Finding Reaction Forces in 3D Equilibrium: Solving a Tricky Bent Rod Problem

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SUMMARY

The discussion focuses on solving a 3D equilibrium problem involving a bent rod supported by a ball and socket joint at point A and a journal bearing at point B. The key reaction forces to determine include Ax, Ay, Az, Bx, By, Dx, Mbx, and Mby. Participants emphasize the importance of applying the equations of equilibrium and suggest using a free body diagram to visualize the forces acting on the rod. The consensus is that while calculating moments around various axes is useful, it is essential to not overlook fundamental equilibrium principles.

PREREQUISITES
  • Understanding of 3D equilibrium concepts
  • Familiarity with free body diagrams
  • Knowledge of reaction forces in mechanics
  • Proficiency in applying the equations of equilibrium
NEXT STEPS
  • Study the principles of static equilibrium in three dimensions
  • Learn how to construct and analyze free body diagrams
  • Explore methods for calculating reaction forces in complex structures
  • Review the application of moment equations in 3D mechanics
USEFUL FOR

Students studying mechanics, particularly those tackling statics problems, engineers working with structural analysis, and anyone interested in understanding reaction forces in 3D systems.

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Homework Statement



in the attached picture are all the information needed to solve the problem.

The bent rod of a negligible weight is supported by a ball and a socket joint at A and a single journal bearing at B. End of D of the rod rests against a friction-less vertical surface. find the reaction forces at A and B.

Homework Equations



sum of forces
sum of moments
Reaction forces:
Dx
By
Bx
Mbx
Mby
Ax
Ay
Az


The Attempt at a Solution



moment around a line AB to get D
but then i am stuck!
should i get the moment around line AD to get By and Bx? or there is even an easier way? double 2D perhaps?
I know i can use the moment around A and the equilibrium of forces in X,Y, and Z
but that will take the whole day, and i am sure the prof created the question in a way that will screw you up if you solve it using the equilibrium equations.

I would be grateful if you help me with this.
 

Attachments

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What's wrong with drawing a free body diagram and showing the reactions? With writing the equations of equilibrium and solving them? You seem so fixated on calculating moments about this axis or that axis that you are ignoring the basics. You have also apparently become a little paranoid, thinking your prof has devised some double secret, tricky problem that you'll screw up.

Well, it seems his secret plan is working.
 

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