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As shown, a space truss is the frame for a building's awning. (Figure 2) Three ball-and-socket joints at A, B, and E support the frame. If a force of F = {120i+ 330j} N is applied at point D, what are the forces in each member? Indicate a tensile force as a positive value and a compressive force as a negative value. Express your answers numerically to three significant figures in newtons separated by commas. • View Available Hint(s) V AZO I1 vec FDA FDC. FDB. FcA, FCB. FCE =

As shown, a space truss is the frame for a building's awning. (Figure 2) Three ball-and-socket joints at A, B, and E support the frame. If a force of F = {120i+ 330j} N is applied at point D, what are the forces in each member? Indicate a tensile force as a positive value and a compressive force as a negative value. Express your answers numerically to three significant figures in newtons separated by commas. • View Available Hint(s) V AZO I1 vec FDA FDC. FDB. FcA, FCB. FCE =

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Structural Analysis of a 3D Space Truss System This figure illustrates a 3D space truss structure suspended in space, with specific dimensions provided for precision in analysis. The geometry of the space truss is defined with respect to three mutually perpendicular coordinate axes: x, y, and z. #### Key Components and Dimensions: - **Point A**: Positioned at a distance of 0.50 m along the y-axis and 1.50 m along the x-axis from Point B. - **Point B**: The reference point grounded on a horizontal plane extending into the structure. - **Point C**: Located 0.50 m in the positive y-direction and 1.50 m in the positive x-direction from Point B. - **Point D**: Elevated vertically above point B at a height of 2.00 m along the z-axis. #### Connections: - **A to B**: A horizontal member connecting points, measuring 1.50 m. - **B to D**: A vertical member perpendicular to both A-B and C-B members, measuring 2.00 m. - **C to B**: Another horizontal member equal in length to A-B, 1.50 m. - **D to C**: A diagonal member slanted to offer support between vertical and horizontal planes. #### Additional Structural Points: - **Point E**: A point of stability anchored vertically below point C and on the ground level. - **Line F**: Extending vertically through point D, continuing the structure upwards. #### Explanation of Geometry: - **Coordinate Planes**: - The x-y plane represents the horizontal directions. - The z-axis represents the vertical direction up from the x-y plane. - **Spatial Relationships**: - The structure forms a triangular arrangement in the vertical plane through points D, E, and C, offering stability and load distribution. - The horizontal distances between A, B, and C ensure that the structure maintains its horizontal alignment. #### Interpretation: This structure is vital for understanding the distribution of forces in a truss system in three dimensions. It allows examination of the stresses and forces acting upon each member when subject to different loads. The spatial coordinates provided help in calculating these stresses precisely using methods of structural analysis such as the method of joints or sections. The 3D space truss system exemplified here can be applied to real-world structures requiring stable, lightweight frameworks, such as in
Transcribed Image Text:### Structural Analysis of a 3D Space Truss System This figure illustrates a 3D space truss structure suspended in space, with specific dimensions provided for precision in analysis. The geometry of the space truss is defined with respect to three mutually perpendicular coordinate axes: x, y, and z. #### Key Components and Dimensions: - **Point A**: Positioned at a distance of 0.50 m along the y-axis and 1.50 m along the x-axis from Point B. - **Point B**: The reference point grounded on a horizontal plane extending into the structure. - **Point C**: Located 0.50 m in the positive y-direction and 1.50 m in the positive x-direction from Point B. - **Point D**: Elevated vertically above point B at a height of 2.00 m along the z-axis. #### Connections: - **A to B**: A horizontal member connecting points, measuring 1.50 m. - **B to D**: A vertical member perpendicular to both A-B and C-B members, measuring 2.00 m. - **C to B**: Another horizontal member equal in length to A-B, 1.50 m. - **D to C**: A diagonal member slanted to offer support between vertical and horizontal planes. #### Additional Structural Points: - **Point E**: A point of stability anchored vertically below point C and on the ground level. - **Line F**: Extending vertically through point D, continuing the structure upwards. #### Explanation of Geometry: - **Coordinate Planes**: - The x-y plane represents the horizontal directions. - The z-axis represents the vertical direction up from the x-y plane. - **Spatial Relationships**: - The structure forms a triangular arrangement in the vertical plane through points D, E, and C, offering stability and load distribution. - The horizontal distances between A, B, and C ensure that the structure maintains its horizontal alignment. #### Interpretation: This structure is vital for understanding the distribution of forces in a truss system in three dimensions. It allows examination of the stresses and forces acting upon each member when subject to different loads. The spatial coordinates provided help in calculating these stresses precisely using methods of structural analysis such as the method of joints or sections. The 3D space truss system exemplified here can be applied to real-world structures requiring stable, lightweight frameworks, such as in
### Part B As shown, a space truss is the frame for a building’s awning. (Figure 2) Three ball-and-socket joints at \( A \), \( B \), and \( E \) support the frame. If a force of \( \mathbf{F} = \{120\mathbf{i} + 330\mathbf{j}\} \, \text{N} \) is applied at point \( D \), what are the forces in each member? Indicate a tensile force as a positive value and a compressive force as a negative value. Express your answers numerically to three significant figures in newtons separated by commas. #### Force Variables \[ F_{DA}, \, F_{DC}, \, F_{DB}, \, F_{CA}, \, F_{CB}, \, F_{CE} = \] #### Input Box Layout There is an input box where you can enter your answers for the forces, separated by commas, followed by the unit (N) for newtons. #### Hint Section By clicking "View Available Hint(s)," you can access further help and hints to guide you through the problem-solving process. #### Submission Instructions After entering your answers, click the "Submit" button to submit your response.
Transcribed Image Text:### Part B As shown, a space truss is the frame for a building’s awning. (Figure 2) Three ball-and-socket joints at \( A \), \( B \), and \( E \) support the frame. If a force of \( \mathbf{F} = \{120\mathbf{i} + 330\mathbf{j}\} \, \text{N} \) is applied at point \( D \), what are the forces in each member? Indicate a tensile force as a positive value and a compressive force as a negative value. Express your answers numerically to three significant figures in newtons separated by commas. #### Force Variables \[ F_{DA}, \, F_{DC}, \, F_{DB}, \, F_{CA}, \, F_{CB}, \, F_{CE} = \] #### Input Box Layout There is an input box where you can enter your answers for the forces, separated by commas, followed by the unit (N) for newtons. #### Hint Section By clicking "View Available Hint(s)," you can access further help and hints to guide you through the problem-solving process. #### Submission Instructions After entering your answers, click the "Submit" button to submit your response.
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