The aim of the course is that students learn about the problem of torsion of prismatic structural elements of arbitrary shapes and cross-sections, and then with thun-walled structural elements of open and closed cross-sections. Also introduce students to the basics of the theory of thin plates with the problem of losing their stability.

By mastering the study program of this course the student acquires the ability to independently: • Account distribution of stress and strain in structures of arbitrary cross-sectional shape that are exposed how complicated twisting and straining • Determines the geometrical characteristics of sectoral cross-sections of arbitrary shape • Dimensioned load-bearing structural elements using different criteria in the field of theories of strength • Solve concrete problems using scientific methods and procedures • Connects basic knowledge in various fields with the aim of further application in practice, by using computer programs

Introductory explanations. Torsion bars of arbitrary cross-section. Shear stress. Angle of twist. Out of plane deformation of cross-section. Compound arbitrary cross-section. The rectangular cross-section. Thin rectangular cross-section. Membrane analogy. Basic Theory of thin-walled structural elements. Unconstrained and constrained torsion. Thin-walled open cross-sections. Stresses and strains in unconstrained torsion. The concept of sectoral coordinates. Sectoral geometric characteristics of the cross-section. Main sector coordinators. Shear center. Constrained torsion. Bimoment. Stresses and strains in constrained torsion. Differential equations of the angle of twist. The general case of stress. Thin-walled elements closed cross-sections. Celled sections. Multicellular sections. Bending of compressed beams. Exact solution. Approximate solution. Beam with initial deflection. Bending of thin plates. Differential equations of thin plate bent. Different contour conditions. Thin rectangular plate. Arbitrary load.

Calculation of torsional characteristics of arbitrary and thin-walled cross-sections, the determination of the relevant geometrical properties of the considered cross-sections. Determination of the stress and strain for the cross-sections discussed in the theoretical teaching.

Set by the Curriculum of the study program.

1.Handouts from the website of the Department.

Total assigned hours: 65

New material: 30
Elaboration and examples (recapitulation): 20

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

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

Activity during lectures: 10
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 40
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 40

M. Milovančević, N. Anđelić, V. Milošević-Mitić, M. Dunjić, D. Ružić, R. Čukić: Strength of matherials-Tables, University of Belgrade, Faculty of Mechanical Engineering, Belgrade, 2015; N. Anđelić, V. Milošević-Mitić, M. Milovančević (in Serbian): Fundamentals of Strength of Structures (in Serbian), University of Belgrade, Faculty of Mechanical Engineering, Belgrade, 2021 ; Ružić, D.,Strength of Structures (in Serbian), University of Belgrade, Faculty of Mechanical Engineering, Belgrade, 1995; Kollbruner, C.F., Hajdin, N., Dunnwandige Stabe, Band 1, Springer Verlag, Berlin, 1970