Flat slab construction has an architectural advantage in providing large window openings or intensive underfloor piping because of no floor beams protruding down from the soffit of floor slabs. It is particularly advantageous for apartment buildings and hence it is widely used in many parts of the world. However it has not been used much in highly seismic countries such as Japan, because it is generally difficult to withstand seismic load solely by columns and floor slabs.
This feasibility study was conducted to see whether fiat slab construction can be made acceptable in seismic zones by providing lateral stiffness and resistance with the use of structural walls.
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Two types of highrise flat slab buildings were adopted as the object of
this study. The first was a fifty-story flat slab condominium with structural core walls, and the second was a forty-story flat slab resort condominium with curved structural walls. They were both designed initially by using materials in Zone II—1 of Fig. 2.1, that is, the combination of ultrahigh strength concrete and high strength reinforcing bars. However it was found during the feasibility study that the use of ultrahigh strength re-bars was indispensable. Hence the target of material usage was changed from Zone II—1 to Zone III.
9.1.1.1. Highrise Flat Slab Condominium with Core Walls
The first building, a highrise flat slab condominium of fifty stories, is shown in Figs. 9.1 and 9.2. One floor area is 2061 m2, and total floor area is 103 058 m2. Story height is 3 m except for the first story of 4.5 m. The total building height is 151.5 m. It has no basement. The foundation, assumed to be placed
Table 9.1. Structural materials.
Concrete Member
Columns, Walls
Slabs, Girders
Story 31-50 21-30 11-20 6-10
1-5 1-roof
Strength (MPa) 60 70 80 90 100
60 Re-bars
Member Slabs
Columns, Girders Wall (vertical) Wall (horizontal)
Lateral Re-bars in Columns, Girders
Grade SD345 USD685 USD685 USD980 USD1275
Yield Points (MPa) 345 685 685 980 1275
on the piles in the intermediate soil, is regarded outside the scope of the study.
Table 9.1 shows the materials used for this building. As mentioned earlier, they belong to Zone III in the New RC material combination.
The structure consists of flat slabs 250 mm thick, square columns ranging from 950 mm in the lower five stories to 800 mm in the upper 25 stories, core walls with thickness from 950 mm in the lower ten stories to 750 mm in the upper 30 stories, coupling girders which connect .L-shaped core walls with the same width as walls, and girders within the core 600 mm wide. Depth of all girders are uniformly 800 mm. Columns have no capitals, and slabs have
Table 9.2. Typical structural member sections.
F l a t S l a b s S t o r y
All floors
T h i c k n e s s 25 c m
C o l u m n S t r i p SD345-D13Q100
Middle S t r i p SD345-D13Q100 L - s h a p e d Walls
S t o r y 2 1 - 5 0 11-20 1-10
T h i c k n e s s 75 c m 85 c m 95 c m
Vertical R e - b a r s USD685-D35 Pg = 3.33%
U S D 6 8 5 - D 3 8 Pg = 3.75%
U S D 6 8 5 - D 4 1 Pg = 4 . 3 5 %
H o r i z o n t a l R e - b a r s USD980-D13O150 Pw = 0.68%
USD980-D13<ai50 P „ = 0.70%
U S D 9 8 0 - D 1 6 Q 1 5 0 P „ = 1.12%
C o l u m n s S t o r y
3 6 - 5 0 1 6 - 3 5 11-15 6 - 1 0
1-5
Section 80 c m X 80 c m 85 cm x 85 cm 90 c m x 90 cm 90 c m x 90 c m 95 c m x 95 c m
Axial B a r s USD685-12-D35 Pt = 0.50%
USD685-12-D35 Pt = 0 . 5 3 % USD685-12-D38 Pt = 0.56%
USD685-16-D38 Pt = 0.70%
USD685-16-D41 Pt = 0.74%
L a t e r a l B a r s
USD1275-4-D10Q100* P „ = 0.36%
USD1275-4-D10@100 Pw = 0 . 3 3 % USD1275-4-D13O100 P „ = 0.56%
USD1275-4-D13@100 Pw = 0.56%
USD1275-4-D13@100 P „ = 0 . 5 3 % G i r d e r s
S t o r y 2 2 - R 1 2 - 2 1
2 - 1 1 w / i n core
S e c t i o n 75 c m X 80 c m 85 c m x 80 cm 95 c m x 80 cm 60 cm X 80 c m
Axial B a r s USD685-10-D38 P , = 2.17%
USD685-12-D38 Pt = 2.30%
USD685-14-D38 P t = 2.40%
USD685-4-D32 Pt = 0.76%
L a t e r a l B a r s
USD1275-4-D16@100 Pw = 1.06%
USD1275-4-D16@100 Pw = 0.94%
USD1275-4-D16Q100 Pw = 0.84%
USD1275-4-D13@100 P „ = 0.85%
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no drop panels. Table 9.2 summarizes the reinforcement arrangement in the structural members.
