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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The bending moment in strength of materials refers to the internal moment or torque that causes a structural element, such as a beam, to bend or undergo deformation. It is a measure of the bending effect induced by external forces or loads applied to the structure. Bending moments play a crucial role in structural analysis
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When a point load P is applied to a beam or structure, it induces reaction forces at the supports. For a simply supported beam (supported at both ends) with a point load at the midpoint, the reaction forces at each support are equal and half of the applied load: ​ where: R = Reaction force
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Shear force in strength of materials refers to the internal force that acts parallel to the cross-section of a structural element, such as a beam, and tends to cause deformation by sliding one part of the element past another, The shear force V at the location of the point load can be calculated using the
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The bending moment M at the location of the point load can be calculated for different beam configurations. For a simply supported beam with a point load at the center, the bending moment is: ​ where: M = Bending moment at the point load location (in newton-meters, N·m) P = Applied point load (in newtons,
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