Calculate Beam Deflection at C using Superposition

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Discussion Overview

The discussion revolves around calculating the beam deflection at point D using the method of superposition, particularly focusing on the effects of applied forces on the beam's geometry and displacement. Participants explore the interactions between different segments of the beam under load, including the implications of tension and rotation.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks assistance in understanding how the various forces acting on the beam will affect the position of point D, particularly the roles of the 12 kN and 9 kN forces.
  • Another participant questions whether the Moment of Inertia for members BC and CD was provided and clarifies the meaning of 'change in position at c' as 'rotation at C'.
  • A participant notes that the angle BCD must remain a right angle before and after loading, suggesting this is crucial for the calculations.
  • There is a discussion about how the tension in AB will cause BCD to rotate and how the 9 kN force will push point D downwards.
  • Concerns are raised about how to account for the forces in BC and the implications of the right angle constraint on the calculations.
  • One participant emphasizes that the rotation at C affects the displacement of D and suggests that the axial deformation of AB due to the 12 kN load is essential for determining the rotation.
  • Participants are encouraged to draw a sketch to visualize the problem better.

Areas of Agreement / Disagreement

Participants express uncertainty about specific calculations and the implications of the geometry involved. There is no consensus on how to approach the problem, as multiple viewpoints and interpretations of the forces and constraints are presented.

Contextual Notes

Participants mention the need for the Moment of Inertia values and the importance of maintaining a right angle in the geometry, indicating potential limitations in the information provided. The discussion also highlights the complexity of the interactions between the forces and the resulting displacements.

hyper
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Hello, I am supposed to find the change in position at c by superposition. But I don't really know how all the parts will act together. Can someone please help?

I do see that when AB is made longer by a 12 kN force, C will rotate down. And C will also go longer down because of the 9 kN force, but what do I do with BC? The 12 kN force in AB will make the point B go more to the left here?

Please help.

http://img217.imageshack.us/my.php?image=defldg9.jpg
 
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Was the Moment of Inertia for members BC and CD given? By 'change in position at c', do you mean 'rotation at C' ? Note that angle BCD must remain a right angle before and after loading. Also note that AB is in tension, and therefore must get longer in accord with the axial deflection formula for the 12kN tensile load.
 
PhanthomJay said:
Was the Moment of Inertia for members BC and CD given? By 'change in position at c', do you mean 'rotation at C' ? Note that angle BCD must remain a right angle before and after loading. Also note that AB is in tension, and therefore must get longer in accord with the axial deflection formula for the 12kN tensile load.

Sorry for beeing somewhat unclear. I meant the vertical displacement of point d. Don't know why I wrote c. And yes the moment of inhertia was given.

I doo see that the tension in AB will cause BCD to rotate, and I do see that the 9kN force will push D downwards. But what do I do about the forces in BC?. What do you mean when you say that BCD must remain a right angle?, how do I account for this in my calculations?
 
hyper said:
Sorry for beeing somewhat unclear. I meant the vertical displacement of point d. Don't know why I wrote c. And yes the moment of inhertia was given.

I doo see that the tension in AB will cause BCD to rotate, and I do see that the 9kN force will push D downwards. But what do I do about the forces in BC?.
You need only be concerned about the rotation of C due to 12kN force at B; the amount of rotation depends on the axial deformation of AB due to the 12 kN load, which must be equal to the "PL^3/3EI" deflection of point B relative to C. This can only happen if C rotates a certain amount, determined from the geometry. The rotation at C thus affects the displacement of D.
What do you mean when you say that BCD must remain a right angle?, how do I account for this in my calculations?
Since BC and CD are joined together by an ideally rigid fixed joint, the angle must stay a right angle by definition of ideal fixity. This will help with the geometry when determining the displacement at D due to the rotation at C. Draw a sketch. Is this a homework problem?
 

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