Course Details

Elasticity and Plasticity

BDA002 course is part of 4 study plans

Bc. full-t. program BPC-SI > spVS compulsory Winter Semester 2nd year 5 credits

Bc. full-t. program BPC-MI compulsory Winter Semester 2nd year 5 credits

Bc. full-t. program BPA-SI compulsory Winter Semester 2nd year 5 credits

Bc. combi. program BKC-SI compulsory Winter Semester 2nd year 5 credits

Basic principles, concepts and assumptions of the theory of elasticity and plasticity. Deflections. Strains. Stresses. Saint-Venant principle of local action. Linear theory of the elasticity. Material laws, Stress-strain diagram. Analysis of a straight bar – basic assumptions. The interaction between the internal force components and the stress components, and between the internal force components and the external load. Basic cases of the loads of a bar. Simple tension and compression – the stress, the strain, the deflection. The influence of the temperature and the initial stresses. Simple shearing load. Simple bending load –calculation of the normal (axial) stresses. Design of the bent beams. The deflection of the bent beams. Differential equation of the deformation line. Method of initial parameters a Mohr’s method. Calculation of the tangent stresses – massive and thin-walled cross-sections. The consideration of the shear stress in the bent beam. The centre of the shear. Pure torsion and warping torsion. Free warping – massive circular and non-circular cross-section. Thin-walled closed and opened cross-section. Composed load cases of the bar. Spatial and biaxial bending. Tension (Compression) and bending in a plane. Eccentric torsion and compression. The core of the section. Design of the beams in the case of the composed (complex) load. The stability and the bucking strength of the compressed bars. Euler’s solution. The critical force and the critical stress. The strength approach to stability. A bar loaded by a bending and buckling load. The check of the buckling bars. The theory of the material strength and failure. The stress and strain state in a point of the body. The principal stress at the plane stress problem.

Course Guarantor

prof. Ing. Zdeněk Kala, Ph.D.

Institute

Institute of Structural Mechanics

Learning outcomes

Students will be acquainted with principles of the theory of elasticity, as stress, strain, deformations and with dimensioning of structures. Students will know the the formulas for longitudional and shear stress states of beams. Students will be able to calculate the stress states and deformations of the beams and columns. Students will know the problems of stability of the slender struts.

Prerequisites

Calculation of support reactions. Components of internal forces, differential equilibrium conditions, internal forces diagrams. Solution of basic types of planar beams. Cross-section characteristics of the planar figures. Steiner’s theorem, extreme values of the second moments of area. Member under space loading.

Corequisites

Solutions of systems of linear algebraic equations, derivative of a function , the indefinite integral, the definite integral, applications of the integral in geometry and physics.

Planned educational activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Methods of teaching are lectures and seminars. Individual consultations complement teaching. Study activities of students includes entering his own independent work. Attendance at lectures is recommended. Participation in other classes is required and controlled.

Forms and criteria of assessment

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.

Objective

Stress, strain, deformations and dimensioning of structures

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

2 hours/week, 13 weeks, elective

Syllabus of lectures

1.Basic principles, conceptions and assumptions of the theory of elasticity and plasticity (the material strength). Material laws, working diagrams. The relation between internal forces and the stresses.
2. Simple tension – stress and strain state. More general cases of the tension (compression).
3. Statically indeterminate cases. The influence of the initial stress and the temperature field.
4. Simple shear, the connections strained by shearing.
5. Simple bending. Normal stresses produced by bending. Design and check of bent girders.
6. The differential equation of the deformation line. The integration of the differential thrust equation. The method of initial parameters, Mohr’s method.
7. Shearing stresses in a bent beam. The centre of the shear. Shearing stress in the thin-walled girders. The effect of the shear on the deflection of the beam.
8. Free torsion of a massive and thin-walled cross-section beams(opened and closed).
9. Complex cases of the load of the beam. Spatial and biaxial bending. Tension (compression) and uniaxial bending.
10. Eccentric tension and compression. The calculation of the position of the neutral axis, the core of the section. Design of the girders in a case of the complex load.
11. Buckling strengths and the stability of the compressed bars. Euler’s solution. Critical force and critical stress. The influence of the boundary conditions.
12. The strength approach to stability. A bar loaded by a bending and buckling load. The check of the buckling bars.
13. The stress and strain state in a point of the body. The principal stress at the plane stress problem.

Practice

2 hours/week, 13 weeks, compulsory

Syllabus of practice

1. Calculation of support reactions. Components of internal forces, differential equilibrium conditions, internal forces diagrams. Cross-section characteristics of the planar figures. Steiner’s theorem, extreme values of 2nd order moments.
2. Simple tension – stress and strain state. More general cases of the tension (compression).
3. Statically indeterminate cases. The influence of the initial stress and the temperature field.
4. Simple bending. Normal stress produced by bending. Design and check of bent girders.
5. Shearing stress in a bent beam. The centre of the shear. Shearing stress in the thin-walled girders.
6. Free warping of a massive and thin-walled (opened and closed) cross-section beams.
7. Complex cases of the load of the beam. Spatial and biaxial bending.
8. Eccentric tension and compression. The calculation of the position of the neutral axis, the core of the section. Design of the girders in a case of the complex load.
9. The differential equation of the deformation line. The integration of the thrust line diff. equation.
10. The method of initial parameters, Mohr’s method.
11. Buckling strengths and the stability of the compressed bars. Euler’s solution. Critical force and critical stress.
12. The strength approach to stability. A bar loaded by a bending and buckling load. The check of the buckling bars.
13. The stress and strain state in a point of the body. The principal stress at the plane stress problem.