Advanced Mechanics of Materials 2

Combined loading of straight beams and bars. Spatial bending. Plane bending and tension-compression. Eccentric loading of a short column, core of a cross section. Bending and torsion. Torsion and tension (compression). Bending and buckling of the strut. Plane bending of curved rods. Statistically determinate and statistically indeterminate thin curved rods and cranked beams. Statically indeterminate frames. Axially (rotationally) symmetric problems. Axi-symmetric thin-walled pressure vessels – membrane theory. Thick cylinders (vessels). Compound cylinder vessels. Rotating disks. Bending of axi-symmetric thin plates. Three-dimensional state of stress. Stresses on the oblique plane. Principal normal stresses. Differential equations of equilibrium. Relations between displacement and strain components. Compatibility of strain conditions. Physical equations for isotropic, linearly elastic homogeneous solid (extended Hooke`s law). Free (simple) torsion of bars of uniform section with non-circular profiles. Stress function. Characteristics of the stress function. Shearing lines, elementary torque carried by the belt between two infinitesimally close shearing lines. General Stoke`s theorem, elementary Stoke`s theorem. Free torsion of open and hollow (closed) thin-walled cross-sections.