The course focuses on explaining the fundamental concepts of structural mechanics. Topics include: the role of structural mechanics, planar force systems, computational models of structures, loads, and external supports. Calculation of support reactions, components of internal force resultants, differential equilibrium conditions, and internal force diagrams. Analysis of statically determinate planar beams—simple, cantilever, inclined, and kinked. Planar composite beam systems and truss structures. Cross-sectional characteristics of planar shapes. Introduction to the analysis of spatial structures.

Outline of lectures

1. Basic concepts and axioms of statics. Planar concurrent force system, resultants, equivalence, and equilibrium. Moment of a force about a point, couple of forces. System of parallel forces in the plane and its static center.
2. General planar force systems. Static models of planar structures, supports and constraints in the plane, loading. Calculation of support reactions.
3. Planar truss structures, static and kinematic determinacy. Calculation of axial forces in truss members, approach to solving non-nodal loading in planar truss structures.
4. Components of internal force resultants (N, V, M) in a straight beam subjected to planar loading. Statistically determinate planar beams and cantilevers, loads, support reactions, computation of internal forces and moments, internal force and moment diagrams.
5. Differential relationships between load, shear force, and bending moment. Differential equilibrium conditions.
6. Planar right-angled kinked beams and cantilevers. Calculation of support reactions, internal force diagrams.
7. Inclined planar beam. Distributed load on an inclined member, decomposition of inclined loading, kinked beams with inclined members, support reactions and internal force/moment diagrams.
8. Statics of planar systems of bodies composed of particles and rigid plates. Static and kinematic determinacy. General method of solving planar systems via decomposition into substructures, reactions and internal forces.
9. Three-hinged kinked beam, three-hinged beam with tie rod, Gerber beam. Support reactions and internal force diagrams.
10. Cross-sectional characteristics: area, static moment, second moments of area (quadratic moments of inertia and product moments of inertia). Parallel axis theorem (Steiner's theorem).
11. Principal axes of a cross-section, principal moments of inertia. Mohr’s circle. Radii of gyration, inertia ellipse, polar moments of inertia.
12. Spatial force systems. Spatial force bundles, general 3D force systems. Supports and reactions of rigid bodies in space, calculation of reactions. Straight member under spatial loading.
13. Spatial right-angled kinked cantilever and beam. Reactions and diagrams of internal forces and moments.

Tutorial outline

1. Resultant, equivalence, equilibrium. Practical applications of planar force systems. General planar force systems: resultant, equivalence, equilibrium. Practical exercises with real-world examples.
2. Support Reactions: Calculation of reactions in simple straight beams, kinked beams, and truss structures subjected to concentrated forces, moments, and distributed loads (including equivalent load substitution).
3. Axial Forces in Trusses: Calculation of axial forces in members of planar truss structures.
4. Straight Beams – Simple Loading: Planar straight beams with basic loading. Calculation of support reactions. Internal forces and moment diagrams – computation and sketching.
5. Straight Beams – Combined Loading: Planar straight beams subjected to arbitrary combinations of loads, including uniformly and linearly distributed loads. Support reactions, internal forces, and moment diagrams.
6. Right-Angled Kinked Beams and Cantilevers: Arbitrary loading including uniform and linear distributions. Reaction forces and diagrams of internal forces and bending moments.
7. Inclined Beam: Decomposition of inclined distributed loading. Support reactions and internal force/moment diagrams.
8. Kinked Beam with Inclined Members: Support reactions and internal force/moment diagrams.
9. Three-Hinged Kinked Beam: With and without tension rod. Reactions and diagrams of internal forces and moments.
10. Gerber Beam: Calculation of support reactions and internal force/moment diagrams.
11. Centroid and Second Moments of Area: Calculation of quadratic and deviational moments for planar composite shapes. Application of the parallel axis theorem (Steiner’s theorem).
12. Principal Moments of Inertia: Numerical and graphical solution. Radii of gyration and inertia ellipse.
13. Spatially Loaded Members: Straight members under spatial loading and right-angled spatial cantilevers or beams. Calculation of support reactions and internal force diagrams.

Learning Outcomes

• Subject Knowledge

The student will know the nomenclature for types of connections and types of beams by their supports, including both statically determinate and indeterminate systems. They will be able to distinguish between static and kinematic determinacy. The student will understand the significance of the two fundamental vectors: force and moment. They will know the names of the types of internal forces in a beam section. The student will comprehend the meaning of the numerical characteristic of planar shapes expressed both with respect to the axes of coordinate system and with recpect to point in the plane of the shape.

• Subject skills

The student will be able to solve support reaction and internal force in planar statically determinate structures, straight and bent beams, three-hinged beams without and with ties, planar beam systems, and truss structure. They will be able to determine centroid of cross-sections, as well as the second moment of area and polar moment of inertia of planar shapes. They will also be able to solve internal forces in simple spatial structures.

• Competencies:

The student will be capable of idealizing simple statically determinate structures, creating their computation model, and analyzing the internal forces. Together with knowledge of the key section properties of members, they will be prepared to analyze the distribution of internal force into its intensity over the cross-sectional area (stress). Along with the ability to calculate beam deformations, they will be ready for designing both ultimate limit state and serviceability limit state.