The coefficient of performance (COP) is a measure of the efficiency of a device that uses work or energy to perform a particular task, such as heating, cooling, or refrigeration. It represents the ratio of the desired output or effect of the device to the required input or work put into the device. COP is […]
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The section modulus (S) is a measure of a beam’s resistance to bending stresses. It is defined as the ratio of the moment of inertia (I) to the maximum distance from the neutral axis (c) of the beam’s cross-section. Mathematically, it can be expressed as: ​ where: S = Section modulus (in meters cubed, m³)
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The maximum bending stress (σmax​) is the highest stress experienced by a beam’s cross-section when subjected to bending moments. It usually occurs at the top or bottom fibers of the beam depending on the bending direction. The formula for maximum bending stress in a beam under a bending moment (M) can be given as: ​
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Hooke’s Law for shear stress is a fundamental principle in the field of strength of materials, stating that the shear stress (Ï„) in a material is directly proportional to the shear strain (γ) experienced by the material, as long as the material remains within its elastic limit. Mathematically, Hooke’s Law for shear stress can be
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The mass fraction is a measure used in chemistry and other scientific fields to express the proportion of one substance (the “component”) in a mixture relative to the total mass of the mixture. It is a dimensionless quantity expressed as a ratio or percentage. Mathematically, the mass fraction (w) of a component in a mixture
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The mass of air refers to the total amount of matter that comprises the Earth’s atmosphere within a certain volume or area. Air is a mixture of gases, primarily nitrogen and oxygen with smaller amounts of other gases such as argon, carbon dioxide, and trace gases. Here’s the formula to calculate the mass of air:
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Torsional stress is the stress that develops in a material due to applied torque. It is denoted by the symbol τ (tau) and is measured in pascals (Pa) or newtons per square meter (N/m²) in SI units. The formula for calculating torsional stress τ on a solid shaft with radius r and subjected to a
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Deflection at the midpoint of a cantilever beam is the vertical displacement or bending experienced by the beam at the exact center (midpoint) of its length when subjected to an applied load or loads. The deflection at the midpoint of a cantilever beam under a point load P applied at the free end can be
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The deflection at the free end of a cantilever beam under a point load P applied at the free end can be calculated using the following formula: ​ where: δ = Deflection at the free end (in meters, m) P = Applied point load at the free end (in newtons, N) L = Length of
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A distributed load in strength of materials refers to a load that is uniformly distributed over a certain length, area, or volume of a structural element. Unlike a concentrated load, which acts at a specific point, a distributed load acts continuously along a portion of the element’s length or area. For a simply supported beam
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