The area of the green section is 17,966 mm². It has the following moments of inertia with respect to the x- and y-axes: \( I_x = 400 \times 10^6 \) mm⁴ and \( I_y = 586 \times 10^6 \) mm⁴.**Diagram Explanation:**- The diagram shows a green irregular shape positioned on a coordinate plane with axes labeled x, y, x', and y'.- The centroid of the shape is marked as \( C \).- Two distances are marked from the origin: - Vertical distance \( 110 \) mm along the y-axis. - Horizontal distance \( 147 \) mm along the x-axis.**Task:**Determine the centroidal moments of inertia \( \bar{I}_{x'} \), \( \bar{I}_{y'} \), and \( \bar{J}_C \) in mm⁴ and the corresponding radii of gyration \( \bar{k}_{x'} \), \( \bar{k}_{y'} \), and \( \bar{k}_C \) in millimeters.**Blanks to Fill:**- \( \bar{I}_{x'} = \underline{\hspace{30mm}} \) mm⁴- \( \bar{I}_{y'} = \underline{\hspace{30mm}} \) mm⁴- \( \bar{J}_C = \underline{\hspace{30mm}} \) mm⁴- \( \bar{k}_{x'} = \underline{\hspace{30mm}} \) mm- \( \bar{k}_{y'} = \underline{\hspace{30mm}} \) mm- \( \bar{k}_C = \underline{\hspace{30mm}} \) mm

Moment of inertia about x-axis(Ix) = 400×106 mm4Moment of inertia about y-axis(Iy) = 586×106 mm4Area…

The area of the green section is 17,966 mm². It has the following moments of inertia with respect to the x- and y-axes: I, = 400 × 106 mm4 and I, = 586 × 106 mm y 110 mm X 147 mm Determine the centroidal moments of inertia I, I, and J, in mm* and the corresponding radii of gyration k, k, and k, in millimeters. mm4 mm mm mm Ky mm kc = mm

The area of the green section is 17,966 mm². It has the following moments of inertia with respect to the x- and y-axes: I, = 400 × 106 mm4 and I, = 586 × 106 mm y 110 mm X 147 mm Determine the centroidal moments of inertia I, I, and J, in mm* and the corresponding radii of gyration k, k, and k, in millimeters. mm4 mm mm mm Ky mm kc = mm

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The area of the green section is 17,966 mm². It has the following moments of inertia with respect to the x- and y-axes: \( I_x = 400 \times 10^6 \) mm⁴ and \( I_y = 586 \times 10^6 \) mm⁴.

**Diagram Explanation:**
- The diagram shows a green irregular shape positioned on a coordinate plane with axes labeled x, y, x', and y'.
- The centroid of the shape is marked as \( C \).
- Two distances are marked from the origin:
- Vertical distance \( 110 \) mm along the y-axis.
- Horizontal distance \( 147 \) mm along the x-axis.

**Task:**
Determine the centroidal moments of inertia \( \bar{I}_{x'} \), \( \bar{I}_{y'} \), and \( \bar{J}_C \) in mm⁴ and the corresponding radii of gyration \( \bar{k}_{x'} \), \( \bar{k}_{y'} \), and \( \bar{k}_C \) in millimeters.

**Blanks to Fill:**
- \( \bar{I}_{x'} = \underline{\hspace{30mm}} \) mm⁴
- \( \bar{I}_{y'} = \underline{\hspace{30mm}} \) mm⁴
- \( \bar{J}_C = \underline{\hspace{30mm}} \) mm⁴
- \( \bar{k}_{x'} = \underline{\hspace{30mm}} \) mm
- \( \bar{k}_{y'} = \underline{\hspace{30mm}} \) mm
- \( \bar{k}_C = \underline{\hspace{30mm}} \) mm

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