Help solving this equation please? 1

[Tygra_1983]

Hi there,

I am trying to use approximate methods to solve for a multi storey rigid frame, and I am going through an old CTBUH book from 1979 that has much interesting informmation on structural analysis on tall steel buildings.

I have been desatisfied with the portal method, cantilever method and even the factor method for the analysis of rigid frames. Hence, I am, hoping this book can give me something better.

There is an equation for solving for the rotation of the building at each storey and this is:

For my structure the storey height is the same through the whole building, and so is the stiffness of the columns and beams at each storey. Therefore, Ci and Gi do not change. The shear going from the top to the bottom is 9.13kN 18.26kN 27.39kN 36.52kN 45.65kN 54.78kN 63.91kN. This for a seven storey building.


I am trying to solve this equation, but I am a little stuck on how to do so. Is there anyone who could help please?

 

[driftLimiter]

This looks like it can be solved in tabular format.

You index each row with i.
Solve The parameter theta at the top most level then work your way down the structure.
I don't have specific experience with this equation, but based on the terms it seems like this is how its meant to be solved.

The question is what are you trying to solve? I believe this equation will get you joint rotation at each level so you can get the drifts.

 

[rb1957]

can "i" = 0 ? (ie this only applies to the intermediate floors, and the end floors (top and bttm) are different ?

shear force, V, is input (from the results of some structural analysis ?)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Tygra_1983]

The question is what are you trying to solve? I believe this equation will get you joint rotation at each level so you can get the drifts.

Hi driftlimiter, I want to solve for the moments in the columns and beams, shear forces, axial forces. Pretty much everything.

The book has these equations for the moments

In regard to solving the equations I made a matrix in Matlab, but I'm still not certain if I'm doing it right.

 

[driftLimiter]

Have you considered just doing the direct stiffness method (i.e. matrix analysis of structures)? Its pretty easy to program up in matlab as well.

Regarding your OP, I would just make a small sample 3 story building, and attempt to run through the solution by hand so that you fully understand it. Only after that would I go to Matlab and do a larger structure.

 

[Tygra_1983]

Yes, I have and I have used the direct stiffness method before. I find inputing the data for a large structure quite tedious though. I know it gives exact answers. I was just hoping to find something that is quick and that gives half decent approximations.

Yes, I will make a smaller building to practise. I will probably be back to see if I am doing it correctly.

Thanks, driftlimter.

 

[Tygra_1983]

In would like to ask another question please:


Is the rotational stiffness of a joint in a rigid frame the sum(E*Ic/h)/sum(E*Ib/L)?


Where Ic and Ib is the second moment of area of the columns and beams, and h and L is the storey height and bay length.

 

[Tygra_1983]

Is there nobody here that knows anything about rotational stiffness??

 

[M.IDR]

Yes, if you have a rigid joint you should account for rotational stiffness.

Time is far more precious than you can imagine.