Calculate Beam Deflection at C using Superposition

[hyper]

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

 

[PhanthomJay]

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.

 

[hyper]

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?

 

[PhanthomJay]

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?