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The tripod is subjected to the vertical 2 kN force as shown, and the weight of the legs is negligible compared with the applied load. 1) Draw the force (3-D) diagram of the joint D; 2) Determine the unit vectors of CAD, CBD, and CCD; 3) Write out three equilibrium equations in scalar form for solving the magnitude of compressive forces CAD, CBD, and CCD; 4) Solve the magnitude of compressive forces CAD, CBD, and CCD

The tripod is subjected to the vertical 2 kN force as shown, and the weight of the legs is negligible compared with the applied load. 1) Draw the force (3-D) diagram of the joint D; 2) Determine the unit vectors of CAD, CBD, and CCD; 3) Write out three equilibrium equations in scalar form for solving the magnitude of compressive forces CAD, CBD, and CCD; 4) Solve the magnitude of compressive forces CAD, CBD, and CCD

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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The tripod is subjected to the vertical 2 kN force as shown, and the weight of the legs is negligible compared with the applied load.
1) Draw the force (3-D) diagram of the joint D;
2) Determine the unit vectors of CAD, CBD, and CCD;
3) Write out three equilibrium equations in scalar form for solving the magnitude of compressive forces CAD, CBD, and CCD;
4) Solve the magnitude of compressive forces CAD, CBD, and CCD

[Partial Ans: CAD=0.925 kN (C)  CBD=0.376  kN (C)  CCD= 0.898 kN (C)]

The image depicts a rigid structure with three legs arranged in a tripod formation, supporting a vertical load of 2 kN applied at point D. The legs are joined at the top, where the force acts downwards along the z-axis. Key components and dimensions are as follows: 1. **Points A, B, and C:** - These points represent the base of each leg on the ground plane. - Point A is located 230 mm along the x-axis and 380 mm along the y-axis from the origin (O). - Point B is 400 mm along the x-axis and 0 mm along the y-axis from the origin (O). - Point C is 240 mm along the x-axis and 440 mm along the y-axis from the origin (O). 2. **Point O:** - The midpoint on the ground plane. - The distances between O and points A, B, and C are shown in the diagram: - Distance OA is 500 mm. - Distance OB is diagonal but shown as deduced from given distances. - Distance OC is diagonal but shown as deduced from given distances. 3. **Vertical Axis (z-axis) and Load:** - The tripod height from the ground to point D is 1100 mm. - A vertical force, F, of 2 kN is applied at the top point D, directed downwards along the z-axis. This structure illustrates a typical engineering problem involving the distribution of forces in a 3D framework. Understanding the spatial arrangement and force application can be essential for students studying statics and mechanics in engineering courses. The diagram helps visualize the concepts of equilibrium and vector forces applied in structural components.
Transcribed Image Text:The image depicts a rigid structure with three legs arranged in a tripod formation, supporting a vertical load of 2 kN applied at point D. The legs are joined at the top, where the force acts downwards along the z-axis. Key components and dimensions are as follows: 1. **Points A, B, and C:** - These points represent the base of each leg on the ground plane. - Point A is located 230 mm along the x-axis and 380 mm along the y-axis from the origin (O). - Point B is 400 mm along the x-axis and 0 mm along the y-axis from the origin (O). - Point C is 240 mm along the x-axis and 440 mm along the y-axis from the origin (O). 2. **Point O:** - The midpoint on the ground plane. - The distances between O and points A, B, and C are shown in the diagram: - Distance OA is 500 mm. - Distance OB is diagonal but shown as deduced from given distances. - Distance OC is diagonal but shown as deduced from given distances. 3. **Vertical Axis (z-axis) and Load:** - The tripod height from the ground to point D is 1100 mm. - A vertical force, F, of 2 kN is applied at the top point D, directed downwards along the z-axis. This structure illustrates a typical engineering problem involving the distribution of forces in a 3D framework. Understanding the spatial arrangement and force application can be essential for students studying statics and mechanics in engineering courses. The diagram helps visualize the concepts of equilibrium and vector forces applied in structural components.
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