Lesson plan
Section modulus
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question. There are two types of section modulus, elastic and plastic: * The elastic section modulus is used to calculate a cross-section's resistance to bending within the elastic range, where stress and strain are proportional. * The plastic section modulus is used to calculate a cross-section's capacity to resist bending after yielding has occurred across the entire section. It is used for determining the plastic, or full moment, strength and is larger than the elastic section modulus, reflecting the section's strength beyond the elastic range. A plastic hinge forms once every fiber across the cross-section has reached the yield stress, σ y ; beyond that point, the section cannot resist any further increase in bending moment. This limiting condition defines the plastic moment, M p , and the plastic section modulus through M p = σ y Z p . Equations for the section moduli of common shapes are given below.…
Article summary
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question. There are two types of section modulus, elastic and plastic: * The elastic section modulus is used to calculate a cross-section's resistance to bending within the elastic range, where stress and strain are proportional. * The plastic section modulus is used to calculate a cross-section's capacity to resist bending after yielding has occurred across the entire section. It is used for determining the plastic, or full moment, strength and is larger than the elastic section modulus, reflecting the section's strength beyond the elastic range. A plastic hinge forms once every fiber across the cross-section has reached the yield stress, σ y ; beyond that point, the section cannot resist any further increase in bending moment. This limiting condition defines the plastic moment, M p , and the plastic section modulus through M p = σ y Z p . Equations for the section moduli of common shapes are given below.…
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Discussion questions
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