The structure is reasonably regular and uniform. The design criteria, sum- marized in Table 9.3, essentially conform with those for general New RC struc- tures, as presented in Chapter 6. These design criteria were commonly applied to this building and the following resort condominium. Additional design criteria were adopted as needed for each building specifically.
As related to the structural design of flat slabs, several points should be mentioned. The first is the protection against punching shear failure. The effective critical section was assumed at half depth away from the column surface as shown in Fig. 9.3, and an equation in the AIJ Reinforced Concrete
Table 9.3. Design criteria for highrise flat slab buildings.
External Force (design condition) Permanent Load
Level 1 Earthquake
Level 2 Earthquake
Design limit Deformation
Performance of Frame (walls, columns, girders) (1) w/in allowable stress
(4) w/in elastic limit
(7.1) walls: before flex, yield (7.2) columns: before
flex, yield (7.3) girders: flex,
yield permitted (11) walls: before
ultimate capacity (12) columns, girders:
w/in limit Deformation (13) no hinges formed at
unexpected positions
Performance of Flat Slabs (2) w/in allowable stress (3) vibration w/in
rank 1 of evaluation standard*
(5) reusable after earthquake with minor repair, and vibration w/in rank 2 of evaluation standard*
(8) reusable after earthquake with repair
(14) w/in limit deformation (aviod shear failure at connections)
Deformation (capacity)
(6) story drift w/in 0.5%
(9) total drift at centroid w/in 0.8%
(15) horizontal capacity w/in 0.25 RtZ
"For explanation of ranks 1 and 2 of evaluation standard, refer to the text.
d/2 Cx d/2 d.effective depth of slab
Fig. 9.3. Effective critical section of flat slab around a column.
Standard (Ref. 9.1) was used for the safety evaluation against punching shear, where effect of both vertical shears and moments around the critical section was taken into account.
The next item is the evaluation of flexural crack width under permanent loading. Crack width was calculated using the equation in the AIJ Structural Design Guideline for Prestressed and Reinforced Concrete (Ref. 9.2) which takes into consideration average steel strain and concrete drying shrinkage.
Calculated crack widths were not to exceed the permissible value of 0.2 mm.
The third item is the evaluation of deflection under permanent loading. An equation in the AIJ Reinforced Concrete Standard (Ref. 9.1) was used for this purpose, which accounted for cracking, creep, and drying shrinkage of concrete.
Calculated values were not to exceed 20 mm nor 1/350 of span length.
