
Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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Transcribed Image Text:**Problem Statement:**
Given the shape below, calculate the moment of inertia about the horizontal axis, which passes through the centroid of the cross section. Use the following dimensions:
- \( b_1 = 22 \)
- \( b_{1a} = 15 \)
- \( t_1 = 0.5 \)
- \( b_2 = 12 \)
- \( t_2 = 0.4 \)
Give the answer to one decimal place.
**Diagram Description:**
The diagram shows a T-shaped cross-section consisting of two rectangles:
1. A vertical rectangle with height \( b_1 \) and width \( t_1 \).
2. A horizontal rectangle with height \( t_2 \) and width \( b_2 \).
The overlapping section of the two rectangles forms a T-shape, with the bottom of the vertical rectangle aligned with the horizontal rectangle's bottom middle. The dotted line represents the horizontal axis through the centroid of the cross-section. The centroid is marked with a small dot where this line intersects the shape.
The measurements for each section are labeled on the diagram:
- The vertical part's height is \( b_1 \).
- The vertical part's horizontal dimension (width) is \( t_1 \).
- The horizontal part's width is \( b_2 \).
- The horizontal part's vertical dimension (height) is \( t_2 \).
**Objective:**
Use the given dimensions to calculate the moment of inertia about the specified horizontal axis.
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