[L1] 1 Section Modulus (Z ; section modulus) [L2] 1) Section Moment and Section Modulus [L4] - The section modulus is affected by the cross-sectional shape, but not by the material. [L4] - The sum of the products of an infinitesimal area within a shape and its distance from the neutral axis is called the first moment of area. [L4] - The sum of the products of an infinitesimal area within a shape and the square of its distance from the neutral axis is called the second moment of area. [L4] - The section modulus is derived from the second moment of area. [L4] - It is the value obtained by dividing the second moment of area about the centroidal axis by the distance from the centroid to the outermost fiber of the section. [c] Section Moment [c] Section Modulus [L2] 2) Characteristics of Section Modulus [L4] - It is used to measure the bending strength of a beam. [L4] - It is determined by the shape of the cross-section. [L4] - The stress in a beam is proportional to the distance from the neutral axis, which is unaffected by tension and compression. The outermost part from the neutral axis experiences the maximum stress, and this maximum value is represented by the section modulus. [L2] 3) Applications of Section Modulus [L4] - A larger section modulus indicates greater bending strength, thus signifying a more stable cross-section. [L5] * The shorter the distance to the outermost fiber and the larger the moment of inertia, the more stable the section is against bending. [L5] * The outermost fiber distance refers to the distance from the centroidal axis to the farthest edge. [L1] 2 Polar Section Modulus (Zp ; polar modulus of section) and Polar Moment of Inertia (Ip) [L5] Note) Prefix 'Polar' - Concepts with the prefix 'polar' are used for calculating torsion, not bending, to create a state independent of horizontal and vertical directions. [L2] 1) Definition of Polar Section Modulus [L4] - A numerical measure of resistance to torsion. [L4] - It is calculated by combining the sectional properties along the x and y axes to determine torsional resistance. [L5] * Torsion is a type of shear stress; a larger Zp indicates a greater capacity to resist shear stress in the object. [c] Polar Section Moment [L2] 2) Polar Second Moment of Area (Polar Moment of Inertia Ip) [L4] - It is used to determine the rotational stiffness (resistance to torsion) of an object. [L4] - A larger polar moment of inertia value indicates greater resistance to torsion, thus suggesting structural safety. [c] Polar Second Moment of Area [L2] 3) Relationship between Polar Section Modulus and Polar Second Moment of Area [L4] - The polar second moment of area is an intermediate step in calculating the polar section modulus. [L4] - The polar section modulus expresses the correlation between torsional force (torque) and shear force.