The fourth item for the flat slab design is the habitability, or serviceabil- ity in ambient vibration. According to the AIJ Guidelines for the Evaluation of Habitability (Ref. 9.3) the response of floor vibration due to human walk was analyzed by elastic finite element time-history analysis, assuming damp- ing coefficient of 0.02 for floors. For the "new" structure prior to level 1 earthquake the result remained within the desired range of rank 1 response, and for the post-level 1 earthquake state it also remained within the range of rank 1 although the design criteria of Table 9.3 allowed rank 2 response in this case. Ranks 1 and 2 here refer to recommended (or more desirable) level and standard level of habitability, respectively. The guidelines (Ref. 9.3) indicate following examples of human senses for a stationary vibration of rank 1
of a floor: (1) in a living room or bedroom, nobody senses the floor vibration,
(2) in a conference room, few people sense the floor vibration, (3) in an office, some people sense the floor vibration. For rank 2, the guidelines give follow- ing examples: (1) in a living room or bedroom, few people sense the floor vibration, (2) in a conference room, some people sense the floor vibration, (3) in an office, most people sense the floor vibration.
The final item was the determination of effective width of flat slabs in the idealized frame in each direction. A three-dimensional finite element analysis was carried out and the result was compared with an equivalent planar frame analysis considering flexural and shear deformation and rigid zones around joints. It was found that effective width to span ratio varied with span length and location of flat slab within the building, that is, whether it is located within exterior frame, interior frame, or frames near the core walls, but did not vary much with the column size. The ratio was approximately from 0.45 to 0.60, most typically 0.50.
Earthquake response analysis was conducted for levels 1 and 2 earthquake ground motions, using condensed model and more elaborate frame model shown in Fig. 9.4, both considering nonlinear restoring force characteristics
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of members which were determined as follows. For the flat slab with the afore- mentioned effective width, Takeda model with the unloading stiffness index 7 of 0.9 was used. The L-shaped walls in the core were first analyzed by fiber models under static incremental loading, and Takeda model with 7 = 0.5 was determined by the best fit. For the columns and connecting girders, Takeda model with 7 = 0.4 was used. Table 9.4 summarizes natural periods in the elastic range for frame model and condensed model.
For five kinds of input earthquake motions of levels 1 and 2 intensity, response of condensed model showed the same trend of larger response val- ues for two kinds of New RC motions (synthetic ground motions developed in New RC project). Frame model was analyzed for these two waveforms only, and all the response values stayed within the prescribed design criteria. The maximum response structural drift at the centroid of lateral forces under level
Table 9.4.
Mode Frame Model (second) Condensed Model (second)
Natural periods.
1st 3.89 3.98
2nd 1.10 1.14
3rd 0.54 0.55
4th 0.33 0.34
5th 0.23 0.23
0.1 0.08
0.06
0.04
0.02
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response drift limit 0.8%
based on dependable strength
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design drift limit
1 1.3%
V .
50 100 150 centroidal deflection 8 (cm)
200 250
Fig. 9.5. Static push-over analysis with response drift limit and design drift limit.
2 earthquake motion was 0.73 percent for New RC 01 waveform. The response drift limit was determined to be 0.83 percent to cover this maximum response.
Static push-over analysis was carried out as shown in Fig. 9.5, and the design drift limit of 1.30 percent was determined from the double-energy criteria as explained in Chapter 6. At this design drift limit, the base shear coefficient based on the dependable material strength was 0.0727 which exceeded the de- sign criterion of 0.25i?t' which was 0.0650. Maximum ductility in the coupling beams and flat slabs are 3.6 and 2.0, respectively.
The building was also analyzed for earthquake input in the 45 degrees di- rection. Under static push-over analysis, the base shear at the design drift limit under diagonal loading exceeded that under parallel loading by 27 per- cent. Dynamic response values in the diagonal direction are generally similar to, or in some cases smaller than, those in the parallel direction.
Thus it was shown that a 50 story flat slab building with core walls was a feasible structure using New RC material. However several problems were pointed out during the course of this feasibility study. The first was that the restoring force characteristics of flat slabs were determined by empirical equations from experimental data for ordinary strength materials which might be different from high strength materials. The second was that there was a need for more experimental data for the behavior of L-shaped walls. The third point was that the condensed model developed for this building did not quite successfully simulate the response of frame model which could be regarded too complicated for practical purposes, hence development of practically accurate and simple model was desired.
