|1) Basic notions. Introduction to statics of structures; main hypotheses of linear theory; types of loads; structures, structural members and connections; equilibrium of forces;
P1. Graphic statics basics. Two forces with parallel lines of action; two concurrent forces; system of concurrent forces; theorem of three forces; funicular polygon; examples (precepts).
2) Static classification of structures. Degrees of freedom; determinacy and stability of beams; determinacy and stability of structures; examples.
3) Internal loads. Stress distribution in cross-section; Equilibrium of beam segments; Internal forces in a point; S and M functions; N, S, M diagrams; examples.
4) Gerber beam. Simply supported beam with cantilevers; beam with one vertical support; beam with no external supports; examples; a famous “Gereber-like” structure; wrong combinations of elements; challenge.
5) Three hinged structures. Graphic statics; equations of equilibrium; example; beam analogy for vertical loads; two beams with “imaginary” pin supports; two beams with an “imaginary” hinge; improper constraints; complex structures; example; a famous three-hinged structure.
6) Arches and suspension bridges. Indirect load. Three hinged arch; arch with tie; deck stiffened arch; suspension bridge; example; a famous deck-stiffened structure; Masonry arch – challenge.
7) Influence lines, simple structures. Note on sign conventions; influence lines – basic notions; simply supported beam; cantilevered beam; determination of influences using influence lines.
8) Influence lines, complex structures. Gerber beam; arches and suspension bridges; determination of maximum influence using influence lines; examples; a non-famous Gerber beam.
9) Simple trusses: Introduction; determinacy and stability of simple trusses; method of joints; example; zero force members; challenge.
10) Compound and complex trusses: Method of sections; compound trusses; complex trusses; systems of trusses; example; determinacy and stability; example.
11) Influence lines for trusses: Simple truss; systems of trusses; example; challenge.
12) Deflections I: Introduction; sources of deflection, strain, curvature; deflection diagram (elastic curve); main hypothesis and border conditions; qualitative deflection diagram; elastic beam theory and integration method; example.
13) Deflections II: Conjugate-beam method; example; principle of virtual works; example.
14) Indeterminate (hyperstatic) structures – force method: Introduction; advantages and disadvantages of indeterminate structures; methods of analysis; force method; Maxwell’s theorem of reciprocal displacements; example.
15) Symmetric structures and deflections: Symmetric structures; deflections of symmetric structures; example.
16) Influence lines for deformations and indeterminate structures: Influence lines for deformations; example; influence lines for indeterminate structures using force method; example; influence lines using kinematic method; example; deflections; example.