Engineering Have I solved this structural engineering equation correctly?

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The discussion focuses on a structural engineering equation for calculating rotations at rigid joints using an iterative procedure. The user has provided a specific formula and MATLAB code to compute these rotations based on given parameters such as horizontal storey shear and storey height. The initial values for rotations are derived from a formula in a 1979 engineering book, and the user seeks validation of their calculations and code. They emphasize that the last rotation value is set to zero due to a fixed support condition. Assistance is requested to confirm the correctness of the approach and calculations.
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Homework Statement
A structural engineering iterative equations to find rotations at joints
Relevant Equations
$$ x_i = \frac {Q_ih_i + Q_{i+1}h_{i+1}}{4K} + \frac {C}{K}x_{i-1} + \frac {C}{K}x_{i+1} $$
Hi all,

I have a structural engineering book from 1979. I am trying to follow it as best as I can. I have come to a formula that calculates the rotations in radians at the rigid joint that requires an iterative procedure. This equation comes in the form of:

$$ x_i = \frac {Q_ih_i + Q_{i+1}h_{i+1}}{4K} + \frac {C}{K}x_{i-1} + \frac {C}{K}x_{i+1} $$

Where:

## Q ## is the horizontal storey shear

## h ## is the storey height

## K = (6G_i + C_i + C_{i+1}) ##

## G = \frac {I_g}{h} ##

## C = \frac {I_c}{L} ##

## L ## is the girder length

## x ## is the rotations for the ## ith ## storey

The book says to use initial values x by using this formula:

$$ x_i = \frac {Q_ih_i + Q_{i+1}h_{i+1}}{24G_i} $$

After you can compute the rotations for each level use the iterative formula to improve the values of the rotations.

Now, I have used MATALB to do this. Here is my code:

Matlab:
x1(1) = (Q*h/4)/(24*G1)
x2(1) = (2*Q*h/4 + Q*h/4)/(24*G1)
x3(1) = (3*Q*h/4 + 2*Q*h/4)/(24*G1)
x4(1) = (4*Q*h/4 + 3*Q*h/4)/(24*G1)
x5(1) = (5*Q*h/4 + 4*Q*h/4)/(24*G1)
x6(1) = (6*Q*h/4 + 5*Q*h/4)/(24*G1)
x7(1) = (7*Q*h/4 + 6*Q*h/4)/(24*G1 + 2*C)
x8(1) = 0

for i = 1:10
     x1(i+1) = Q*h/(4*K) + C/K*x2(i);
     x2(i+1) = (Q*h + 2*Q*h)/(4*K) + C/K*x1(i) + C/K*x3(i);
     x3(i+1) = (2*Q*h + 3*Q*h)/(4*K) + C/K*x2(i) + C/K*x4(i);
     x4(i+1) = (3*Q*h + 4*Q*h)/(4*K) + C/K*x3(i) + C/K*x5(i);
     x5(i+1) = (4*Q*h + 5*Q*h)/(4*K) + C/K*x4(i) + C/K*x6(i);
     x6(i+1) = (5*Q*h + 6*Q*h)/(4*K) + C/K*x5(i) + C/K*x7(i);
     x7(i+1) = (6*Q*h + 7*Q*h)/(4*K) + C/K*x6(i);
     x8(i+1) = 0;
end

So from this is get my rotations at each storey. I haven't posted my results. I merely hope for someone to check the above workings and let me know if I have done this correctly.

For a visual aid, here is a typical structure of seven storeys with 8 rotations. Note, x8 equals zero because it is clamped against rotation because I am using a fixed support.
7 Storey Rigid Frame.webp


I am hoping someone can help?

Many thanks
 

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