Learning Goal: An object's moment of inertia is calculated analytically via integration, which involves dividing the object's area into the elemental strips that are parallel to the axes and then performing the integration of the strip's moment of inertia. In practice, engineers often encounter structural members that have areas composed of the common geometric shapes, such as rectangles, triangles, and circles, whose areas, centroidal locations, and moments of inertia about their centroidal axes are either known or can be calculated easily. Determining the moment of inertia of a composite area with respect to any axis is based on the following definitions: Iz = Sy² dA I₁ = √x² dA For a composite area consisting of a finite number of components, the integration is replaced by summation and the general equation simplifies to m A composite area consisting of the rectangle, semicircle, and a triangular cutout is shown (Figure 1). Calculate the moment of inertia of the triangle with respect to the x axis. The dimensions are m = 70.0 mm and n = 35.0 mm. Express your answer to three significant figures and include the appropriate units.
Learning Goal: An object's moment of inertia is calculated analytically via integration, which involves dividing the object's area into the elemental strips that are parallel to the axes and then performing the integration of the strip's moment of inertia. In practice, engineers often encounter structural members that have areas composed of the common geometric shapes, such as rectangles, triangles, and circles, whose areas, centroidal locations, and moments of inertia about their centroidal axes are either known or can be calculated easily. Determining the moment of inertia of a composite area with respect to any axis is based on the following definitions: Iz = Sy² dA I₁ = √x² dA For a composite area consisting of a finite number of components, the integration is replaced by summation and the general equation simplifies to m A composite area consisting of the rectangle, semicircle, and a triangular cutout is shown (Figure 1). Calculate the moment of inertia of the triangle with respect to the x axis. The dimensions are m = 70.0 mm and n = 35.0 mm. Express your answer to three significant figures and include the appropriate units.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Learning Goal:
An object's moment of inertia is calculated analytically via
integration, which involves dividing the object's area into the
elemental strips that are parallel to the axes and then
performing the integration of the strip's moment of inertia.
In practice, engineers often encounter structural members that
have areas composed of the common geometric shapes, such
as rectangles, triangles, and circles, whose areas, centroidal
locations, and moments of inertia about their centroidal axes
are either known or can be calculated easily.
Determining the moment of inertia of a composite area with
respect to any axis is based on the following definitions:
Iz =
Sy² dA
I₁ = √x² dA
For a composite area consisting of a finite number of
components, the integration is replaced by summation and the
general equation simplifies to
m
A composite area consisting of the rectangle, semicircle, and a triangular cutout is shown (Figure
1). Calculate the moment of inertia of the triangle with respect to the x axis. The dimensions are m =
70.0 mm and n = 35.0 mm.
Express your answer to three significant figures and include the appropriate units.
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