The polar moment of inertia J is a property of the shaft’s cross-sectional area and is needed to calculate torsional stress. For a circular shaft with radius r, the polar moment of inertia J is given by: where: J = Polar moment of inertia (in meters to the fourth power, m⁴) r = Radius […]
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For a circular cross-section with radius r, the moment of inertia I about an axis perpendicular to the plane of the circle and passing through its center is given by: where: I = Moment of inertia (in meters to the fourth power, m⁴) r = Radius of the circular cross-section (in meters, m)
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For a rectangular cross-section with width b and height h, the moment of inertia I about an axis perpendicular to the base and passing through the centroid is given by: where: I = Moment of inertia (in meters to the fourth power, m⁴) b = Width of the rectangular cross-section (in meters, m) h =
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Flexural stress, also known as bending stress, is a type of stress that occurs when a material or structural element is subjected to bending or flexural loads. This type of stress is common in beams, bridges, columns, and other structural components. The flexural stress formula calculates the stress experienced by a material due to bending.
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Elongation, also known as tensile strain or engineering strain, is a measure of the deformation of a material along the axis of an applied tensile force. It is defined as the ratio of the change in length (ΔL) of a material to its original length (L0). The formula for elongation is given by: Where:
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Hooke’s Law describes the linear relationship between the stress applied to a material and the resulting strain within the elastic limit of the material. Mathematically, Hooke’s Law is expressed as: Where: σ is the stress applied to the material (in pascals, Pa or N/m²). E is the Young’s modulus or modulus of elasticity of the
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Shear strain, denoted by the symbol γ, is a measure of deformation in a material caused by shear stress. It describes the relative displacement of layers within the material parallel to a plane where the shear stress is applied. The formula for shear strain is given by: Where: γ is the shear strain (unitless,
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Energy can exist in numerous forms, such as chemical, electrical, kinetic, potential, mechanical, thermal, and nuclear, and their sum constitutes the total energy E of a system. The total energy of a system per unit mass is denoted by e and is defined as Where: e is the specific energy in joules per kilogram (J/kg),
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Volumetric strain, also known as bulk strain or volume strain, is a measure of the change in volume of a material under the influence of stress or pressure. It is defined as the ratio of the change in volume (ΔV) to the original volume (V) of the material. The formula for volumetric strain (ϵvol) in
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Normal strain, also known as axial strain, is a measure of the deformation or change in size of a material along the direction of the applied force or stress. It is defined as the ratio of the change in length (ΔL) to the original length (L) of the material. The formula for normal strain (ϵaxial)
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