**CEE 2110-002 Statics Fall 2021 - Homework Assignment**Prepared by Dr. Jane Liu**Problem 2:**The given composite areas in diagrams a), b), and c) can be divided into multiple elementary shapes. Their centroids can be found in the handout of Geometric Properties of Area Elements.**Tasks:**1. Determine the x and y coordinates of the centroid \((\bar{x}, \bar{y})\) and the area \(A\) of each divided elementary shape as shown.2. Complete the table in diagram d) to fill in the information for each composite in a), b), and c).**Diagrams Overview:**- **Diagram a):** Shows a composite L-shaped area divided into three parts with dimensions in meters. - **Diagram b):** Displays a composite trapezoidal shape divided into five parts with dimensions in inches. - **Diagram c):** Demonstrates a composite shape with a quarter-circle and straight elements, divided into six parts with dimensions in inches. - **Diagram d):** Contains an empty table to be filled out with the designated areas, centroid coordinates, and calculations for each part of the composites in the diagrams.**Table Structure (Diagram d):**- Columns include: - Part number - Area (\(A_i\)) - Centroid x-coordinate (\(\bar{x}_i\)) - Centroid y-coordinate (\(\bar{y}_i\)) - Product \(A_i \bar{x}_i\) - Product \(A_i \bar{y}_i\)Ensure accurate calculations for each section and populate the table to reflect the composite areas and centroids. **Geometric Properties of Areas**1. **Triangle** - Diagram: A triangle with a base \( b \) and height \( h \) is shown. The centroid (C) is marked. - Area Formula: \( A = \frac{1}{2} bh \) - Centroid Location: \( \bar{x} = \frac{1}{3} b \)2. **Trapezoid** - Diagram: A trapezoid with two parallel sides of lengths \( b_1 \) and \( b_2 \), and height \( h \). - Area Formula: \( A = \frac{1}{2} (h_1 + h_2) \) - Centroid Location: \( \bar{x} = \frac{b(2h_1 + h_2)}{3(h_1 + h_2)} \)3. **Semi Parabola** - Diagram: A semi-parabolic shape with width \( b \) and height \( h \). - Area Formula: \( A = \frac{2}{3} bh \) - Centroid Location: \( \bar{x} = \frac{3}{8} b \)4. **Parabolic Spandrel** - Diagram: A parabolic spandrel with base \( b \) and height \( h \). - Area Formula: \( A = \frac{1}{3} bh \) - Centroid Location: \( \bar{x} = \frac{1}{4} b \)5. **Semi-segment of nth Degree Curve** - Diagram: A semi-segment with base \( b \) and height \( h \). - Area Formula: \( A = bh \left(\frac{n+1}{n+2}\right) \) - Centroid Location: \( \bar{x} = \frac{b(n+1)}{2(n+2)} \)6. **Spandrel of nth Degree Curve** - Diagram: A spandrel curve with width \( b \) and height \( h \). - Area Formula: \( A = bh \left(\frac{n+1}{n+2}\right) \) - Centroid Location: \( \bar{x} = \frac{b(n+1)}{2(n+2)} \)Each section

The centroid of a body is the point at which the mass of the body is uniformly distributed. The…

Problem 2) : The given composite areas in a), b) and c) can be divided into multiple elementary shapes and their centroids can be found in the handout of Geometric properties of Area Elements. 1) Determine the x and y coordinates of the centroid(ï ,ỹ) and area, A of each divided elementary areas as shown; 2) Generate the table in d) to fill the information for each composite in a), b) and c).

Problem 2) : The given composite areas in a), b) and c) can be divided into multiple elementary shapes and their centroids can be found in the handout of Geometric properties of Area Elements. 1) Determine the x and y coordinates of the centroid(ï ,ỹ) and area, A of each divided elementary areas as shown; 2) Generate the table in d) to fill the information for each composite in a), b) and c).

