[L1] 1 Rigidity [L2] 1) Definition of Rigidity [L4] - The property of a material to resist deformation when it undergoes elastic deformation, and the degree to which it resists this deformation. [L4] - When an external force is applied to an elastic body, the deformation varies depending on the shape, support method, and elastic modulus of the elastic body, in addition to the magnitude of the force or moment. [L4] - Generally, the rigidity of a material is expressed as the value of the external force per unit change. (rigidity) [L4] - Refers to the degree of resistance to deformation of a material. [L4] - The deformation of a material can be classified by the degree of torsion or bending, and this can be broadly categorized into axial rigidity, bending rigidity, shear rigidity, and torsional rigidity. [L2] 2) Characteristics of Rigidity [L4] - While strength refers to the hardness of a material, rigidity refers to the property of a material to resist deformation. [L4] - The hardness (degree of resistance to change) within the elastic range of a material can be expressed by E, but the resistance to deformation that considers its shape is called rigidity. [L4] - Rigidity refers to the degree of deformation considering the shape of the material, but since it varies with length (size condition), the concept that considers the length condition (unit length) is stiffness. [L2] 3) Types of Rigidity [L3] ① Axial Rigidity (Extensional Rigidity) [L4] - Elongation is proportional to external force, and the external force per unit elongation is called extensional rigidity. [L4] - Axial Rigidity: E x A [L3] ② Bending Rigidity [L4] - The property that resists deflection (bending moment); Elastic Modulus (E) X Second Moment of Area (I) is bending rigidity. [L4] - When a beam is bent, the curvature of the beam's deflection curve is proportional to the bending moment (M) and inversely proportional to the elastic modulus (E) × second moment of area (I). The curvature is greater when E×I is smaller, even if the bending moment M is the same. In other words, EI is a coefficient that represents the magnitude of curvature in the deflection curve, and this is the bending rigidity. [L4] - Bending Rigidity: E x I (I: Second Moment of Area) [L3] ③ Shear Rigidity [L4] - Shear Rigidity: G x A [L3] ④ Torsional Rigidity [L4] - When a rod is twisted, the angle of twist per unit length is proportional to the torsional moment, but the torsional moment that produces a unit angle of twist is called torsional rigidity. [L4] - Torsional Rigidity: G x J (J: Polar Second Moment of Area) [L3] ※ Bending Rigidity and Bending Stiffness [L1] 2 Difference between Rigidity and Stiffness [L2] 1) Rigidity [L4] - Axial Rigidity (EA) [L4] - Bending Rigidity (EI) [L4] - Shear Rigidity (GA) [L4] - Torsional Rigidity (GIp) [L5] ※ E: Elastic Modulus, G: Shear Modulus, A: Cross-sectional Area, I: Second Moment of Area, Ip: Polar Second Moment of Area [L2] 2) Stiffness [L4] - Considers Member Length (L) [L4] - Axial Stiffness (EA/L) [L4] - Bending Stiffness (EI/L) [L4] - Shear Stiffness (GA/L) [L4] - Torsional Stiffness (GIp/L) [L5] ※ E: Elastic Modulus, G: Shear Modulus, A: Cross-sectional Area, I: Second Moment of Area, Ip: Polar Second Moment of Area [L1] 3 Expressing the Degree of Material Change (Rigidity) [L2] 1) Strength (E) [L4] - Refers to the degree of deformation per stress within the elastic region. It means the elastic modulus. [L5] * Strength: The degree to which a material resists external stress. (within the elastic region, the degree of change) [L4] - Although the definition of strength and the meaning of rigidity are very similar, it is more appropriate to express the degree of deformation using rigidity / stiffness. [L2] 2) Rigidity [L4] - Refers to the degree of resistance that considers the shape in the degree of deformation. [L4] - Can express rigidity in all areas of bending and torsion. [L4] - There is a limit where rigidity increases with larger size. [L2] 3) Stiffness [L4] - Refers to the degree of resistance that considers both shape and size. [L4] - For the most accurate meaning of resistance to deformation, stiffness is used. [L1] Reference) Strength [L2] 1) Definition of Strength [L4] - When a material is subjected to a load, the resistance to deformation (stress) until the material breaks is called its strength. [L4] - The unit of strength is expressed as force per unit area. (Same as the unit of stress) [L5] * cf) MPa, kN/m^2. [L4] - There are tensile strength, compressive strength, bending strength, torsional strength, and others. [L2] 2) Measurement of Strength [L4] - Tensile strength is measured by a tensile test where a test piece is slowly pulled. [L4] - Compressive strength is measured by applying an axial compressive load to a short column-shaped specimen. [L4] - Torsional strength is calculated from the torsional moment applied when a cylindrical specimen breaks due to torsion.