Torsion Formula
Torsion Formula - Related Videos
01:16
Torsion of Noncircular Members
0 Views •
2024
Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
02:52
Chemical Formulas
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2020
A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of elements and numbers. At times other symbols, such as dashes, parentheses, brackets, commas, plus, and minus signs, are also used. A chemical formula can be one of three types – molecular, empirical, and structural. Molecular Formula The molecular formula represents a molecule or a chemical compound using chemical symbols (to indicate the...
01:09
Torsional Pendulum
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2025
A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected. As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
07:05
Determining the Empirical Formula
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2023
Source: Laboratory of Dr. Neal Abrams - SUNY College of Environmental Science and Forestry Determining the chemical formula of a compound is at the heart of what chemists do in the laboratory every day. Many tools are available to aid in this determination, but one of the simplest (and most accurate) is the determination of the empirical formula. Why is this useful? Because of the law of conservation of mass, any reaction can be followed gravimetrically, or by change in mass. The empirical...
03:10
Molecular Compounds: Formulas and Nomenclature
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2020
Molecular compounds or covalent compounds result when atoms share electrons to form covalent bonds. Since there is no electron transfer, molecular compounds do not contain ions; instead, they consist of discrete, neutral molecules. Since covalent compounds are formed from the combination of nonmetals, the periodic table can help recognize many of them. The position of a compound’s elements in the periodic table can predict whether the compound is ionic or covalent (although there are...
FAQs
In τ = Tr/J, shear stress increases with radial distance r when torque T and polar moment of inertia J remain fixed. Material farther from the shaft center therefore experiences greater shear stress than material near the center. This relationship helps engineers identify the critical location for strength checks and evaluate how a member responds across its cross-section.
The polar moment of inertia J appears in both torsion relationships and represents the member’s geometric contribution to resisting twisting. A larger J reduces calculated shear stress and angle of twist for the same loading and length. The shear modulus G appears in θ = TL/GJ, linking material stiffness specifically to deformation rather than directly to the stress calculation.
The stated relationships apply to a circular member in elastic torsion, so the material must remain within the range where the equations appropriately describe its response. Engineers compare calculated shear stress with allowable stress limits and calculated twist with serviceability limits. These checks address both structural strength and whether deformation remains acceptable during operation.
A typical evaluation identifies the applied torque T, member dimensions needed for the polar moment of inertia J, the relevant radial location r, and the shaft length L. Engineers then calculate shear stress with τ = Tr/J and angle of twist with θ = TL/GJ. The results are compared with allowable stress and serviceability requirements before accepting the design.
For a proposed circular component, engineers use the stress relationship to determine whether its geometry can withstand the applied twisting moment and use the deformation relationship to check stiffness over the required length. Adjusting the member geometry changes J, while material selection changes G. Together, these calculations support sizing decisions for drive shafts and other power-transmission components.
A torsional analysis provides two complementary outcomes: the shear stress distribution associated with the applied torque and the member’s total angular deformation over its length. The first supports strength assessment, while the second supports stiffness and serviceability assessment. Considering both outcomes helps engineers predict operational behavior and determine whether a design remains within its intended limits.