# Are the displacements the same?

## 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?

Stiffness matrix

## The Attempt at a Solution

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mfb
Mentor
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.

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

The setup is symmetric, sure.

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