9.1.1.2. Highrise Flat Slab Condominium with Curved Walls
The second building for the feasibility study, shown in Figs. 9.6 and 9.7, is a highrise flat slab resort condominium of forty stories. One floor area is 1440 m2, and total floor area is 57600 m2. Story height is 3 m with the exception of the first story of 6 m, and the total building height is 123 m above ground. It has no basement.
The structure consists basically of flat slabs 250 mm thick and structural walls 400 mm thick except for the first story where walls are 600 mm thick.
In addition the exterior wall of service core is made into a curved shape with flanges, called "hyper-wall", and is connected to the main structure at three levels with so-called "superbeams", having the depth of 3 m, that is, one story
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high. This structural planning provided a variety of architectural possibilities in addition to flat slab, such as wide frontage of condominium rooms to enjoy open view, sky lounge or sky discotique above the superbeams, mesonette (two-storied) units at stories of superbeams (which block the hallway) to
increase the variety of dwelling units, exterior surface of hyper-wall used as sign board or large screen for outdoor events. At the same time the structural planning gave rise to several structural design problems. Walls arranged into various directions and curved hyper-wall were intended to prevent torsional vibration, but they required three-dimensional analysis against seismic ground motion in any directions. A megastructure composed by superbeams con- necting the main building and hyper-wall required development of a suitably simplified model for earthquake response analysis, and a more complicated model for static structural analysis. Walls in the first story had to have large openings to provide open spaces for entrance reception, lounge and restaurant, and the structural effect of large openings had to be investigated in full detail.
Table 9.5 summarizes the material to be used for this building. Like the previous example of a flat slab structure, this building also utilizes material in Zone III of Fig. 2.1, concrete up to 100 MPa compressive strength and main bars in walls, columns and superbeams of 980 MPa yield point.
The structural design criteria were essentially same as those in Table 9.3 for general New RC buildings, with several additions specifically for this building.
The design for gravity loading follows the same principle of allowable stress
Table 9.5. Structural materials.
Concrete Member
Walls, Columns, Superbeams
Flat Slabs
Story 28-40 22-27 15-21 8-14
1-7 1-roof
Strength (MPa) 60 70 80 90 100
60 Re-bars
Member
Walls, Columns, Superbeams Shear Reinforcement
Flat Slabs
Beams
Size D28, D32, D35, D38
D16
D19
D22
Grade USD980 USD1275
SD490
SD345
design as for general RC buildings. In other words the high strength of materi- als used for this building has no particular advantage. The check for allowable shear stress was substituted by the check for shear cracking. In addition to the conventional design for gravity loading, the floor slab vibration was required to remain within the severest criterion of rank 1 of the Evaluation Guidelines for Habitability by AIJ (Ref. 9.3).
The design for level 1 earthquake motion is basically same as Chapter 6.
Walls and columns must remain essentially within the elastic limit. Elastic limit is defined by maximum concrete strain on the compression fiber or steel yield strain in the outermost re-bar in tension. Superbeams which couple two shear walls and other coupling beams subjected to stress concentration may yield, up to the ductility factor of 2.0. As for flat slabs, residual crack width after the level 1 earthquake is to be controlled in order that the structure is serviceable after a light amount of repair works. For this purpose the response deformation at the slab-wall connection was limited so that the residual crack width remains within certain permissible value. Experimental works carried out for this feasibility study were referred to in establishing relationship be- tween the deformation angle and residual crack width. The yield deformation of flat slab-wall connection is very large, to be about 2 to 3 percent in terms of drift angle, so the crack width control is more critical. The effective width of floor slab is to be determined by static elastic analysis. In addition the floor slab vibration after the level 1 earthquake was required to remain within rank 2 of the Evaluation Guidelines (Ref. 9.3) after the light repair work such as epoxy injection.
