**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.

As per the dimension given in the question, Free body diagram of section:

Given the shape below, calculate the moment of inertia about the horizontal axis, which passes through the centroid of the cross section. Use b1 = 22, b1a = 15, t1 = 0.5, b2 = 12 and t2 = 0.4. Give the answer to one decimal place. %3D bia bi tz + b2 + to

Given the shape below, calculate the moment of inertia about the horizontal axis, which passes through the centroid of the cross section. Use b1 = 22, b1a = 15, t1 = 0.5, b2 = 12 and t2 = 0.4. Give the answer to one decimal place. %3D bia bi tz + b2 + to

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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Question

**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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