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

In summary, the problem involves a bent rod supported by a ball and socket joint at A and a single journal bearing at B, with end D of the rod resting against a frictionless vertical surface. The task is to find the reaction forces at A and B using equations of equilibrium and free body diagrams. The student is initially stuck on calculating moments around different axes, but is reminded to focus on the basics and not overthink the problem or become paranoid about the professor's intentions.
  • #1
U of T Student
1
0

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.
 

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  • #2
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.
 

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

What is 3D equilibrium?

3D equilibrium refers to a state where an object is in balance and not moving in any direction in three-dimensional space. This means that all external forces acting on the object are balanced and there is no net force or torque acting on it.

What is moment in 3D equilibrium?

Moment, also known as torque, is a measure of the force that causes an object to rotate around a specific point or axis. In 3D equilibrium, the sum of all the moments acting on an object must be equal to zero for it to be in rotational equilibrium.

How do you calculate 3D equilibrium?

To calculate 3D equilibrium, you must first identify all the external forces acting on the object and their respective magnitudes and directions. Then, you must also determine the position vectors of these forces with respect to a chosen point or axis. Finally, using the principles of vector addition and the concept of moment, you can solve for the unknown forces or distances to achieve equilibrium.

What are some real-life applications of 3D equilibrium and moment?

3D equilibrium and moment are important concepts in engineering and physics, and they have numerous real-life applications. For example, they are used in the design of structures such as bridges and buildings to ensure they can withstand external forces and remain stable. They are also crucial in the design and operation of machines and vehicles, such as cranes and airplanes, to maintain balance and prevent accidents.

How does 3D equilibrium relate to other principles of physics?

3D equilibrium is closely related to other principles of physics, such as Newton's laws of motion and the concept of center of mass. These principles help us understand and analyze the motion and stability of objects in three-dimensional space. Additionally, 3D equilibrium is also related to other topics in physics, such as rotational dynamics and statics, which further expand our understanding of equilibrium in different contexts.

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