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Torsion of a square section bar Example of torsion mechanics. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2].Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6].
The torsion constant or torsion coefficient is a geometrical property of a bar's cross-section. It is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear elastic bar. The torsion constant, together with material properties and length, describes a bar's torsional stiffness.
where ΔL is the change in gauge length, L 0 is the initial gauge length, and L is the final length. The force measurement is used to calculate the engineering stress, σ, using the following equation: [5] = where F is the tensile force and A is the nominal cross-section of the specimen.
The first Frenet-Serret formula holds by the definition of the normal N and the curvature κ, and the third Frenet-Serret formula holds by the definition of the torsion τ. Thus what is needed is to show the second Frenet-Serret formula. Since T, N, B are orthogonal unit vectors with B = T × N, one also has T = N × B and N = B × T.
Animation of the torsion and the corresponding rotation of the binormal vector. Let r be a space curve parametrized by arc length s and with the unit tangent vector T.If the curvature κ of r at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors
Calculation of the steam turbine shaft radius for a turboset: Assumptions: Power carried by the shaft is 1000 MW; this is typical for a large nuclear power plant. Yield stress of the steel used to make the shaft (τ yield) is: 250 × 10 6 N/m 2. Electricity has a frequency of 50 Hz; this is the typical frequency in Europe.
It expresses the condition that the torsion of ∇ is zero, and as such is also called torsion-freeness. [7] There are alternative characterizations. [8] An extension of the fundamental theorem states that given a pseudo-Riemannian manifold there is a unique connection preserving the metric tensor, with
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.