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The Timoshenko–Ehrenfest beam theory was developed by Stephen Timoshenko and Paul Ehrenfest [1][2][3] early in the 20th century. [4][5] The model takes into account shear deformation and rotational bending effects, making it suitable for describing the behaviour of thick beams, sandwich composite beams, or beams subject to high- frequency ...
Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: [1] where. P c r {\displaystyle P_ {cr}} , Euler's critical load (longitudinal compression load on column), E {\displaystyle E} , Young's modulus of the column material, I {\displaystyle I ...
is the rolling resistance coefficient or coefficient of rolling friction with dimension of length, and N {\displaystyle N} is the normal force (equal to W , not R , as shown in figure 1). The above equation, where resistance is inversely proportional to radius r {\displaystyle r} seems to be based on the discredited "Coulomb's law" (Neither ...
Traction (mechanics) Traction, traction force or tractive force is a force used to generate motion between a body and a tangential surface, through the use of either dry friction or shear force. [1][2][3][4] It has important applications in vehicles, as in tractive effort. Traction can also refer to the maximum tractive force between a body and ...
The bending stiffness ( ) is the resistance of a member against bending deflection/deformation. It is a function of the Young's modulus , the second moment of area of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending stiffness of a beam can analytically be derived from the equation of ...
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
The atoms (or particles) that might stop a beam particle are shown in red. The magnitude of the mean free path depends on the characteristics of the system. Assuming that all the target particles are at rest but only the beam particle is moving, that gives an expression for the mean free path: ℓ=(σn)−1,{\displaystyle \ell =(\sigma n)^{-1},}
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. [2][3] Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of the processes involved is called tribology, and has a history of more than 2000 years.
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