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Engineering Mechanics
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
The radius of gyration indicates the distribution of the components of an object around an axis. In terms of the mass moment of inertia, it is measured as the perpendicular distance from the axis of rotation to a point mass (of mass, m) which gives an equivalent inertia to the original object (of mass, m). Mathematically, the radius of gyration is the root mean square distance of the parts of the object from either its center of mass or a given axis. The radius of gyration is given by the following formula: k=IA
Mechanical principles of dynamic engineering systems
Published in Alan Darbyshire, Charles Gibson, Mechanical Engineering, 2023
Alan Darbyshire, Charles Gibson
For complex rotating objects such as motor vehicle wheels, motor armatures and turbine rotors, the value of radius of gyration is generally found from experimental test data. For more simple systems such as a concentrated mass, a rotating ring, a disc and a rotating link, the values of k can be found from simple reasoning or by applying integral calculus as follows.
Mechanical Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
Describing the theory of microcantilever, simple beam theory is restricted to a prismatic (equal cross section), homogeneous, straight, and untwisted structure (Figure 4.11). The beam is a structural member, usually horizontal, whose main function is to carry loads transverse to its longitudinal axis. These loads usually cause bending of the beam member. The beam is defined as a structure having two of its dimensions much smaller than the third. The thickness (t) and width (w) of the cantilever are small compared to the length (L), which reduces the analysis to a one-dimensional problem along the length of the beam. Additionally, it is presumed that the normal stresses (σ) in the y and z direction are negligible. The following derivation only holds if the maximum deflection (in y) is smaller than the radius of gyration (K). The radius of gyration of an object describes its dimensions. The radius of gyration of an object or body about a given axis is computed in terms of the moment of inertia around its center of gravity or a specified axis, and the total mass. It equals the square root of the ratio of the moment of inertia of the body about the given axis to its mass. Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It plays the same role in rotational dynamics as mass in linear dynamics. The measure of the inertia in the linear motion is the mass of the system, and its angular counterpart is the so-called moment of inertia. The moment of inertia of a body is not only related to its mass but also to the distribution of the mass throughout the body. It must be specified with respect to a chosen axis of rotation. For a point mass, the moment of inertia is simply the mass times the square of the perpendicular distance to the rotation axis. Flexural behavior of a straight beam: (a) prismatic beam, (b) co-ordinate system, (c) force and bending moment components, and (d) strain in the cantilever. (Duemling, M., Modeling and Characterization of Nanoelectromechanical Systems. MS Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 6, 2002.)
Architectural design and emergencies in double staircase high-rise buildings: the effect of geometric shape parameters on travel time
Published in Architectural Science Review, 2022
Mahdi Rismanian, Esmaeil Zarghami, Marzieh Azadarmaki
Another geometric property of surfaces that can indicate the extent of surface dispersion around an axis or a point is the first moment of inertia. It is a measure of the spatial distribution of a shape in relation to an axis. Assuming that people are almost uniformly dispersed in the plan of a residential floor, then surface dispersion can be substituted for dispersion of individuals, and the concept of moment of inertia can be used to determine the extent of surface dispersion. However, since the amount of the first moment of inertia is proportional to both the shape geometry and the area (large or small) of the shape, the gyration radius can be an excellent parameter to replace it. The gyration radius or gyroradius of a body about an axis of rotation is defined as the radial distance to the point that would have a moment of inertia the same as the body actual mass distribution if the total mass of the body were concentrated there. The following formula gives the gyration radius:
Thigh loaded wearable resistance increases sagittal plane rotational work of the thigh resulting in slower 50-m sprint times
Published in Sports Biomechanics, 2022
Paul Macadam, John B. Cronin, Aaron M. Uthoff, Ryu Nagahara, James Zois, Shelley Diewald, Farhan Tinwala, Jono Neville
where m = total segment mass, k = distance of the radius of gyration. The radius of gyration represents the object’s mass distribution with respect to a given axis of rotation. It is the distance from the axis of rotation to a point at which the mass of the body can theoretically be concentrated without altering the inertial characteristics of the rotating body. Due to the specific short lengths, the WR was placed at the end of the shorts, equivalent to approximately 80% distal from the hip joint centre as shown by the dashed line in Figure 2.
Ultrasonic inspection for the detection of debonding in CFRP-reinforced concrete
Published in Structure and Infrastructure Engineering, 2018
Emma La Malfa Ribolla, Mohsen Rezaee Hajidehi, Piervincenzo Rizzo, Giuseppe Fileccia Scimemi, Antonino Spada, Giuseppe Giambanco
This novel damage-sensitive feature finds its roots in the way of measuring the distribution of the components of an object around an axis. In fact, Equation (4) is similar to the definition of the radius of gyration of a planar mass distribution around an axis x used in mechanics (Mukundan & Ramakrishnan, 1998). The radius of gyration can be defined as the distance from the axis to a point mass that gives an equivalent inertia to the original object(s):