Walls in rigid diaphragm with mezzanine 1

[jims3251]

I am evaluating a single story reinforced concrete structure with a mezzanine. For the sake of discussion assume a rectangular building with the mezzanine running the full length along the back (long wall). When developing the rigidities for the walls supporting the roof are the front walls twice as tall as the back walls that are attached to the mezzanine and therefore substantially less rigid although length, thickness and openings are approximately the same?

 

[ishvaaag]

Yes, for the same horizontal force atop and along each wall the twice tall will show twice displacement, and rigidities relate the applied force with the displacement.

 

[JoshPlumSE]

No, at the roof level, the walls have essentially the same stiffness. I think Ishvaag mis-read your initial e-mail and assumed you were asking about two walls that were actually different heights rather than the same height walls where the only difference is that one has a mezzanine connected to it.

The wall that has a mezzanine at mid-height could be referred to as two spring loaded in series. But, the net results is that the roof sees nearly the same stiffness at the top of each wall.

 

[ishvaaag]

Certainly I was only considering equal section walls with different heights, irrespective of any connection.

If a mezzanine connects two of such walls but at the same height, of course the rigidity of the wall level under it is the same, for a mezzanine whole diaphragm.

Contrarily, if what is wanted is some diaphragm following the slope of the roof, and we forfeit any effects some mezzanine connecting just to the tall side may be adding, the case is the contrary, for for the same force atop each wall, the tall wall will displace more.

F=G·A·gamma leading to equal gamma but displacement atop is gamma·2·L where at the lower gamma·L both for the same force, hence stiffness a half for the tall wall (F related to horizontal displacement).