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Re: Consideration of Column Cracking

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In a message dated 98-04-20 09:29:46 EDT, you write:

<< Subj:	 RE: Consideration of Column Cracking
 Date:	98-04-20 09:29:46 EDT
 From:	kaa(--nospam--at) (Cezar Aanicai)
 Reply-to:	seaoc(--nospam--at)
 To:	seaoc(--nospam--at) ('seaoc(--nospam--at)')
 Abdi wrote:
 Reducing gross inertia of columns by 80% seems reasonable. You can
 also check the table 4.1 on page 163 of the following book for
 more accurate values of effective member moment of inertia:
   Seismic Design of Reinforced Concrete and Masonry Buildings
     By: T. Paulay and M.J.N. Priestley
 The Clause 10.14.1 of the Canadian standard CSA A23.3-94 
 and also the explanatory notes N21.2.2.1 and N21.2.2.2 of 
 this standard suggests that flexural rigidity of the beams
 may be taken as 0.35 of their gross section value. Also there, it
 is suggested that the flexural rigidity of the columns   
 may be taken as 0.70 of their gross section value.
 Abdi (A.S. Moghadam)
 A more flexibile elements (columns and beams) will be "easy loaded".
 I don't agree this idea especially when we talk about the eigenvalues.
 To check other STATICAL conditions maybe it is right, but speaking
 by the point of view of dynamic analysis I can not be so sure that it
 is a good way to design the concrete structures.
 Cezar Aanicai

Cracked sections should be used for the computer modeling of the concrete
buildings.  1997 UBC 1630.1.2 requires the stiffness properties of reinforced
concrete and masonry consider the effects of cracked sections.  The effective
moment of inertia (Ie) can be calculated from the curvature properties of the
sections based upon the reinforcing steel layout, confinement reinforcing,
cross section of the element, concrete strength, reinforcing strength and
axial loads.  See text books by "Park and Paulay" and "Paulay and Priestley"
for curvature explanations. 

Calculation of the curvature of an element (beam or column) is very time
consuming;  moment frame beams can require separate calculations based upon
top reinforcing in tension and bottom reinforcing in tension.  Moment frame
columns require consideration of maximum and minimal axial loads acting as
well as calculation about both the y and x axis if the reinforcing pattern is
not symmetrical.  You end of with a envelope of effective moment of inertia
values, which you then determine an appropriate weighted average value for
each frame element of the building.  

Concrete by its very nature will crack during curing.  During an earthquake we
know that the concrete is also going to crack, this changes the stiffness, and
therefore changes the period of the building.  The problem is with the reduced
building stiffness, you must still meet code drift requirements to control
overall building P-delta effects.  The effective moment of inertia for cracked
walls may only be 10% -25% of the gross section moment of inertia.  Highly
loaded columns may have "I effectives" of 30% to 50% of gross properties and
beams may also be in this range.  As you can imagine, this makes building
design a time consuming iterative process;  select initial member sizes and
stiffness, check drift, check stresses, check curvature of actual elements
used and see if matches assumed stiffness, modify member properties as
required (change geometry, reinforcing, concrete strength, etc.).  

The reason to use the cracked section for stiffness is to more reliably
account for the actual expected performance of the building and control
displacements which are underestimated when using gross section properties.
It is almost easier to evaluate an existing building since all material and
geometry of the frame elements/walls are known or can be determined.  Then you
determine the elastic lataral capacity of the building and then determine if
strengthening is required.

Michael Cochran