Help with this equation (approximate methods for calculating rotations, displacements and moments etc for rigid frames)

[Tygra]

Hi there,

I am a graduated structural engineer and I am going through a book that has section on approximate methods for calculating rotations, displacements and moments etc for rigid frames. I have come to an equation in the book that I am finding difficult to solve. The book gives this equation (2.23) in two forms which are below:



And






I want to solve for the rotation at the joints "theta". Where theta _{i +1} is the storey/floor above and theta _{i –1} is the storey/floor below. Is there anyone here that could help me solve it?

Many thanks!

 

[blamocur]

I want to solve for the rotation at the joints "theta".

What do you mean? They give you an expression for [imath]\theta_i[/imath] assuming [imath]\theta_i = \theta_{i-1} = \theta_{i+1}[/imath] -- is it not what you looking for?

 

[Tygra]

Yes it says in the book at even numbered joints (joint 2, 4...etc) the assumption is made that
theta_(i-1) = theta_(i) = theta_(i+1) and that it follows that:

It goes on to say that the initial values are obtained from the above formula (at even numbered joints). Next, the odd numbered joints for the first approximations are calculated from:

Next, improved values can be calculated at even numbered joints from this equation. Lastly, it says the equation is then used alternately for the set of both odd and even numbered joints until a satisfactory degree of convergence is achieved.

I am working on it currently and have got further than when I first posted, but can someone go through it for me please?