Course detail

# Structural Mechanics 1

Tasks of structural mechanics,space and plane systems of forces,cross-section characteristics of the planar figures. Calculation model of structure,load actions,supports.Calculation of support reactions,components of internal forces, differential equilibrium conditions, nternal forces diagrams.Solution of basic types of statically determinate planar beams – simply supported beam, cantilever, the slant, broken and curved beam. Planar composed systems and planar trusses. Space statically determinate member, broken member in the space.The basic principles of the linear theory of elasticity. Deflection, strain, stress. Material laws, stress-strain diagram.Simple tension and compression, simple shearing load, simple bending load. The deflection of the bent beams. Calculation of the tangent stresses, the shear stress in the bent beam, the centre of the shear, torsion.Composed load cases of the bar.The stability and the bucking strength of the compressed bars, a bar loaded by a bending and buckling load.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Student will be able to solve reactions and internal forces of the plane statically determinate structures, to design centroid and second order moments of cross-section, solve simple and compound stresses and to compute strain in a section, to find materials and dimensions, to calculate deformation during bend.

Prerequisites

The basic secondary school knowledge from mathematics and physics are request.

Co-requisites

Linear algebra, fundaments of matrix calculus, solutions of systems of linear algebraic equations, vector calculus, derivative of a function , the indefinite integral, the definite integral.

Recommended optional programme components

Not applicable.

Not applicable.

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.

Assesment methods and criteria linked to learning outcomes

The subject is finished by abridged examination and final examination. 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.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

1. Tasks of structural mechanics, basic conceptions, presumptions, principles and axioms. Plane and space systems of forces. Equilibrium and equivalence.
2. Basic types of statically determinate beams. Calculation model of planar beam, load actions, supports. Static and kinematic determination, exceptional cases of supporting.
3. Calculation of support reactions. Components of internal forces, differential equilibrium conditions, internal forces diagrams.
4. Solution of basic types of planar beams – simply supported beam and cantilever.
Straight beams with overhangs, the slant and broken beam. Planar composed systems. Curved beam – arch.
5. Cross-section characteristics of the planar figures. Steiner’s theorem, extreme values of second order moments. Radius and ellipse of second order moments of cross-section.
6. Planar trusses. Calculation model, static determination, exceptional cases. Method of joints and method of sections.
7. Space member. Supports and reaction, internal forces. Broken member in the space.
8. Basic principles of the theory of elasticity. Deflection, strain, stress. Linear behaviour, material laws, working diagram. The relation between internal forces and the stresses. Simple tension – stress, strain, deflection.
9. More general cases of the tension (compression). Statically indeterminate cases. The influence of the initial stress and the temperature field. Simple shear, the connections strained by shearing.
10. Simple bending. Normal stress produced by bending. Design and check of bent girders.
11. The deflection of the bent bars. The differential equation of the deformation line. The methods of solution of the deformation line.
Shearing stress in a bent beam. The centre of the shear. Shearing stress in the thin-walled girders. The influence of the shear on the deflection of the beam.
12. Free warping of a massive and thin-walled opened and closed cross-section beams. Complex cases of the load of the beam. Spatial and biaxial bending. Tension (compression) and uniaxial bending.
13. Eccentric tension and compression, the position of the neutral axis, the core of the section. Design of the girders in a case of the complex load. Buckling strengths and the stability of the compressed bars. The check of the buckling bars. The principal stresses.

Aims

The students will be acquainting with reactions and internal forces of the plane static determinate structures, centroid and second order moments of cross-section. They also will be acquainting with basic principles of the theory of elasticity, as stress, strain, deformations and with dimensioning of structures.

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-APS (N) Bachelor's

branch APS , 1. year of study, winter semester, 3 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Tasks of structural mechanics, basic conceptions, presumptions, principles and axioms. Plane and space systems of forces. Equilibrium and equivalence.
2. Basic types of statically determinate beams. Calculation model of planar beam, load actions, supports. Static and kinematic determination, exceptional cases of supporting.
3. Calculation of support reactions. Components of internal forces, differential equilibrium conditions, internal forces diagrams.
4. Solution of basic types of planar beams – simply supported beam and cantilever.
Straight beams with overhangs, the slant and broken beam. Planar composed systems. Curved beam – arch.
5. Cross-section characteristics of the planar figures. Steiner’s theorem, extreme values of second order moments. Radius and ellipse of second order moments of cross-section.
6. Planar trusses. Calculation model, static determination, exceptional cases. Method of joints and method of sections.
7. Space member. Supports and reaction, internal forces. Broken member in the space.
8. Basic principles of the theory of elasticity. Deflection, strain, stress. Linear behaviour, material laws, working diagram. The relation between internal forces and the stresses. Simple tension – stress, strain, deflection.
9. More general cases of the tension (compression). Statically indeterminate cases. The influence of the initial stress and the temperature field. Simple shear, the connections strained by shearing.
10. Simple bending. Normal stress produced by bending. Design and check of bent girders.
11. The deflection of the bent bars. The differential equation of the deformation line. The methods of solution of the deformation line.
Shearing stress in a bent beam. The centre of the shear. Shearing stress in the thin-walled girders. The influence of the shear on the deflection of the beam.
12. Free warping of a massive and thin-walled opened and closed cross-section beams. Complex cases of the load of the beam. Spatial and biaxial bending. Tension (compression) and uniaxial bending.
13. Eccentric tension and compression, the position of the neutral axis, the core of the section. Design of the girders in a case of the complex load. Buckling strengths and the stability of the compressed bars. The check of the buckling bars. The principal stresses.

Exercise

13 hours, compulsory

Teacher / Lecturer

Syllabus

1. Plane systems of forces. Equilibrium and equivalence.
2. Basic types of statically determinate beams. Calculation of support reactions. Components of internal forces, differential equilibrium conditions, internal forces diagrams.
3. Straight beams with overhangs, the slant and broken beam. Planar composed systems.
4. Planar trusses. Method of joints and method of sections.
5. Cross-section characteristics of the planar figures. Steiner’s theorem, extreme values of 2nd order moments. Radius and ellipse of inertia of cross-section.
6. Simple tension – stress, strain, deflection. General cases of the tension (compression). Statically indeterminate cases. Simple bending. Normal stress produced by bending. Shearing stress in a bent beam. Design and check of bent girders.
7. Free torsion of a massive cross-section bar and thin-walled opened and closed cross-section beams.