Have I solved this structural engineering equation correctly?

[Tygra]

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:

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.

I am hoping someone can help?

Many thanks

 

[osilmag]

Looking at your code, I think your Q and h variables need to have indexed values...Q(1) h(1), Q(i+1), etc. Otherwise, it looks ok.

It seems that you have loaded it backwards in the code or the image. As you have written it, a +1 height in your code has it going a higher floor instead of lower floor like you have in the image.