Dear Sirs, I have a technical q

[Shahin]

Dear Sirs,

I have a technical question concerning on calculations of P-Delta effects on concrete structures. I will be very appreciated if I could have your opinion on the following case:

According to NEHRP and other codes, it is convenient that in order to estimate the maximum inelastic deflection, the deflections computed from an elastic analysis are amplified by a deflection amplification factor named Cd.

Also in concrete structures, according to section 10.11.1 of ACI building code (1995), in order to estimate the P-Delta effects we have to use the reduced sections moment of inertia in static analysis.

The main question is that is it true that we use both Cd factor and reduced sections moment of inertia in conjunction with each other in order to get the estimated deflections or only Cd factor is sufficient for this propose? On the other hand, is the effects of cracked sections are considered within the Cd factor or not?

 

[ERV]

I am not sure if I understand your question, however,

P-Delta Effect = The secondary effect on shears and moments of structural members due to the action of the vertical loads induced by displacement of the structure resulting from various loading conditions (Section 9, ASCE 7-98)

Cd = deflection amplification factor
Stiffness properties and cracked sections are not included.

P-Delta effects on story shears and moments, the resulting member forces and moments, and the story drifts induced by these effects are not required to be considered when the stability coefficient is equal or less than 0.10.

See also ASCE 7-98, Section 9, for comprehensive design criteria (highly recommended).

http://www.pubs.asce.org/BOOKdisplay.cgi?9990609

 

[JAE]

Some others may want to weigh in on this but I believe that the Cd factor (or the omega factor in the IBC) should be used in addition to the reduced I values in the ACI. The Cd factor is intended to adjust the seismic design forces ( which were reduced by R) to represent the actual seismic event.

Remember that the R factor reduces the actual seismic event down to a level where the applicable lateral system type can work while still maintaining ductility beyond this point up to the actual level of seismic energy applied.

So the Cd factor is an adjustment to the seismic load, while the reduced I values in concrete are dealing with the cracked, reduced stiffness due to those loads.

 

[Shahin]

I am sorry that I have not been able to give you exactly my idea about the matter. The Cd factor that I meant is as JAE mentioned, is called the deflection amplification factor as expressed in UBC 1994 or NEHRP 1994, not the Cd factor that is used in concrete column design. The Cd that I meant is normally defined as Cd=(3/8)*Rw or 0.4R.

The main point that confused me is that as Dr. Farzad Naeim expressed in his book, in order to estimate the P-Delta effect we have to use either Cd to increase deflection or cracked sections (not both together). In ACI it is expressed that in order to calculate the P-delta effect we have to use cracked sections. Now do we have to use both of the factors? On the other hand, do we have to use cracked sections in first order analysis and then increase the deflections Cd times or one of them is enough? Or is the effects of cracked sections are considered within the Cd factor or not?

 

[Taro]

Use both factors together. As mentioned previously, Cd adjusts the deflections to account for the R-factor force reduction to arrive at the maximum inelastic displacement. At this displacement, the concrete sections will inevitably cracked so the moment of inertia must be adjusted accordingly.

 

[Shahin]

This case is open to discussion. Are you sure about using both parameters together? First of all, as you described by using Cd we increase the elastic displacement of structure Cd times so we reach to the maximum inelastic displacement. On the other hand, it is used to estimate the ultimate (i.e.actual) expected deformation of the structure.

Second, in most codes using cracked section in analyses is only recommended (not required). In these codes, using cracked or uncrecked sections is up to engineer. So I think that the cracked sections properties should be included in calculating Cd by codes. It means that in defining Cd factor for concrete structures, the codes have considered the reduction of section of concrete members.

I will be very appreciated if you help me finding any paper or references that this case (using both cracked section and Cd) is explicitly notified on it.

 

[Taro]

Shahin,
Since you mentioned NEHRP, refer to section 5.4.6. This section cleary specifies that cracked sections are to be used in conjunction with the deflection amplification factor.