Portale di Ateneo - En.Unibs.it

Kinematic analysis of planar beam systems. Degrees of freedom and virtual displacements. The constraints.
Iperstatic, isostatic and ipostatic beam systems.
Determination of reaction forces and internal actions (axial force, shear, and bending moment) in statically determinate planar beam systems. Anomalous cases.
Planar system of trusses statically determined

Stress analysis
Forces and stresses in 3d continuum medium
The stress tensor
The equations of equilibrium
Principal stresses, principal directions, and invariants
Decomposition of stresses in volumetric and deviatoric part
Plane stress. The Mohr's Circle for plane stress

Strain analysis
Small strain kinematics in a continuum medium
Rigid body motion and deformations.
The equations of external compatibility
Physical interpretation of the components of the tensor of small strains
Principal strains, principal strain directions and invariants of strain.
The equations of internal compatibility

Principle of Virtual Works for continuum mediums

Elasticity
Definition of elasticity
The linear elastic material
The isotropic assumption
The constitutive equations for a liner elastic, isotropic material.

Bending
Right bending
General bending
Bending and tension/compression

Torsion
Torsion in cylindrical circular beams
Torsion in small thickness beams with closed hollow sections.
Torsion in beams with rectangular section.
Torsion in small thickness open beam

Shear
Approximate shear stress evaluation: computations of the average shear stress along a generic segment
Bending and shear symmetric in beams with shear parallel to the symmetry axis
Bending and shear symmetric in small thickness open beam.
The center of shear

The equation of the elastic line
Computation of displacements and hyperstatics in beams.
Non elastic effects
Elastic boundary conditions

Applications of the Principle of Virtual Works for planar beams
Computation of displacements
Computation of hyperstatics

Instability
Computation of the Euler collapse load.