Are these Methods/formulas really any good?

[Tygra_1983]

Hi there everyone,

I have a couple of books by Stafford Smith and Coull (Tall Building Structures) and Zalka (Structural Analysis of Multi Storey Buildings) which present some approximate methods to use to compute horizontal deflections of tall buildings under horizontal loads. However, for me at least they have proved pretty useless as they don't even give a good approximation to the real solution.

Some of these equations come as follows:

For the stiffness of a frame Zalka gives:

K = (1/Kb + 1/Kc)^-1

Where:

Kb = 12*E*I/(l*h)
Kc = 12*E*I/(h^2)

l = bay width and h = storey height

Zalka also provides the stiffness for a single diagonal braced frame as:

K = (d^3/(Ad*E*h*l^2) + l/(Ah*E*h)^-1

Where:

Ad = cross-sectional area of the diagonal
Ah = cross-sectional area of  the beam in the frame

I was thinking that I could apply hooke's law that is F = K*U seeing that these formulas claim to give the stiffness??

Stafford-Smith and Coull give the following formula for the deflection of diagonal braced frame as:

delta = Q/E*(d^3/(l^2*Ad) + l/Ah)

Where Q is the storey shear

I have tried to apply these formulas to certain problems that I am practising on, but sorry to say they seem to be pretty useless. Does anyone here I have any experience with this that could perhaps shed some light on them, because surely a published book would not present incorrect methods?

Many thanks!

 

[driftLimiter]

These equations without any context is hard to understand what you perceive to be wrong about them.

They appear to be stiffness contributions from individual elements within a specific type of structure.

For a large multistory building you will need to carefully understand how the stiffnesses of individual elements are combined in order to yield adequate results.

This is something taught in structural dynamics class, or perhaps in structural analysis.

 

[Tygra_1983]

[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1701981664/tips/General_Information_b6cg6n.pdf[/url]

Hi there, driftLimiter, I have attached a file which gives some context to using these formuals. Sorry for the delay.

 

[Celt83]

Your story shear at the roof is incorrect if the columns are 6m tall then the roof tributary is half that or 3m.