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Learning Goal: To be able to calculate the moment of inertia of composite areas. 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: ▸ View Available Hint(s) Iz = 1.00×106 mm² Submit Previous Answers Correct The parallel-axis theorem is Iz = I+Ad Iy = I + Ad² where I and I are the moments of inertia of an area about its centroidal axes, A is the entire area, and dy, and d₂ are the perpendicular distances between the parallel axes. The parallel-axis theorem relates the moment of inertia of an area about an axis passing through the area's centroid to the moment of inertia of the area about a corresponding parallel axis. I₁ = Ly = √ y² dA √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 ▼Part B - Moment of inertia of the composite area about the x axis Figure 1 = ΣΙ 1 of 1 < The moment of inertia of the triangular shaped area is I = 1.00 x 106 mm. Given m = 70.0 mm and n = 35.0 mm, calculate the moment of inertia of the shaded area shown (Figure 1) about the x axis. Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) Ix = Value Units Submit Part C Complete previous part(s) n < Return to Assignment Provide Feedback ?

Learning Goal: To be able to calculate the moment of inertia of composite areas. 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: ▸ View Available Hint(s) Iz = 1.00×106 mm² Submit Previous Answers Correct The parallel-axis theorem is Iz = I+Ad Iy = I + Ad² where I and I are the moments of inertia of an area about its centroidal axes, A is the entire area, and dy, and d₂ are the perpendicular distances between the parallel axes. The parallel-axis theorem relates the moment of inertia of an area about an axis passing through the area's centroid to the moment of inertia of the area about a corresponding parallel axis. I₁ = Ly = √ y² dA √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 ▼Part B - Moment of inertia of the composite area about the x axis Figure 1 = ΣΙ 1 of 1 < The moment of inertia of the triangular shaped area is I = 1.00 x 106 mm. Given m = 70.0 mm and n = 35.0 mm, calculate the moment of inertia of the shaded area shown (Figure 1) about the x axis. Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) Ix = Value Units Submit Part C Complete previous part(s) n < Return to Assignment Provide Feedback ?

Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Charles Gilmore
Chapter1: Introduction
Section: Chapter Questions
Problem 11CQ
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Learning Goal: To be able to calculate the moment of inertia of composite areas. 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: ▸ View Available Hint(s) Iz = 1.00×106 mm² Submit Previous Answers Correct The parallel-axis theorem is Iz = I+Ad Iy = I + Ad² where I and I are the moments of inertia of an area about its centroidal axes, A is the entire area, and dy, and d₂ are the perpendicular distances between the parallel axes. The parallel-axis theorem relates the moment of inertia of an area about an axis passing through the area's centroid to the moment of inertia of the area about a corresponding parallel axis. I₁ = Ly = √ y² dA √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 ▼Part B - Moment of inertia of the composite area about the x axis Figure 1 = ΣΙ 1 of 1 < The moment of inertia of the triangular shaped area is I = 1.00 x 106 mm. Given m = 70.0 mm and n = 35.0 mm, calculate the moment of inertia of the shaded area shown (Figure 1) about the x axis. Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) Ix = Value Units Submit Part C Complete previous part(s) n < Return to Assignment Provide Feedback ?
Transcribed Image Text:Learning Goal: To be able to calculate the moment of inertia of composite areas. 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: ▸ View Available Hint(s) Iz = 1.00×106 mm² Submit Previous Answers Correct The parallel-axis theorem is Iz = I+Ad Iy = I + Ad² where I and I are the moments of inertia of an area about its centroidal axes, A is the entire area, and dy, and d₂ are the perpendicular distances between the parallel axes. The parallel-axis theorem relates the moment of inertia of an area about an axis passing through the area's centroid to the moment of inertia of the area about a corresponding parallel axis. I₁ = Ly = √ y² dA √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 ▼Part B - Moment of inertia of the composite area about the x axis Figure 1 = ΣΙ 1 of 1 < The moment of inertia of the triangular shaped area is I = 1.00 x 106 mm. Given m = 70.0 mm and n = 35.0 mm, calculate the moment of inertia of the shaded area shown (Figure 1) about the x axis. Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) Ix = Value Units Submit Part C Complete previous part(s) n < Return to Assignment Provide Feedback ?
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