**Problem 2: Cross Section Analysis for Bending about the z-axis**For the given cross section, which is assumed to be bending about the z-axis, perform the following tasks:a) **Section Division and Reference Axis**: Divide the cross section into distinct sections. Label each section clearly. Draw the reference axis, and for each section, label the distance \( y_i \) from the reference line.b) **Neutral Axis Distance Calculation**: Create a table (similar to a class example) to determine the distance from the reference axis to the neutral axis, denoted as \(\bar{y}\), in inches. - **Answer to Check**: \(\bar{y} = 1.03 \, \text{in from the reference axis}\)c) **Labeling Neutral Axis Distance (\(d_i\))**: Determine and label the \( d_i \) for each section.d) **Moment of Inertia Calculation**: Develop another table (following class instructions) to compute the moment of inertia about the z-axis, denoted as \( I_z \), in inches to the fourth power (\( \text{in}^4\)). - **Answer to Check**: \( I_z = 1.017 \, \text{in}^4\)**Diagram Explanation:**The diagram provided is a U-shaped cross section with the following dimensions:- **Width** of each vertical side: 0.125 inches (typical thickness)- **Outer width** of the U-section: 3.25 inches- **Height** of the U-section: 2.50 inches- **Depth of each horizontal flange** on top and bottom: 0.75 inchesThe reference axis is denoted as \( z \). There is a central point marked, indicating the centroidal location of the cross section. Arrows indicate the distance \( y \), from the reference axis to the centroidal axis. The overall shape forms a channel with equal flanges on the top and bottom and equal lateral sides.

Answered: Image /qna-images/answer/e2b08299-af59-4ec4-9619-c46e9c17ec34.jpg

2) For the cross section shown, assume it is bending about the z-axis. a) Divide the cross section into sections and label each section, draw the reference axis, and label the y, for each section from the reference line. b) Develop Table 1 as shown in class and determine the distance from the reference axis to the neutral axis, y in in. [Ans. to Check: y = 1.03 in from the reference axis] c) Determine and label di for each section. d) Develop Table 2 as shown in class and compute the moment of inertia about the z-axis, Iz, in inº [Ans. to Check: I,= 1.017 in'] 0.75 in. 0.125 in. (typ) 3.25 in. 0.75 in. 2.50 in.

2) For the cross section shown, assume it is bending about the z-axis. a) Divide the cross section into sections and label each section, draw the reference axis, and label the y, for each section from the reference line. b) Develop Table 1 as shown in class and determine the distance from the reference axis to the neutral axis, y in in. [Ans. to Check: y = 1.03 in from the reference axis] c) Determine and label di for each section. d) Develop Table 2 as shown in class and compute the moment of inertia about the z-axis, Iz, in inº [Ans. to Check: I,= 1.017 in'] 0.75 in. 0.125 in. (typ) 3.25 in. 0.75 in. 2.50 in.

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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Concept explainers

Coordinate Geometry of Survey

Coordinate geometry (COGO) is a method of inserting surveying or engineering data into geographic information system (GIS), computer-aided design (CAD), or mapping software. These data can be collected on the proposed construction site using standard surveying techniques and instrumentation or may be taken from existing maps, engineering plans, drawings, or records. Data gathered on the site includes coordinates of points, bearings, and distances between points. The data are noticed and noted through conventional surveying procedures, like a traverse or layout measurement series and it can be either digital or non-digital. The maps and plans are inclusive of boundaries, divisions, and other components, and these features are shown with coordinate values, the lengths, offset distance, and bearings between them.

Question

**Problem 2: Cross Section Analysis for Bending about the z-axis**

For the given cross section, which is assumed to be bending about the z-axis, perform the following tasks:

a) **Section Division and Reference Axis**: Divide the cross section into distinct sections. Label each section clearly. Draw the reference axis, and for each section, label the distance \( y_i \) from the reference line.

b) **Neutral Axis Distance Calculation**: Create a table (similar to a class example) to determine the distance from the reference axis to the neutral axis, denoted as \(\bar{y}\), in inches.
- **Answer to Check**: \(\bar{y} = 1.03 \, \text{in from the reference axis}\)

c) **Labeling Neutral Axis Distance (\(d_i\))**: Determine and label the \( d_i \) for each section.

d) **Moment of Inertia Calculation**: Develop another table (following class instructions) to compute the moment of inertia about the z-axis, denoted as \( I_z \), in inches to the fourth power (\( \text{in}^4\)).
- **Answer to Check**: \( I_z = 1.017 \, \text{in}^4\)

**Diagram Explanation:**

The diagram provided is a U-shaped cross section with the following dimensions:
- **Width** of each vertical side: 0.125 inches (typical thickness)
- **Outer width** of the U-section: 3.25 inches
- **Height** of the U-section: 2.50 inches
- **Depth of each horizontal flange** on top and bottom: 0.75 inches

The reference axis is denoted as \( z \). There is a central point marked, indicating the centroidal location of the cross section. Arrows indicate the distance \( y \), from the reference axis to the centroidal axis. The overall shape forms a channel with equal flanges on the top and bottom and equal lateral sides.

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