Statics Homework problem - Reactions of Ball and Socket

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SUMMARY

The discussion focuses on calculating the reactions at a ball and socket joint (point A) and the tensions in cords BC and BD for a pipe assembly under vertical loads. The user initially calculated the tensions in cords BC and BD to be equal and opposite at 12.6 kN but expressed uncertainty about the accuracy of this value. Key insights include the understanding that the ball and socket joint can only exert force in the AB direction, and that moments around this joint should sum to zero. The user is encouraged to verify their calculations by taking moments about point A.

PREREQUISITES
  • Understanding of static equilibrium principles, specifically the equations for the sum of forces and moments.
  • Familiarity with free body diagrams and how to draw them accurately.
  • Knowledge of vector calculations, particularly for determining unit vectors in three-dimensional space.
  • Basic concepts of tension in cables and how they relate to forces in a system.
NEXT STEPS
  • Review the principles of static equilibrium in three-dimensional structures.
  • Study how to accurately draw and analyze free body diagrams for complex systems.
  • Learn about the mechanics of ball and socket joints and their force capabilities.
  • Practice calculating tensions in cables using vector analysis and equilibrium equations.
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Homework Statement


The pipe assembly shown in the picture supports the vertical loads shown. Determine the reactions at the ball and socket joint (point A) and the tension in the two cords BC and BD.

ip18h2.jpg

Homework Equations


Sum of Forces = 0
Sum of Moments = 0

The Attempt at a Solution


I first caluclated the unit vector for the BC and BD connections and then I drew a free body diagram at point B. I've attempted many differ way to go about this, but none of them seem right. I came up with the Tensions BC and BD being equal (and opposite) to 12.6 kN though that's probably not right.

I'm not sure about the reactions at point A, because I thought that any moment around a ball and socket is zero?

I've been stuck on this for days and it's due tomorrow at 3!

Please help me,
Thanks so much
 
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The ball and socket joint can only push in the AB direction. My instinct is telling me that A is the point the moments should be taken from. Certainly the sum of the moments there is zero or it would turn. Anyway doing it that way would be an excellent check on your work.
Curious, I see in the diagram that BC and BD are in the horizontal plane but the diagram dimensions indicate B is only half as high as C and D.
 
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