Flat-plate structure - sway analysis

[Prascad]

I performed lateral (wind load) analysis for a 24 story
shear walled flat plate structure as per ACI 318-99
clause 10.11.1. All the floors are post-tensioned slabs.
Plate bending elements were used to model the floor slabs
and walls in the 3D computer model. I used a reduced
floor slab stiffness of 0.25 Ig in my computer model.
For prestressed concrete slabs the code suggests to
take a higher value. But I used 0.25 Ig conservatively
for all my post tensioned slabs.

Many storys in the longitudinal direction were found
to be in sway condition (ACI 318-98 clause 10.11.4.2 )
and the maximum Q = 0.095. Shear walls are found to be
attracting 98 % of the lateral wind. Architect is not
willing to increase the wall length to make the building
non-sway. The column moments due to design wind load
combinations are not significant from design point
because most of the wind load goes to the walls.

Lateral displacements determined using the service load
combinations (ACI R10.11.1) are less than building height/400 limit, which is common for most structures of this type.

At this stage I decided to design the building for the
sway effects. As per ACI 10.13, analysis was performed to
consider the effect of second-order displacements
for the two design wind load combinations. The second order
moments for 50% of the columns are found to be less than
the first order moments. This is because of the
redistribution of the forces within the structure where
in the stiff walls attracted even more lateral shear.

My questions are ...

1. My approach to the problem - is it correct ?

2. What stiffness reduction to be adopted for PT slabs ?
Where can I get the supporting information (published)
to convince the design reviewer ?

3. ACI 10.11.1 procedure - is it applicable for shear-walled
flat-plate buildings when 98 % lateral load goes to the walls ?

4. For some columns the second-order moments are higher
than first-order moments ( both are less than 20% of the
moment capacity of the columns ). My reviewer feels that the PT floor slab need to be checked for the second-order
moments because it is the floor that it transfering the
moment to the columns. To satisfy his querry I had included
the additional moment in the punching shear checks. Any
comments on this ??

 

[ishvaaag]

The 25% of brute stiffness it is said in the code commentary to 10.11.1 (of ACI 318-95 last that I own) to be derived for nonprestressed members.

Meyer in Earthquake-Resistant Concrete Structures Inelastic response and Design ACI SP-127 p. 208 22. recommends to avoid extremes ratios between stiffnesses.

He also says in 2nd paragraph in p. 205 that due to the standing ability of redistribution there's usually scarce damaging effect to exèct by some loose consideration of the stifnesses.

At service level you will or should have near integral stiffness out of balancing of standing actual loads.

On the contrary, the final limit stiffness will depend on how big the final demand is respect the plate capacity in its actual status. If you allow by your design of the plates the joints go near its capacity there, more likely the behaviour will be approaching what you have assumed since the limit strength of prestressed an non prestressed sections are quite the same...yet I feel a more stiff behaviour will be truer representation, since prestressed, and factored demand is close to but not just the limit strength.

On the contrary, if the forces at joints at factored levels are far from the limit capacity, far bigger stiffness will
be extant and maybe 50% to 80% of the brute stiffness would give a better model.

What in all makes me thing that maybe you should bracket the
stiffness by adding analyses to say 50 or 80% of the brute stiffness and then see what happens.

Then joint design may be based in the chosen model, or in the results of the bracketing analyses.

I don't remember reference for simplified stiffness of the prestressed plate as of now.

 

[JAE]

Prascad.

Question 1 - overall, your approach to the problem appears to be rational and proper.

Question 2 - The stiffness reduction level affects BOTH your column design and your slab design in reciprocal (sp) fashion. By underestimating the stiffness of the slab (0.25Ig) you are minimizing the flow of moment into the slab due to the lateral distortion of the structure, but...you are maximizing the flow into the shearwalls and diaphragms. By overestimating the stiffness of the slab (due to the post-tensioning which increases Mcr and therefore increases Ie)you are maximizing the flow of moment into the slab and reducing the load into the walls.

