• modul-, Semester 2, position 4

The purpose of this course is that students understand and learn the basic concepts of the theory of elasticity and to acquire the basis of the tensor calculus. Students will be enabled to model and solve some rheological problems. Students are enabled to independently determine stress and strain fields in complex types of loading. Through understanding the rheological processes, they will be able to use computer programs in this field.

- By taking of this course, students will master some basic methods and procedures of the theory of elasticity and of the tensor calculus. - They will be able to calculate stress components on the base of equilibrium equations and to form appropriate tensors of stress and strain for an ideal elastic body. - They will be introduced with principal stresses (intensity, position) and with maximum shear stress. - They will be able to calculate stress and strain for some complex types of loading. - Students will master application of material failure theories. - They will understand elasticity and stiffness matrices. - They will be able to solve some real problems related to thin simply supported plates.

Introduction. Stress tensor. Stress components and equilibrium equations in Cartesian and cylindrical coordinate system. Stresses in an arbitrary plane - transformation of stress tensor. Plane state of stress. Pressure vessels. Curved beams, deformation and stress. Compatibility equations. The principal strains. Principal stresses. Stress invariants. Volumetric and deviatoric components. Material failure theories. Torsion expressed over stress function. Membrane theory. Column buckling and stability. Generalized Hooke's law. Lame constants. Plane state of strain. Thin plates. Rheological models and modeling.

Determination of the stress components on the base of equilibrium equations. Transformation of stress tensor. Principal stresses, the intensity, the position. The maximum shear stress, the intensity and position. Stress invariants. Calculation of the main strains. Application of failure theories. Tensors of stress and strain for an ideal elastic body. Stress and deformation of the curved beam. Stress distribution in pressure vessels. Torsion of the beams of different cross-sections. Stability of compressed columns by the energy method. Thin simply supported plates.

Set by the Curriculum of the study program.

Handouts from the website of the Department for Strength of the constructions

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 20
Laboratory exercises: 0
Calculation tasks: 5
Seminar paper: 5
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 5
Review and grading of the project: 0
Test: 5
Test: 0
Final exam: 5

Activity during lectures: 10
Test/test: 40
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 10
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 40

T. Atanacković, Theory of elasticity, FTN University of Novi Sad, 1993. (in Serbian); S. Tymoshenko, J. N. Gudier, Theory of elasticity, Građevinska knjiga - Beograd, 1962.; T. Maneski, V. Milosevic-Mitic, D. Ostric, Sets of the structural strength, University of Belgrade, 2002. ISBN 86-70803-435-9 ; Hlitčijev J., Chapters in Theory of elasticity, Naučna knjiga Beograd, 1950. (in Serbian)