowledge from mathematics and physics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

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 supports. 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 targets of the topic are: Reactions and internal forces of the plane static determinate structures, 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

Kadlčák, Kytýr: Statika stavebních konstrukcí I. VUTIUM Brno 2001

Recommended reading

Adamča L. - Marton P.- Pavlík M. - Trávníček F.: Teoretická mechanika. Bratislava 1992
Beer F. P. - Johnston E. R.: Mechanics for Engineers. McGraw - Hill Book Company. New York, Toronto, London 1957
Novotná H. - Cais S. - Ptáček M.: Teoretická mechanika. SNTL Praha 1983

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

prof. Ing. Zdeněk Kala, Ph.D.

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 supports. 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 hours, compulsory

Teacher / Lecturer

prof. Ing. Zdeněk Kala, Ph.D.