Statics Homework problem - Reactions of Ball and Socket

In summary, the problem involves determining the reactions at the ball and socket joint (point A) and the tension in cords BC and BD to support the vertical loads shown in the picture. The equations used are the sum of forces and sum of moments equalling zero. The solution involves calculating the unit vectors for BC and BD, drawing a free body diagram at point B, and finding equal and opposite tensions in BC and BD. The reactions at point A are still uncertain and may require further calculation.
  • #1
nrp88
4
0

Homework Statement


The pipe assembly shown in the picture supports the vertical loads shown. Determine the reactions at the ball and socket joint (point A) and the tension in the two cords BC and BD.

ip18h2.jpg

Homework Equations


Sum of Forces = 0
Sum of Moments = 0

The Attempt at a Solution


I first caluclated the unit vector for the BC and BD connections and then I drew a free body diagram at point B. I've attempted many differ way to go about this, but none of them seem right. I came up with the Tensions BC and BD being equal (and opposite) to 12.6 kN though that's probably not right.

I'm not sure about the reactions at point A, because I thought that any moment around a ball and socket is zero?

I've been stuck on this for days and it's due tomorrow at 3!

Please help me,
Thanks so much
 
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  • #2
The ball and socket joint can only push in the AB direction. My instinct is telling me that A is the point the moments should be taken from. Certainly the sum of the moments there is zero or it would turn. Anyway doing it that way would be an excellent check on your work.
Curious, I see in the diagram that BC and BD are in the horizontal plane but the diagram dimensions indicate B is only half as high as C and D.
 
  • #3
bump?
 

1. What is a ball and socket joint?

A ball and socket joint is a type of joint in which a spherical surface of one bone fits into a cup-like depression of another bone, allowing for a wide range of motion in multiple directions.

2. How do you calculate the reactions at a ball and socket joint?

To calculate the reactions at a ball and socket joint, you need to use the principles of statics and apply the equations of equilibrium. This involves analyzing the forces acting on the joint and using the equations of equilibrium to solve for the unknown reactions.

3. What are the main types of forces acting on a ball and socket joint?

The main types of forces acting on a ball and socket joint are axial forces, shear forces, and bending moments. Axial forces act along the length of the joint, shear forces act perpendicular to the length of the joint, and bending moments cause the joint to rotate.

4. How do you determine if a ball and socket joint is in equilibrium?

A ball and socket joint is in equilibrium when all the forces acting on it are balanced and there is no net force or moment acting on the joint. This can be determined by applying the equations of equilibrium and solving for the unknown reactions.

5. What factors can affect the reactions at a ball and socket joint?

The reactions at a ball and socket joint can be affected by various factors such as the angle of the joint, the magnitude and direction of the applied forces, the stiffness of the joint, and the material properties of the joint and the bones connected to it.

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