Are the displacements the same?

[shreddinglicks]

Homework Statement

I have already completed both problems. I have the same answer for both of them. I was wondering if that is possible? Are the two point loads equivalent to the distributed load?

Homework Equations

Stiffness matrix

The Attempt at a Solution

 

[mfb]

As far as I can see you assumed that the middle section is perfectly rigid. With this assumption you get the same result; applying a force uniformly over a perfectly rigid element is the same as applying half of the total force on each end. Drop that assumption and you'll see a difference.

 

[shreddinglicks]

I want to make sure I understand. When you say assuming the middle section is rigid. That means the assumption that I made that the angular displacements at the two ends of the center piece are equal to zero?

 

[mfb]

What are the three beam elements you used? What did you assume for these beam elements?

The setup is symmetric, sure.

 

[shreddinglicks]

I used the stiffness matrix on each element. The three elements range from 0<x<914, 914<x<2134, 2134<x<3048. I assumed since the ends were fixed that the displacements and rotations about those ends were not applicable which simplified my stiffness matrix. The nodes at my center element I assumed angular displacement was equal to zero. So my matrix looked like this.

[K][displacements] = [F]
[K] [v2;theta2;v3;theta3]=[ql/2;0;ql/2;0]

where
ql/2 = -1000