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Stop Share The horizontal boom AO is supported by cables AB and CD, and a ball-and-socket joint at O. Calculate the tensions in the cables, and support reactions at O in terms of x. Neglect weight of the boom. L=10 kN, a= 7 m, b=3 m, c-2 m, d=4 m x A C B X b C D

Stop Share The horizontal boom AO is supported by cables AB and CD, and a ball-and-socket joint at O. Calculate the tensions in the cables, and support reactions at O in terms of x. Neglect weight of the boom. L=10 kN, a= 7 m, b=3 m, c-2 m, d=4 m x A C B X b C D

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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1. **Problem Statement:** - The horizontal boom AO is supported by cables AB and CD, and a ball-and-socket joint at O. Calculate the tensions in the cables, and support reactions at O in terms of x. Neglect weight of the boom. - \( L = 10 \, \text{kN} \) - \( a = 7 \, \text{m} \) - \( b = 3 \, \text{m} \) - \( c = 2 \, \text{m} \) - \( d = 4 \, \text{m} \) 2. **Figure Explanation:** - The figure depicts a 3D structural system, consisting of a horizontal boom labeled AO. - The boom AO is supported at point O by a ball-and-socket joint, and by two cables AB and CD. - Cable AB connects the point A on the boom to point B which is at height \( c \) vertically above the base level where A is located, implying cable AB runs diagonally upwards. - Cable CD extends from point D to point O, where point D is at a horizontal distance \( d \) and a vertical distance \( b \) from point A. - An external load \( L \) is applied vertically downward at point A. - Coordinates referenced: - \( A \): Horizontal coordinate \( x \), vertical coordinate \( a \) - \( B \): Vertical coordinate \( b \), height \( c \) - \( O \): Located where the boom and cables intersect - \( D \): Horizontal distance \( d \) from O on the z-axis and \( d \) on the y-axis 3. **Coordinate System:** - The coordinate system is oriented such that: - \( x \)-axis extends along the horizontal projection of the boom AO. - \( z \)-axis is the vertical axis, starting at the reference base level upwards. - \( y \)-axis extends from point O horizontally with respect to point D, forming the triangular 3D coordinate reference points where the cables attach. 4. **Key Parameters and Known Variables:** - Known forces: Load \( L = 10 \, \text{kN} \) applied at point A. - Geometry: Distances \( a = 7 \, \text
Transcribed Image Text:1. **Problem Statement:** - The horizontal boom AO is supported by cables AB and CD, and a ball-and-socket joint at O. Calculate the tensions in the cables, and support reactions at O in terms of x. Neglect weight of the boom. - \( L = 10 \, \text{kN} \) - \( a = 7 \, \text{m} \) - \( b = 3 \, \text{m} \) - \( c = 2 \, \text{m} \) - \( d = 4 \, \text{m} \) 2. **Figure Explanation:** - The figure depicts a 3D structural system, consisting of a horizontal boom labeled AO. - The boom AO is supported at point O by a ball-and-socket joint, and by two cables AB and CD. - Cable AB connects the point A on the boom to point B which is at height \( c \) vertically above the base level where A is located, implying cable AB runs diagonally upwards. - Cable CD extends from point D to point O, where point D is at a horizontal distance \( d \) and a vertical distance \( b \) from point A. - An external load \( L \) is applied vertically downward at point A. - Coordinates referenced: - \( A \): Horizontal coordinate \( x \), vertical coordinate \( a \) - \( B \): Vertical coordinate \( b \), height \( c \) - \( O \): Located where the boom and cables intersect - \( D \): Horizontal distance \( d \) from O on the z-axis and \( d \) on the y-axis 3. **Coordinate System:** - The coordinate system is oriented such that: - \( x \)-axis extends along the horizontal projection of the boom AO. - \( z \)-axis is the vertical axis, starting at the reference base level upwards. - \( y \)-axis extends from point O horizontally with respect to point D, forming the triangular 3D coordinate reference points where the cables attach. 4. **Key Parameters and Known Variables:** - Known forces: Load \( L = 10 \, \text{kN} \) applied at point A. - Geometry: Distances \( a = 7 \, \text
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