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Wind-induced responses of super-tall buildings with various atypical building shapes
J. Wind Eng. Ind. Aerodyn. 133 (2014) 191–199
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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Wind-induced responses of super-tall buildings with various atypical building shapes Y.C. Kim a,n, Y. Tamura b,c, H. Tanaka d, K. Ohtake d, E.K. Bandi e, A. Yoshida c a
School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Republic of Korea Beijing Jiaotong University, China c Wind Engineering JURC, Tokyo Polytechnic University, Kanagawa, Japan d Research & Development Institute, Takenaka Corporation, Chiba, Japan e Department of Mechanical Engineering, Madanapalle Institute of Technology and Science (MITS), Madanapalle, Chittoor (Dt), Andhra Pradesh, India b
art ic l e i nf o
Keywords: Time history analysis Peak normal stress Damping ratio Loading condition
a b s t r a c t A wind tunnel tests were conducted on 13 super-tall building models with atypical building shapes under an urban area flow. The primary purpose of the present study was to directly compare the wind load effects on atypical super-tall buildings. Time history analyses were conducted using a frame model by inputting local wind forces at the center of each floor. The results show that the peak normal stresses on a square model are the largest among all the models tested, the setback model shows the smallest peak normal stresses of the single modification models tested, and CC þTPþ 360Hel shows the smallest peak normal stresses of the multiple modification models tested. The contributions of bending moments are about 20% of the total, and most of the peak normal stresses resulted from axial force. The increase in bending moment in the across-wind direction becomes significant as the damping ratio decreases, and the sensitivity of the peak normal stresses for the helical and multiple modification models to damping ratio is smaller than those of the other models. From the analyses for the various loading conditions, it was found that the contribution of bending moment in the along-wind direction is the largest and that of torsional moment is almost negligible. & 2014 Elsevier Ltd. All rights reserved.
1. Introduction According to Tamura et al. (2011), more than 50% of the 100 highest super-tall buildings have been completed since 2000, and many super-tall buildings higher than 600 m are under construction, including Ping An Finance Center (660 m, China), which will be completed in 2016, and Kingdom Tower (at least 1000 m, Saudi Arabia), which will be completed in 2019. As is well-known, as buildings become higher, wind loads become more important than earthquake loads in safety design as well as in serviceability design including occupants’ vibration perception. Thus, many attempts have been made to comprehensively suppress wind-induced responses by changing building shapes: so called aerodynamic modification. As wind forces largely depend on building shape regardless of structural system, studies on various aerodynamic modifications have been one of the most challenging issues in wind-resistant design. Aerodynamic modifications include taper,
n
Corresponding author. E-mail addresses: [email protected] (Y.C. Kim), [email protected] (Y. Tamura), [email protected] (H. Tanaka), [email protected] (K. Ohtake), [email protected] (E.K. Bandi), [email protected] (A. Yoshida). http://dx.doi.org/10.1016/j.jweia.2014.06.004 0167-6105/& 2014 Elsevier Ltd. All rights reserved.
set-back, helical twist, openings and combinations of them, and a comprehensive study on these aerodynamic characteristics was recently made by Tanaka et al. (2012). These atypical and unconventional building shapes are a resurrection of an old characteristic, but they have the advantage of suppressing across-wind responses, which is a major factor in safety and serviceability design of supertall buildings. The effectiveness of aerodynamic modification in reducing wind forces has been widely reported since the late 1980s (Kwok et al., 1988; Hayashida and Iwasa, 1990; Cooper et al., 1997; Kawai, 1998; Kim et al., 2011; Bandi et al., 2013; Kim and Kanda, 2013). Furthermore, Kim and Kanda (2010) reported that aerodynamic modifications such as taper and setback are also effective in suppressing mean along-wind forces, and Tanaka et al. (2013) showed high correlations between along- and across-wind forces. Wind pressure measurements were conducted on super-tall building models, which showed superior aerodynamic characteristics. Models tested included corner modifications, taper, setback, helical, cross void, and combinations of them (Tanaka et al., 2012). Following the previous report (Tanaka et al., 2012), time history analyses were conducted in the present study using wind pressures. First, time histories of local wind forces were obtained from the wind pressures, and the time histories of local wind forces
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Table 1 Test models for pressure measurements.
Square (SQ)
Chamfered (CF)
Corner cut (CC)
90 helical (90Hel)
180 helical (180Hel)
Cross void (CV)
CC+180Hel
TP+180Hel
CC+TP+180Hel
were input at the center of each floor of the frame model to investigate the wind load effects. The purpose of the present study was to directly compare the wind load effects on super-tall
Taper (TP)
CC+TP+360Hel
Setback (SB)
SB+45RT
buildings with various atypical building shapes, focusing on peak normal stresses in columns. These comparisons can advise the structural designers regarding the effectiveness of each aero-
Y.C. Kim et al. / J. Wind Eng. Ind. Aerodyn. 133 (2014) 191–199
dynamic modification and provide them with comprehensive information that can be used in the preliminary design stage. Also, it would be helpful to evaluate the most effective structural shape in wind-resistant design of atypical super-tall buildings.