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

Types of Composite

Composite materials are formed by merging two components that have different chemical and physical properties. The merged output is termed as a composite, whose properties are completely different from the individual components. Composite materials also have better strength than the individual components.Composite materials usually have two main parts, reinforcement material, and matrix material. The matrix material acts as a binder and surrounds the fiber of another material that bears a much higher strength. This material is known as the reinforcement material. The matrix materials are usually high-strength additives resins, while the fibers of the reinforced material can be random, oriented, and in a mat format.Composite materials are also known as fiber-reinforced composite polymers because they are composed of the polymer matrix which is reinforced to laboratory-created fibers or naturally occurring fibers, such as glass fibers, carbon fibers, or aramid fibers. Under the application of external loads, the matrix material absorbs and transfers the loads to the fibers, these fibers in return provide good compressive strength, tensile strength, and stiffness to the fiber-reinforced composite materials.Depending upon the matrix and the reinforcement material, different properties can be induced to the fiber-reinforced composite materials, including good corrosion resistance properties. The most common matrix material is the resin while the glass fibers act as the reinforcement material. Strong fibers provide strength and stiffness to the composite materials while, a soft and flexible resin provides shape to the composite materials.

Question

**CEE 2110-002 Statics Fall 2021 - Homework Assignment**

Prepared by Dr. Jane Liu

**Problem 2:**

The given composite areas in diagrams a), b), and c) can be divided into multiple elementary shapes. Their centroids can be found in the handout of Geometric Properties of Area Elements.

**Tasks:**

1. Determine the x and y coordinates of the centroid \((\bar{x}, \bar{y})\) and the area \(A\) of each divided elementary shape as shown.
2. Complete the table in diagram d) to fill in the information for each composite in a), b), and c).

**Diagrams Overview:**

- **Diagram a):** Shows a composite L-shaped area divided into three parts with dimensions in meters.

- **Diagram b):** Displays a composite trapezoidal shape divided into five parts with dimensions in inches.

- **Diagram c):** Demonstrates a composite shape with a quarter-circle and straight elements, divided into six parts with dimensions in inches.

- **Diagram d):** Contains an empty table to be filled out with the designated areas, centroid coordinates, and calculations for each part of the composites in the diagrams.

**Table Structure (Diagram d):**

- Columns include:
- Part number
- Area (\(A_i\))
- Centroid x-coordinate (\(\bar{x}_i\))
- Centroid y-coordinate (\(\bar{y}_i\))
- Product \(A_i \bar{x}_i\)
- Product \(A_i \bar{y}_i\)

Ensure accurate calculations for each section and populate the table to reflect the composite areas and centroids.

**Geometric Properties of Areas**

1. **Triangle**
- Diagram: A triangle with a base \( b \) and height \( h \) is shown. The centroid (C) is marked.
- Area Formula: \( A = \frac{1}{2} bh \)
- Centroid Location: \( \bar{x} = \frac{1}{3} b \)

2. **Trapezoid**
- Diagram: A trapezoid with two parallel sides of lengths \( b_1 \) and \( b_2 \), and height \( h \).
- Area Formula: \( A = \frac{1}{2} (h_1 + h_2) \)
- Centroid Location: \( \bar{x} = \frac{b(2h_1 + h_2)}{3(h_1 + h_2)} \)

3. **Semi Parabola**
- Diagram: A semi-parabolic shape with width \( b \) and height \( h \).
- Area Formula: \( A = \frac{2}{3} bh \)
- Centroid Location: \( \bar{x} = \frac{3}{8} b \)

4. **Parabolic Spandrel**
- Diagram: A parabolic spandrel with base \( b \) and height \( h \).
- Area Formula: \( A = \frac{1}{3} bh \)
- Centroid Location: \( \bar{x} = \frac{1}{4} b \)

5. **Semi-segment of nth Degree Curve**
- Diagram: A semi-segment with base \( b \) and height \( h \).
- Area Formula: \( A = bh \left(\frac{n+1}{n+2}\right) \)
- Centroid Location: \( \bar{x} = \frac{b(n+1)}{2(n+2)} \)

6. **Spandrel of nth Degree Curve**
- Diagram: A spandrel curve with width \( b \) and height \( h \).
- Area Formula: \( A = bh \left(\frac{n+1}{n+2}\right) \)
- Centroid Location: \( \bar{x} = \frac{b(n+1)}{2(n+2)} \)

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