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Re: Drift at top and rotation/curvature

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Even though we do not design columns to hinge at design loads, but under
real loads, the magnitude of which may be much higher than the design
loads, columns will be hinged.  Therefore, overall understanding of
building's limit state behavior is very essential to an attempt to predict
collapse scenario.

The performance based design (see FEMA 273 and ATC 40 guidelines) attempts
to calculate a structure's capacity by performing a push over analysis and
drawing a capacity spectrum of the structure.  By overlaying a demand
spectra, one could find the so called performance point.

It should be noted, however, that many engineers believe that by designing
to Code forces (static) they can predict the building's behavior to a
future strong motion.  By performing push over analysis, one will find out
readily that the forgoing belief is unfounded and one needs to look at form
displacement controlled point of view, for which calculations of
deflection, understanding of plastic hinge characteristicsand sequence of
their formation in a three dimensional structre is very important.

One should also note that formation of plastic hinge does not automatically
mean collapse or partial collapse.  For definition of plastic hinge and
allowed rotations refer to ATC 40 and FEMA 273.  A plastic hinge may rotate
by a factor of as much as 7 before a perfect pin is formed.  A collapse
mechanism is formed only when sufficient number of beams and columns have
hinged to a true hinge level and system has become unstable.

"Juan C. Gray" <juangray(--nospam--at)> on 07/30/99 01:54:47 PM

Please respond to seaint(--nospam--at)

 To:      seaint(--nospam--at)                                   
 cc:      (bcc: Niaz A. Nazir/EQE)                            
 Subject: Re: Drift at top and rotation/curvature             

You should never, never! allow plastic hinges to form on the columns, as
this will cause the structure to fail mechanically (just think of floors
moving relative to each other without any constraint) . What you have to
do is guarantee that the hinges form first in the beams or slabs
supported by the column and design the moment capacity of columns to be
greater than that of beams (speaking generally of the joint). You may
check this in ACI 318-95 , eq. 21-1.
The relationship you seek between curvature and displacement is affected
by various factors as axial force , compression strength and yield
strength; you may like to check this in "Ssismic design of reinforced
concrete structures" by Paulay and Priestley , which is one of the best
reference books on seismic design.

Juan C. Gray

james korff pe pmp wrote:
> Good point.
> For steel columns the solution may be more straightforward (pun
> intended).
> We only have to assume the point of rotation, or location of the
> plastic hinge.
> For concrete, it is a little more complicated - or am I missing the
> forest for the trees.
> The underlying reason for my question is that some existing buildings,
> such as
> parking structures, need to have the ends of columns confined so that
> they will be able to deflect in a manner compatible with the slab
> deflection during the EQ. That is why the plastic hinges must be at the
> column ends, and not at the beams.
> I am trying to calculate how much confinement is required to meet code
> requirements.
> Thus, I am trying to correlate the results of a moment curvature
> analysis with the required (by code) drift at the top of the columns.
> In other words, what I'm looking for is a relationship between
> curvature in the plastic hinge, or hinges if there is a point of
> inflection, and the code mandated drift of 0.005h.
> Could it be that for such a relationship, only empirical results from
> testing each individual case will give the answer?
> --- Roger Turk <73527.1356(--nospam--at)> wrote:
> > Hm-m-m.
> >
> > Unless I have forgotten something from Theory of Plasticity, rotation
> > in a
> > plastic hinge is going to continue indefinitely without increase in
> > moment
> > (until strain hardening range is reached) as long as the moment
> > (plastic
> > moment) doesn't unload into an elastic state.  (Same as elongation in
> > a
> > tension member stressed to yield.  Elongation will continue
> > indefinitely
> > without increase in load until strain hardening range is reached.)
> >
> > A. Roger Turk, P.E.(Structural)
> > Tucson, Arizona
> >
> >
> ===
> James Korff, PE, PMP
> Structural Composite Consultants
> 985 E. Hillsdale Blvd, Suite 128, Foster City, CA 94404
> Phone 650-796-8997 / Fax 650-345-1355
> "May the DISPLACEMENT be With You !!"
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