Strength of Materials and Structural Elements II

General Foundation

The course is also offered to exchange programme students.

The course aims to: • offer the knowledge towards the engineering analysis and the design of civil engineering structures like buildings, bridges, pipelines, geotechnical and underground structures by building the knowledge for the behavior of materials and structural elements. • define normal and shear stresses, strains and deformations that are being developed to any section of a structural element, symmetric or non-symmetric, open or close thin or thick. • improve the knowledge of elastic and plastic behavior of materials. • cover energy techniques and methodologies for the analysis of fundamental and simple structures. • provide the knowledge of instability for compressive members focusing on buckling. Acquiring skills. After the successful attendance of the course the student will have the ability to: • calculate internal forces and convert them to normal and shear stresses, deformation and strain, for elastic and elastoplastic materials and for complex cross-sections. • calculate the maximum moments and in general forces that a simple structure can withstand. • check the failure of a structural element due to flexure or due to the critical external force for buckling. • design a structural element for a specific external force in order not to exceed the maximum strength of the material. • calculate the deformed shape of a structural element so as not to prevent its functionality.

1. Elastic technical theory of beam resistance: Basic assumptions, exact solution of elasticity for the flexural behavior of cantilever beam, normal and shear stresses of symmetrical cross-section beams, oblique bending and eccentric loading of non-symmetrical cross sections, shear stresses of thin-wall cross-sections (shear stresses due to bending, due to torsion for open and close cross sections, center of shear), Strain Deformation Energy. 2. Deformation of beams – Elastic line applications: Theory of deformation of an infinate element inside its plane, differential equation of elastic line, Mohr method, the three moment method (Clapeyron), the effect of normal and shear forces in beam deformations. 3. Linear energy methods: Elastic deformation energy, principle of possible work, the theorem of Betti and Maxwell-Mohr, Castigliano theorem, general formulation of the principle of possible works 4. Inelastic technical theory of linear elements: Bending of symmetric sections, the effect of axial loading to plastic moment, the effect of shear loading to plastic moment, inelastic analysis of structures, theorem of frame limit analysis. 5. Buckling: buckling of joint-joint column, effect of eccentricity, effect of shear loading, stress control, equivalent buckling length, limits of elastic buckling. 6. Stress functions.

Engineering theory of beam strength, beam deformations, elastic line, energy methods, bending.

13-03-2018