Constructing forces (mechanics)

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SUMMARY

The discussion focuses on determining the reactions at points A and C in a statics problem involving a frame and loading scenario. Participants emphasize the importance of understanding force directions and their applications, particularly in the context of equilibrium where the sum of forces equals zero. The conversation highlights the necessity of writing equations of equilibrium for each component, utilizing a total of six equations for the six unknown forces. Additionally, it notes that member AB represents a two-force body while member BCD is a three-force body, underscoring the complexity of analyzing forces in static systems.

PREREQUISITES
  • Understanding of statics principles, specifically equilibrium conditions.
  • Familiarity with force diagrams and vector components.
  • Knowledge of moment calculations in rigid body mechanics.
  • Ability to write and solve equations of equilibrium for multiple forces.
NEXT STEPS
  • Study the method of joints in statics to analyze force distributions.
  • Learn about the equilibrium of two-force and three-force bodies in mechanics.
  • Explore the application of free-body diagrams in solving statics problems.
  • Review the principles of moment calculations around points in static systems.
USEFUL FOR

This discussion is beneficial for students and professionals in mechanical engineering, civil engineering, and physics, particularly those focusing on statics and structural analysis.

masterflex
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Homework Statement


I've attached a picture of my problem (with diagram): 4.70 .

"For the frame and loading show, determine the reactions at A and C."

From the diagram, you can see that the metal object is made up of 2 parts:
1) A to B
2) B to D


Homework Equations





The Attempt at a Solution


how do you arrive at the correct direction of the forces (ie: angle of the force; direction of its "application"). I have 2 interpretations and they will give different angles with which the force is applied (same magnitudes though). Which one is the correct interpretation? Because this is a statics problem (bodies at equilibrium), the sum of the forces = 0 (illustrated by the triangles).

How do you logically determine which interpretation (of force directions) is correct when you do these problems?

Thank you.
 

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The simple minded thing to do is just assume there is a horizontal and vertical compoent of force at A B and C. There are no moments at A B or C because the joints are all pinned.

Then write the equations of equilibrium for each two components. There are 3 equations for each component, that's 6 equations for the 6 unknown forces.

If you want top do it by a "neater" method, start by looking at the equlilbrium of AB. Take moments about A (or B) and it should be clear what is the direction the forces at A and B.

Hint: one of the options you drew is right.
 
It is worth also mentioning, the member AB is the special case of a two forces body, and the member BCD of a 3 forces (no parallel) body of statics.
 
Thanks guys. Even though something is pinned though, there can still be a moment of the reaction forces at that point. I have a test tomorrow so when I'm done with it (may take a day or 2 for me to get remotivated, but I'll post something that shows that). I'll also try your way to figure out the prob. Hopefully this won't be asked before I figure it out :)

I'm appending what I wrote: above... the moment of the forces where something in "pinned" = 0.
 

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