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For a beam of uniform cross-section along its length, the angle of twist (in radians) is: = where: T is the applied torque L is the beam length G is the modulus of rigidity (shear modulus) of the material
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].
For example, if a person places a force of 10 N at the terminal end of a wrench that is 0.5 m long (or a force of 10 N acting 0.5 m from the twist point of a wrench of any length), the torque will be 5 N⋅m – assuming that the person moves the wrench by applying force in the plane of movement and perpendicular to the wrench.
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 moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations.
is the torque exerted by the spring in newton-meters, and is the angle of twist from its equilibrium position in radians κ {\displaystyle \kappa \,} is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient , torsion elastic modulus , rate , or just spring constant , equal to the change in torque ...
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
The beam is originally straight, and any taper is slight; The beam experiences only linear elastic deformation; The beam is slender (its length to height ratio is greater than 10) Only small deflections are considered (max deflection less than 1/10 of the span).