# Direct Stiffness Method for a distributed load

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1. Apr 20, 2017

### lawa44

I'm working on a question which asks to determine the deflection, curvature, forces and moments of a simply supported beam with a distributed load. diagram shown in here http://imgur.com/a/wpI4k

Initially, I've done the calculation with 1 plane beam element with 2 nodes. At L = 0 and L = 3. But that doesn't give me the deflection of the beam at L = x/2.

So I'm trying to use 2 elements with 3 nodes as shown here.

I've reduced the matrix down to a 4 x 4 with {theta_1; v_2; theta_2; theta_3} as unknowns.

The result i got were:

• theta_1 = -0.0462
• v_2 = -0.0865
• theta_2 = 0
• theta_3 = 0.0462
The results from the 2 node analysis were:

• Q_1 = 3N
• theta_1 = -0.0231
• Q_2 = 3N
• theta_2 = 0.0231
Which do not agree with the results from the 3 node analysis.

Moreover, from using the Euler beam equation I calculated a deflection result of -21.6mm which does not agree with v_2 either.

Because of the difference in values, I got from the 3 node analysis, I have yet to substitute the values back in to calculate the other nodal values.

Did I make a mistake?

Is it correct to use L/2 instead of L for my three node equivalent loads?

i.e. -w(L/2)/2 instead of -wL/2 as was the case in the 2 node analysis.

2. Apr 25, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.