Free body diagram of a beam construction

In summary, the problem involves two light beams conjoined at a fixed point B, with fixed points A and D at either end. The radius of the wheel is R and there is a hanging mass m on the pulley. The goal is to draw a free body diagram and use the equations Fx=0, Fy=0, and M=0 to determine the forces at play. To start, consider the force of gravity on the hanging mass and work backwards from there, using convenient points to take moments about.
  • #1
Kagrim
2
0

Homework Statement


Beams AC and BD are light (no mass) and they're conjoined at B. Points A and D are fixed but frictionless. The radius of the wheel is R and the weight hanging on the pulley has the mass m.

Homework Equations


Fx=0
Fy=0
M=0

The Attempt at a Solution


I'm stuck at the very beginning of the problem which is to draw a free body diagram (the body is in equilibrium) of the construction however my equations don't add upp. The obstacle I'm currently facing is knowing which way the all the different forces are facing.
 

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  • #2
You know that the hanging mass m is affected by gravity. Start there and work back into the structure.

If you need more detailed help, you should post your FBD and the equations you're having trouble with.

P.S.: I'm moving this thread to the Engineering HW forum, which is a more relevant forum than Advanced Physics.
 
  • #3
Make free body diagrams of each piece. You know the sum of moments about any point is zero and that all forces add to zero. The trick is to choose convenient points to take moments about.
 
  • #4
Solved it! Thank you both for the reply.
 

What is a "Free Body Diagram" of a beam construction?

A "Free Body Diagram" is a simplified representation of a beam construction that shows all the external forces acting on the beam. It helps to analyze the structural integrity of the beam and determine the forces that need to be accounted for in its design.

Why is it important to create a Free Body Diagram for a beam construction?

Creating a Free Body Diagram for a beam construction is important because it allows us to visualize and understand the forces acting on the beam. This information is crucial in designing a structurally sound and safe beam that can withstand the expected load.

How is a Free Body Diagram different from a typical diagram of a beam construction?

A typical diagram of a beam construction shows the physical dimensions and materials used in the beam, while a Free Body Diagram focuses solely on the external forces acting on the beam. It is a simplified version that helps in the analysis of the beam's structural integrity.

What are the different types of forces that can be shown in a Free Body Diagram of a beam construction?

The different types of forces that can be shown in a Free Body Diagram include:

  • Gravity: The force pulling the beam downwards.
  • Support Reactions: The forces exerted by the supports on the beam.
  • Applied Loads: Any external forces or loads acting on the beam, such as weight, wind, or pressure.
  • Internal Forces: The forces that are generated within the beam itself, such as bending, shear, and axial forces.

How can a Free Body Diagram be used to analyze the structural integrity of a beam construction?

A Free Body Diagram can be used to analyze the forces acting on the beam and determine if it can withstand the expected load. By summing up all the forces and moments in different directions, we can determine the magnitude and direction of each force and identify any potential weak points in the beam's design.

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