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Structural Analysis
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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Suppose that L = 12 in.
### Centroid Calculation of Shaded Area **Task:** Locate the centroid (\(\bar{x}, \bar{y}\)) of the shaded area. **Instructions:** Express your answers using three significant figures separated by a comma. ##### Input Fields: - The entry box is present for inputting the \( \bar{x}, \bar{y} \) values. - The unit, "in.", suggests the input values are to be provided in inches. ##### Interface Elements: - **Symbols and Functions:** - The interface contains various mathematical symbols and functions, enabling users to input their answers accurately. - **Square root (√)** - **Summation (Σ)** - **Vectors (vec)** - **Additional Options:** - **Undo (⟲)** - **Redo (⟳)** - **Reset (⟲)** - **Help (?)** - **Unit Conversion (↕)** **Submission:** - Upon entering the coordinates, click "Submit". - Options for reviewing "Previous Answers" and "Request Answer" are also available. By following these instructions and utilizing the functions provided, you can accurately determine and input the centroid coordinates for the shaded area. --- **Please make sure to cross-check your calculations and ensure that your answer is expressed using the required significant figures.**
Transcribed Image Text:### Centroid Calculation of Shaded Area **Task:** Locate the centroid (\(\bar{x}, \bar{y}\)) of the shaded area. **Instructions:** Express your answers using three significant figures separated by a comma. ##### Input Fields: - The entry box is present for inputting the \( \bar{x}, \bar{y} \) values. - The unit, "in.", suggests the input values are to be provided in inches. ##### Interface Elements: - **Symbols and Functions:** - The interface contains various mathematical symbols and functions, enabling users to input their answers accurately. - **Square root (√)** - **Summation (Σ)** - **Vectors (vec)** - **Additional Options:** - **Undo (⟲)** - **Redo (⟳)** - **Reset (⟲)** - **Help (?)** - **Unit Conversion (↕)** **Submission:** - Upon entering the coordinates, click "Submit". - Options for reviewing "Previous Answers" and "Request Answer" are also available. By following these instructions and utilizing the functions provided, you can accurately determine and input the centroid coordinates for the shaded area. --- **Please make sure to cross-check your calculations and ensure that your answer is expressed using the required significant figures.**
### Understanding Composite Shapes: Trapezoid Example In this educational graphic, we explore a composite shape through the combination of rectangular and triangular sections. This geometry lesson provides an example of how to calculate areas and understand dimensions when given a detailed diagram of the shapes. ### Diagram Explanation: #### Diagram Components: - **Overall Shape**: The diagram showcases a blue-colored composite shape that consists of a rectangle topped with a right-angled triangle. #### Dimensions: - **Rectangle**: - **Height**: 6 inches - **Base Length**: 6 inches - **Triangle**: - **Height**: 3 inches (the vertical side of the triangle) - **Base Length (L)**: L (this length is not specified in the diagram) The diagram is plotted on an x-y coordinate system to illustrate how these shapes align with respect to each other. ### Step-by-Step Calculation Approach: 1. **Rectangle Area Calculation**: - The rectangle has a base length of 6 inches and a height of 6 inches. - **Area of Rectangle** = Base × Height - **Area of Rectangle** = 6 inches × 6 inches = 36 square inches 2. **Triangle Area Calculation**: - The triangle has a base length of L (inches) and a height of 3 inches. - **Area of Triangle** = 0.5 × Base × Height - **Area of Triangle** = 0.5 × L × 3 inches 3. **Total Area of Composite Shape**: - The total area is the sum of the areas of the rectangle and triangle. - **Total Area** = Area of Rectangle + Area of Triangle - **Total Area** = 36 square inches + (0.5 × L × 3 inches) ### Conclusion: Understanding the components of this composite shape helps in calculating the total area efficiently. By learning how to split complex shapes into simpler ones, students can handle various geometric problems effectively.
Transcribed Image Text:### Understanding Composite Shapes: Trapezoid Example In this educational graphic, we explore a composite shape through the combination of rectangular and triangular sections. This geometry lesson provides an example of how to calculate areas and understand dimensions when given a detailed diagram of the shapes. ### Diagram Explanation: #### Diagram Components: - **Overall Shape**: The diagram showcases a blue-colored composite shape that consists of a rectangle topped with a right-angled triangle. #### Dimensions: - **Rectangle**: - **Height**: 6 inches - **Base Length**: 6 inches - **Triangle**: - **Height**: 3 inches (the vertical side of the triangle) - **Base Length (L)**: L (this length is not specified in the diagram) The diagram is plotted on an x-y coordinate system to illustrate how these shapes align with respect to each other. ### Step-by-Step Calculation Approach: 1. **Rectangle Area Calculation**: - The rectangle has a base length of 6 inches and a height of 6 inches. - **Area of Rectangle** = Base × Height - **Area of Rectangle** = 6 inches × 6 inches = 36 square inches 2. **Triangle Area Calculation**: - The triangle has a base length of L (inches) and a height of 3 inches. - **Area of Triangle** = 0.5 × Base × Height - **Area of Triangle** = 0.5 × L × 3 inches 3. **Total Area of Composite Shape**: - The total area is the sum of the areas of the rectangle and triangle. - **Total Area** = Area of Rectangle + Area of Triangle - **Total Area** = 36 square inches + (0.5 × L × 3 inches) ### Conclusion: Understanding the components of this composite shape helps in calculating the total area efficiently. By learning how to split complex shapes into simpler ones, students can handle various geometric problems effectively.
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