Fundamentals of Moment of Inertia.pdf - Prof Caliendo EM300 Draft-Fundamentals of Moment of Inertia Fundamentals of Moment of Inertia 2nd Moment of Area

Fundamentals of Moment of Inertia.pdf - Prof Caliendo EM300...

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Prof. Caliendo Draft -Fundamentals of Moment of Inertia EM300 Page 1 of 5 Fundamentals of Moment of Inertia, 2 nd Moment of Area Calculations Inertia is the tendency of a body at rest to stay at rest, and for a body in motion to stay in motion. The term Moment of Inertia (MOI) or 2 nd moment of Area, this tendency is applied to a plane area and its tendency to rotate about an axis. This plane area could be the cross section of a structural element, or it could be the water plane of a ship. In the case of structural analysis, MOI is used to determine stresses and deflections of structural elements. In the case of vessel hydrostatics, MOI is used to determine the heel or trim of a vessel. In both cases, the calculation of MOI is required as a first step. By definition, the MOI of an area about the x or y axis is stated as: (1) I x = y 2 dA (2) I y = x 2 dA (Note: dA = dx•dy) Figure 1 – graphical interpretation of equations 1 & 2 Where I x or I y are the MOIs of an area about the x or y-axis, respectively, y or x is the distance from the axis in question, and dA is a very small or differential area. It is seen from this definition that the inertia is a function of dA’s distance from some reference axis squared . This tells us that a unit area far away from a reference axis has a much greater contribution to the MOI than does the same area near a reference axis. (See figure 2) Figure 2 – relative contribution of areas to a moment of inertia based on position
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Prof. Caliendo Draft -Fundamentals of Moment of Inertia EM300 Page 2 of 5 As the units for distance is length, and the units for area is length squared, the resulting units for Inertia are length to the forth power [L 4 ]. In the US system this would be expressed as [in 4 , ft 4 , in 2 -ft 2 ], and in the SI system [mm 4 , m 4 , mm 2 -m 2 ]. The choice of units utilized is dependent on the purpose. For small structural elements, such as an I- beam, in 4 or mm 4 would be used.
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