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The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).
The classical theory of contact focused primarily on non-adhesive contact where no tension force is allowed to occur within the contact area, i.e., contacting bodies can be separated without adhesion forces. Several analytical and numerical approaches have been used to solve contact problems that satisfy the no-adhesion condition.
Tension is the pulling or stretching force transmitted axially along an object such as a string, rope, chain, rod, truss member, or other object, so as to stretch or pull apart the object. In terms of force, it is the opposite of compression. Tension might also be described as the action-reaction pair of forces acting at each end of an object.
Belt friction is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard.When a force applies a tension to one end of a belt or rope wrapped around a curved surface, the frictional force between the two surfaces increases with the amount of wrap about the curved surface, and only part of that force (or resultant belt tension) is transmitted ...
This does cause frictional shear stresses in the contact area. In the final situation the bollard exercises a friction force on the rope such that a static situation occurs. The tension distribution in the rope in this final situation is described by the capstan equation, with solution:
The side of the threaded fastening having the least friction should receive torque while the other side is counter-held or otherwise prevented from turning. A common relationship used to calculate the torque for a desired preload takes into account the thread geometry and friction in the threads and under the bolt head or nut.
The vector T may be regarded as the sum of two components: the normal stress (compression or tension) perpendicular to the surface, and the shear stress that is parallel to the surface. If the normal unit vector n of the surface (pointing from Q towards P ) is assumed fixed, the normal component can be expressed by a single number, the dot ...
The formula to calculate average shear stress τ or force per unit area is: [1] =, where F is the force applied and A is the cross-sectional area.. The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.