p-delta in multistorey buildings

[arcofante]

I am a student preparing an exam at the Milan Polytechnic and have come across an affirmation in the lecture notes which leave me perplexed.

Analysing multistorey buildings, a poor control of deformations of
horizontal structures can produce second-order referred to as p-delta.
Usually, the mechanism is illustrated in the following manner: An eccessive
rotational deformation fi causes an eccentricity in the application points
of the vertical loads on the columns in the lower stories, which in turn
(second-order), produce a torque on the horizontal plane in the lower stories.

The question is the following: How is it in any way possible that a
vertical load, however eccentric, produce a torque in the horizontal plane?
If a moment can be represented by a vector normal to the plane of torque,
the inner product of any vertical load or resultant thereof, and the normal
of a horizontal plane will always be the modulus of the vertical load, and
thus the cross product (torque), zero...

thank u for any responses!

 

[ishvaaag]

Maybe they refer to a moment which axis is perpendicular to a vertical plane frame, and then lays (the vector) in the horizontal plane. In any case hope you have clear what P-Delta means, both at end of defined members and for in-member length. P-Delta for out of plumnb is quite ordinarily dealt with in many design packages. The in-member P-delta is dealt normally by industry limits to out-straight plus conventional conforming the code checks; for some tall columns it may be interesting to split it in submembers, or even preassign directly initial deformations to better ascertain the effects and observe them as results in the analysis. A uncommonly made but still worth check for critical columns is to see if the final in-member deformations of such slender columns fall within the industry warranted (and code implied) separation from the straight line.