Basic equations of linear elasticity: The concept of stress, Analysis ofthe state of stress at a point, Equilibrium equations, The state of planestress, The concept of strain, Analysis of the state of strain at a point,Plane strain and plane stress in polar coordinates, Problem featuringcylindrical symmetry. Constitutive behaviour of materials: Constitutive laws for isotropicmaterials, Allowable stress, Yielding under combined loading, Materialselection for structural performance, Composite materials, Constitutivelaws for anisotropic materials, Strength of a transversely isotropiclamina. Engineering structural analysis: Solution approaches, Barunder constant axial force, Pressure vessels.
Euler-Bernoulli beam theory: The Euler-Bernoulli assumptions,Implications of the Euler-Bernoulli assumptions, Stress resultantsBeams subjected to axial loads, Beams subjected to transverse loads,Beams subjected to combined axial and transverse loads.Three-dimensional beam theory: Kinematic description, Sectionalconstitutive law, Sectional equilibrium equations, Governing equations,Decoupling the three-dimensional problem, The principal centroidalaxes of bending. The neutral axis, Evaluation of sectional stiffness.
Torsion: Torsion of circular cylinders , Torsion combined with axialforce and bending moments, Torsion of bars with arbitrary cross-sections, Torsion of a thin rectangular cross-section, Torsion of thinwalledopen sections.Thin-walled beams: Basic equations for thin-walled beams, Bending ofthin-walled beams, Shearing of thin-walled beams. The shear centre.Torsion of thin-walled beams, Coupled bending-torsion problemsWarping of thin-walled beams under torsion. Equivalence of the shearand twist centres, Non-uniform torsion, Structural idealization.
Virtual work principles: Introduction, Equilibrium and workfundamentals, Principle of virtual work, Principle of virtual workapplied to mechanical systems, Principle of virtual work applied to trussstructures. Principle of complementary virtual work, internal virtualwork in beams and solids.Energy methods: Conservative forces, Principle of minimum totalpotential energy, Strain energy in springs, Strain energy in beams,Strain energy in solids, Applications to trusses, Development of a finiteelement formulation for trusses, Principle of minimum complementary,Energy theorems, Reciprocity theorems, Saint-Venant’s principle.
Yielding: Yielding under combined loading, Applications of yieldcriteria to structural, Application to bars, trusses and beams. Buckling ofbeams: Rigid bar with root torsion spring, buckling of beams, bucklingof sandwich beams. Shearing deformations in beams, Shear deformablebeams: an energy approach.Kirchhoff plate theory: Governing equations of Kirchhoff platetheory, The bending problem, Anisotropic plates, Solution techniquesfor rectangular plates, Circular, Energy formulation of Kirchhoff platetheory, Buckling of plates.