If you can get a rational floor-ceiling estimate between which you know the true stiffness occurs, you can simply do the analysis twice, once to maximize the wall forces and once to maximize the slab moments.

Also...in your analysis, how do you reduce the plate bending stiffness without altering the shear response of the diaphragm which is independent of the bending stiffness? Just wondering.

Question 3 - I don't think its inappropriate to use the 10.13 method....its just giving you a more exact consideration of the fact that the non-lateral system columns (which, as you say, take only 2% of the load) do bend with the building movement and ....Hooke's Law: what bends has moment.

Question 4 - see question 2 above.

 

[Prascad]

Thanks for the responses.

ETABS permits application of different reduction factors for membrane and bending stiffnesses.

Lateral analysis of flat-plate structures was traditionally based on equivalent beam methods, using manual / simplified frame analysis techniques. The width of equivalent beam considered was critical for the stiffness analysis. The use of pate bending elements however, enabled the analyst to model the floor geometry and structural load transfer more realistically. This led to significant analysis accuracy in terms of accounting for mass distribution, P-Delta effects, large displacements, second-order effects.

I agree that the 0.25 reduction factor for floor stiffness is much less. I have collected some more information on this problem. I got some reference for the use of 0.25 Ig in case of non-prestressed slabs .....

----------------------------------------------
Author GAMBLE
Title “Design of Two-Way Slabs”
page 125 states “This differential state of cracking is undoubtedly the source of ACI 318-95 Section 10.11.1(b) which lists the ... reduced moments of inertia which may be used in investigating column length effects. Slabs 0.25 Ig....While these relative stiffness values were not necessarily intended for use with the frame analysis of an unbraced slab and column structure, this has apparently been done, perhaps widely.

The 0.25 value may be thought of as a 50% reduction in Ig which reflects the effective width concept and another 50% reduction which reflects the expected state of cracking.
-----------------------------------------------

In effecting the floor stiffness reduction, one need adopt different values for the two kinds of modeling approaches 1) 3D model with floor elements and 2) Equivalent frame model. From the last paragraph it is clear that one can use 0.50 Ig for the floor elements in the 3D computer model for non-prestressed slabs.

If we consider 50% increase in stiffness due to prestress, then 0.75 Ig may be appropriate for PT slabs in the 3D computer model to satisfy the codal requirement (ACI commentary R10.11.1).

In any event, the assumption is empirical and is based on engineering judgement !

I am also interested to know what other contries codes say in this regard.

Thanks again.

 

[abdelmageed]

dear,Pascard,,,
,,,As far as the case u mentioned is concerned i need to hilight the following:-
1/In general the approach seems to be rational,and the structure looks braced as shear walls care of more than 90% of lateral shear (ceb-fip requirements)but some members to be sway ,,,but i have slight reservations as per following points.
2/The stiffness of the plate is excessively reduced(0.25Ig),,,accordingly higher moments go to columns affecting accordingly the sway value???while long term effects on column were not considered in terms of stiffness<<<so, i think as per british code 8110 (part1) (50% of full panel width to be considered as analysing against horizontal load i.e 50%Ig),,no special consideration for PT-slab as far as analysis is concerned,,,effects due to second order on slab are to be catered for,,,ur approach seems to be of logic (shear considerations),,,
3/The shear wall to be designed as sway element if it does not meet the min. requirements for non-sway..,simply as sway frame columns,,,,(if first order moment not increased by more than 10% due to drift effects then no consideration for 2nd order is necessary ( consider non-sway))(as per ceb-fip)
4/An important issue is to consider the long term effects of column shortening over the whole structure and particularly at the connection with plates(This is why,,reduced section of the column is important in analysis of tall buildings),,,
More,,literature may be helpful in )CEB-FIP MODEL CODE 1990 AND THE SAME IN EURO CODE EC2 PART1-1992IN TERMS OF BRACED AND UNBRACED, SWAY AND NON-SWAY FRAMES),,,,later i may get u some excerpts in the main topic from both,,,
regards