3D Equillibrium Statics Problem - Reaction Forces/Moments

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Discussion Overview

The discussion revolves around a statics problem involving a rigid body in 3D equilibrium. Participants are exploring how to determine the reaction forces and moments acting on a beam subjected to various loads, including vertical and horizontal forces, as well as the influence of a supporting rod at an angle. The scope includes theoretical and mathematical reasoning related to static equilibrium.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant describes a scenario involving a beam fixed at one end with vertical and horizontal forces applied, seeking guidance on finding reaction forces and moments.
  • Another participant questions the application of the forces, noting that 1000 pounds is a significant amount of force.
  • A participant clarifies that the forces mentioned are arbitrary and intended to illustrate the problem-solving process rather than represent real-world values.
  • One suggestion is made to sum the forces in the x, y, and z directions and equate them to zero, as well as to choose convenient points for summing moments.
  • A participant expresses uncertainty regarding the moments calculated after summing forces and moments, indicating potential issues with the added fixed rod's influence.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the accuracy of the moments calculated or the impact of the fixed rod. There are multiple viewpoints regarding the approach to solving the problem, and uncertainty remains about the correctness of the forces and moments involved.

Contextual Notes

Participants have noted potential complications arising from the geometry of the system, particularly the angle of the rod and its effect on the calculations. There may be missing assumptions or unresolved mathematical steps that could affect the analysis.

mjgarrin
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Hello, it has been quite some time since my statics class, and I am having a problem determining the reaction forces and moments in a rigid body. I have included a sketch of my problem, and I am hoping someone can help guide me to a solution. I apologize if the sketch is a bit crude.I have a beam that is fixed at one end. On the opposite end, there is a vertical force acting directly on the beam (F1 = 1,000 lbf), and a horizontal force acting on a bar attached to the beam (F2 = 250 lbf).

The beam is supported by a roller, and has a reaction load in the vertical directly only, located 30 inches from the end of the beam.

The beam is also supported by a rod, located 12 inches from the fixed support, and the rod is at an 18 degree angle.

I am trying to find the reaction Forces as well as the Moments to show this scenario in static equilibrium.

Thank you.
 

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  • Statics problem.png
    Statics problem.png
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Can you describe the application? 1000 pounds is a lot of force...
 
I just gave made up numbers just to get an idea how to solve such a problem. I agree, the forces may not translate well to the size of the beam. Any force would work.
 
Sum forces in the x, y, and z directions and equate to zero. Also choose a convenient point(s) to sum moments around and equate to zero. Start here and let's see how many unknowns you have. Also since it's a 3D system I would recommend using cartesian vector notation.
 
I think the added fixed rod is causing me some issues. I tried summing the forces and moments, and got the following in the attached sketch. I think the forces are right, but I am not sure the moments are accurate...
 

Attachments

  • Statics problem2.png
    Statics problem2.png
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