Educational guide 2020_21 Centro Universitario da Defensa na Escola Naval Militar de Marín (Pontevedra)

Elasticity and additional topics in resistance of materials

Contents

Topic	Sub-topic
Review of Strength of Materials	Axial loading. Shear. Pure bending and nonuniform bending.
Fundamentals of elasticity	Introduction to Elasticity. Goals of Elasticity and Strength of Materials. Definition of stress in elastic solids. Stress tensor. Principal stresses and principal directions. Graphic representation of three-dimensional stress. Mohr´s Circles. Deformation analysis in continuum media. State of strain at a point. Strain tensor. Graphic representation of deformational state. Mohr´s Circles. Stress-Strain relations. Stress-Strain experimental relations. Generalized Hooke´s laws.
Torsion	Torsion of a prismatic bar of circular cross section. Coulomb’s theory. Design of transmission shafts. Strain energy stored by torsion. Statically indeterminate torsion members. Torsion of noncircular prismatic bars.
Combined loadings	Combined Loadings. Combined bending and torsion in bars of circular cross section Bending of beams of nonsymmetrical section. Shear center. Combined axial and bending load in non-slender bodies. Thin-wall pressure vessels.
Lateral bending. Buckling.	Buckling. Introduction. Centric compression load in slender column. Euler critical load. The effect of end conditions on critical load. Eccentric load in slender column. Validity range in Euler buckling theory. Design formulas for columns. Bucking coefficients method for column design.
Strain energy. Energy methods.	Strain energy concept. External loads and strain relations. Influence coefficients concept. Strain energy expressions. Clapeyron theorem. Principle of virtual works. Castigliano´s theorems.
Criteria for initiation of inelastic material behavior. Failure condition.	Plastic deformation of materials. Failure condition. Maximum normal stress theory or Rankine theory Maximum normal strain theory or Sain-Venant theory. Maximum shear stress theory or Coulomb theory. Maximum strain energy theory or Beltrami-Haigh theory Maximum distorsion energy theory or von Mises theory Comments about failure theories. Safety factor.
Experimental methods in elasticity	Electrical strain gages method. Fundamentals. Electrical strain gages. Data analysis. Photoelasticity. Fundamentals. Basic optical concepts in photoelasticity. Photoelasticity equipment. Interpretation of the stress contours.