The course focuses on stress and deformation analysis and basic design principles of beam structures. It covers the relationships between internal forces, stress, deformation, and strain in linearly elastic conditions under axial force, bending, shear, and torsion. Stability and basic plasticity are also addressed. Further topics include spatial stress states, the use of von Mises equivalent stresses under combined loading, and an introduction to plate and wall structures. The course includes solving typical problems.

Lecture outline

1. Introduction. Basic assumptions, relations, terminology. Displacement, deformation, stress. Saint-Venant's principle. Linear elasticity theory. Beam analysis – fundamental assumptions. Relations between internal force components and stress components. Beam loading – simple and combined. Axial tension and compression – stress, deformation, strain. Thermal effects.
2. Pure bending. Derivation of stress formula. Design of bending members.
3. Deformation of bending members. Differential equation of the deflection curve and its integration. Method of initial parameters (Clebsch), Mohr's method.
4. Eccentric axial force. General eccentric loading. Core of the section. Oblique and spatial bending.
5. Shear stress under bending. Derivation of stress formula. Stress calculation in solid and thin-walled sections.
6. Shear deformation effects. Simple shear. Design. Shear center based on equilibrium.
7. Polar coordinates and torsion. Use of polar coordinates in shear center calculation. Torsion – free and restrained. Bimoment. Normal and shear stress.
8. Free torsion. Solid circular and non-circular cross-sections. Thin-walled sections – closed and open.
9. Stability and buckling strength. Second-order theory. Critical load. Euler's solution. Buckling length. Slenderness ratio. Buckling coefficient. Design.
10. Spatial stress state. Point deformation in a body. Principal stresses under plane stress. Maximum shear stresses. Mohr's circle.
11. Basics of plasticity. Mises and Tresca criteria. Derivation of von Mises equivalent stress. Structural assessment using von Mises equivalent stress.
12. Energy principles. Strain energy. Potential and complementary energy. Principles of virtual work.
13. Introduction to plate and wall structures. Advanced problems of elasticity and plasticity. Summary.

Tutorial outline:

1. Review. Support reactions, internal force diagrams (N, V, M). Cross-sectional characteristics of plane figures. Parallel axis theorem. Principal moments of inertia.
2. Axial tension/compression – statically determinate and basic statically indeterminate cases. Stress, elongation, contraction. Thermal expansion. Design.
3. Pure bending. Normal stress due to bending. Design of beams.
4. Differential equation of the deflection curve. Integration. Clebsch's method.
5. Eccentric axial loading. Stress computation. Neutral axis location. Core of the section.
6. Combined axial force and bending. Stress in bent and curved beams.
7. Spatial and oblique bending. Stress calculation. Neutral axis.
8. Shear stress under bending – part I. Solid cross-sections.
9. Shear stress under bending – part II. Thin-walled sections. Shear center.
10. Torsion. Free torsion of solid and thin-walled open and closed sections. Shear stress.
11. Stability and buckling. Buckling design. Euler's solution. Critical force and stress.
12. Plane stress. Principal stress calculation and direction. Mohr's circle. Combined loading. Von Mises equivalent stress.
13. Completion. Comprehensive examples. Exam preparation.

Learning outcomes

Students will learn to analyze stress, deformation, and strain in beam structures under linearly elastic conditions for axial force, bending, shear, and torsion. They will be able to solve stress and deformation in beams under basic combined loadings, including eccentric and spatial cases. They will understand cross-sectional properties, fundamentals of stability and plasticity, and von Mises equivalent stress usage. Students will be able to perform basic design checks of beam elements and understand principles of plate and wall structure analysis.