Elasticity and plasticity in civil engineering

concepts and initial assumptions of the classical theory of linear elasticity. Saint-Venant's principle of local effect.
2. Stress: Basic concepts and initial assumptions, differential conditions of equilibrium. The concept of stress, the state of stress of 3D element. Relationships between stresses and internal forces in the cross-section of a bar. Basic types of stress – simple and compound.
3. Deformation: Deformation and displacements in a body. Physical relations between stresses and deformations, Hooke's law. Physical constants and work diagrams of building materials. Deformation from uniform temperature change.
4. Axial stress: Basic relations and assumptions of the solution. Calculation of normal stress and deformation of an axially loaded member. Solution of statically indeterminate axially loaded structures in the elastic and elastic-plastic domain.
5. Torsion: Basic relations and assumptions of the solution. Calculation of shear stress and deformation of an element with rotationally symmetric cross-section under torsion, general and thin-walled cross-section. Solution of a statically indeterminate problem of an element under torsion.
6. Bending: Basic relations and assumptions of the solution. Calculation of normal stress in members subjected to bending. Solution of a bent beam in the elastic-plastic field.
7. Shear: Basic relations and solution assumptions. Calculation of shear stress in members of selected cross-sections subjected to shear. Calculation of shear flows and shear center. Composite beams.
8. – 9. Deformation of bent beams: Basic relations and assumptions of solution. Deformation of beams due to uneven heating. Solution methods based on integration of the differential equation of the bending line. Deformation of beams subjected to bending stress with variable cross-section. Statically indeterminate cases of bending. Effect of shear on the deformation of a bent beam.
10. Composite stresses in bars: Spatial bending. Eccentric tension and compression, core of the cross-section.
11. Stability of slender compressed members, buckling pressure: Euler's solution of the stability of a slender compressed member, critical load and critical stress. Loss of stability of slender compressed members in the elastic-plastic domain.
12. Introduction to plane stress: Stress components in an oblique section in plane stress. Principal stresses and extreme shear stresses. Principal stress trajectories. Strength and plasticity criteria in plane stress.
13. Planar structures: Plane state of stress, plane state of deformation, derivation of wall equation. Distribution of load-bearing plates, theory of thin plates, components of stress and specific internal forces, principal moments, plate equation.