The design for level 2 earthquake motion is more conservative than Chapter 6. Considering that walls carry essentially all the lateral load due to earthquake, no yield hinges are allowed at the wall base. Also no yield hinges are allowed in the columns considering high level of axial load. Wall coupling beams, on the other hand, may yield under level 2 earthquake motion, but its deformation should remain within the ultimate deformation limit. The overall deformation of building is limited as shown in Table 9.3, which is same as Chapter 6. This will automatically protect flat slab-wall connection from yielding. The criteria associated with the ultimate limit under static push-over analysis are same as in Chapter 6.
In carrying out structural analysis as well as response analysis, the direction of loading must be carefully considered because of uneven arrangement of walls.
Four directions shown in Fig. 9.8, including two principal axes of X and Y, were chosen as representative directions. It turned out that principal axes were the most fundamental in representing the stress and deformation in any direction.
Fig. 9.8. Direction of loading.
Fig. 9.9. Space model of linear elements.
Figure 9.9 illustrates the three-dimensional frame model composed of linear vertical elements for each wall and linear horizontal elements for fiat slabs.
Effective width of flat slab was determined from the finite element (FEM) analysis. Table 9.6 shows natural periods of vibration for first four modes in the direction of two principal axes. Numbers in parentheses indicate natural periods determined from the FEM analysis. The first mode periods are in reasonable agreement.
Table 9.6. Natural periods of linear model [FEM Model in ( )]•
Longitudinal (X)
Transversal (Y)
Ti = 2.077s e c o n d ( 2 . 1 7 3s e c o n d)
T2 = 0.592 (1.454)
T3 = 0.296 (0.834)
T4 = 0.177 (0.575)
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T2 = 0.483 (0.431)
T3 = 0.220 (0.207)
T4 = 0.126 (0.200)
Earthquake response analysis was carried out using mass-and-spring models consisting of equivalent shear springs and equivalent torsional springs. Two floors above and below superbeams, connecting the main building with the hyper-wall at three levels, were concentrated into a single mass, hence the 40- story building was idealized into 37 masses. The restoring force characteristics of each spring was assumed to be bilinear, connecting the flat slab cracking point and the deformation associated with base shear coefficient of Co = 0.25.
Damping of 3 percent for first mode and 4 percent for second mode was as- sumed to define a Rayleigh-type damping. Two synthetic waves, introduced in Chapter 6, were chosen and assumed in four direction in Fig. 9.8. Both level 1 and 2 responses were found to satisfy all the design criteria depicted in Table 9.3.
Flat slabs with 25 cm thickness were found to be satisfactory for both serviceability and seismic safety. D19 bars at 200 mm on centers are to be provided in two directions, top and bottom. The natural frequency in elastic range was about 10 Hz, and that after level 1 earthquake was about 6 Hz, both of which happened to be within rank 1 of the Evaluation Guidelines.
Among walls, the most intensively stressed portions were found to be in the first story, notwithstanding the wall thickness increased to 600 mm from 400 mm in upper stories. Figure 9.10 illustrates bar arrangement in some part of the first story walls.
Thus, it was shown that a 40-story flat slab building with shear walls was a feasible New RC building in seismic zones. By conducting structural as well as response analyses in four directions, major structural members could be
key plan (1st story)
wall in line C, 1st story 15-D38
hoop:D16D-@100
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wall with opening, 1st story vertical : 4 8 - D 3 8 ( Pg = 2.1% ) hoop:D16D-@100 (Pw = 0.66% )
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Fig. 9.10. Sections of 1st story walls.
shown to be proportioned in the practically reasonable dimensions. Under two levels of earthquake motions, major structural members with the exception of superbeams remained within the elastic limit, and flat slabs maintained their serviceability. It should be mentioned that the experimental works carried out in conjunction with this study gave helpful evidence of satisfactory performance of flat slab-vertical member connections within the deformation range assumed in the design. The use of high strength materials enhances the strength of the structure, and increases the possibility of remaining within the elastic limit even under the severest earthquake motion for design.