2. Outlines of experiments 2.1. Test models The test models used for the pressure measurements are listed in Table 1. The width B of the square (SQ) model is 0.05 m, which is used as the representative width in this work, and the height H is 0.4 m, giving an aspect ratio H/B of 8. The geometric scale of the wind tunnel tests is 1/1000, so the height of the super-tall buildings is 400 m in full scale. The total volumes of the super-tall buildings are set to be the same: about 106 m3 in full scale. Eight different single modification models were used. For corner modifications, chamfered (CF) and corner-cut (CC) were focused on, and the modification length was set at 0.1B, where B is the building width. This modification length was determined considering the previous result (Kawai, 1998) which showed that the optimistic modification length is 0.1B. For the tapered model (TP), although models with larger tapering ratios show better aerodynamic characteristics (Kim and Kanda, 2010), a taper ratio of about 10% was used considering practicality. Taper ratio is defined as (base width roof width)/height 100, and the taper ratio of the John Hancock Center on its long side is about 9.1%. The taper ratio of 10% roughly corresponds to an area ratio of the top floor to the bottom floor of 1/6. A 4-layer setback (SB) is used, and the area ratio of the roof floor to the base floor is also set at 1/6. Two helical models were used, whose helical angles between roof floor and base floor were 901 (90Hel) and 1801 (180Hel).
Turbulence intensity Iu 0
0.1
0.2
193
A cross-void model whose void was provided at the top-center was used. The void size was set at 5H/24. Five multiple modification models were also used, which combined the above aerodynamic modifications, i.e. corner-cut (CC), taper (TP), setback (SB), and two helical angles (90Hel and 180Hel). Multiple modification models included corner-cutþ180 helical (CCþ180Hel), taperþ 180 helical (TPþ180Hel), corner-cutþtaperþ 180 helical (CCþ TPþ180Hel), and corner-cutþtaperþ180 helical (CCþTPþ 360Hel). Besides, the effects of rotation of each portion of setback shape on load effect characteristics were also examined (SBþ 45RT). 2.2. Wind pressure measurement Wind tunnel experiments were performed in a closed-circuit boundary-layer wind tunnel whose working section was 1.8 m high by 2.0 m wide. Fig. 1 shows the condition of the approaching turbulent boundary layer flow with a power-law index of 0.27, which represents an urban area flow. The wind speed and turbulence intensity at the top of the model were about UH E11.8 m/s and Iu,H E0.09%, respectively. The turbulence scale near the model tip was about 0.360 m, and that of Architectural Institution of Japan (2004) is 365 m. Therefore, when considering a length scale of 1/1000, the flow conditions of the present work are thought to be appropriately simulated. The fluctuating wind pressures of each pressure tap were measured and recorded simultaneously using a vinyl tube 80 cm long through a multi-channel pressure transducer. The sampling frequency was 1 kHz with a low-pass filter of 500 Hz. The total number of data was 32,768. The fluctuating wind pressures were revised considering the transfer function of the vinyl tube. There were about 20 measurement points on one level on four surfaces, and the measurement points were instrumented at 10 levels, giving about 200 measurement points. The local wind force coefficients were obtained for the structural axes by considering the dynamic velocity at model height qH and the building width of the square model B regardless of building shape.
0.3
1
2.3. Frame model for time history analyses
U/UH
0.8
The frame model for the time history analyses and the first three mode shapes are shown in Fig. 2. Building dimensions (B D H) are 50 50 400 in common, and all beams were assumed to be rigid (Fig. 2(a)). Square tube columns were used and column sizes were adjusted such that the first translational natural period becomes about H/50 (Tamura , 2012) assuming steel buildings. Local wind force coefficients were converted into fullscale local wind forces, and input at the center of each floor. A design wind speed of 70 m/s was used, corresponding to a 500year return period wind speed in Tokyo. In the frame model, no eccentricities were considered, and dead and live loads were not applied, so that only the effects of various building shapes on load effect were evaluated. For mode shapes, as no eccentricities were considered, there was no coupled motion, as shown in Fig. 2(b). The frame model was designed approximately as bending type.
h0.27
0.6 Height (m)
Iu
0.4 Model height
0.2 3. Results and discussion 3.1. Variations of peak normal stresses with wind direction
0 0
0.5 1 Mean wind speed U/UH
1.5
Fig. 1. Profiles of mean wind speed U/UH and turbulence intensity Iu.
Fig. 3 shows the variations of peak tensile stresses with wind direction for two single modification models (square (SQ) and setback (SB)) and two multiple modification models (CC þTP þ 360Hel and SB þ 45RT). For SQ, the largest peak tensile stress was
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D
B
H
B×D×H=50m×50m×400m
1st mode
2nd mode
3rd mode
Fig. 2. Schematic view of frame model and first three mode shapes. (a) Frame model, (b) first three mode shapes.
observed for wind directions of 01 and 901. The peak tensile stresses of Col. 1 were generally large and those of Col. 4 were generally small in the ranges between 01 and 901. Col. 3, which was on the windward side, showed a large peak tensile stress, but the peak tensile stresses decreased with increasing wind directions because Col. 3 was located on the leeward side for large wind directions. The opposite trend was found for Col. 2. One thing to be noted is that when the wind direction ranged from 01 to about 201, the peak tensile stresses in Col. 3 were larger than those in Col. 1.
This seems to be because, for these wind directions, as the separated shear layer approached the side surface of Col. 1 and Col. 2, relatively large peak tensile stresses occurred at Col. 3. Similarly, relatively large peak tensile stresses were found in Col. 2 for wind directions from 701 to 851. Similar discussions can be made for SB, although the peak normal stresses were smaller than those for SQ for the considered wind directions. For the multiple modification models, the peak tensile stresses in Col. 1 were the largest for the considered wind directions, and the variations with
Y.C. Kim et al. / J. Wind Eng. Ind. Aerodyn. 133 (2014) 191–199
wind direction for Col. 1 and Col. 4 were small compared with those for SQ and SB. One more difference was that there were no stress reversals between Col. 1 and Col. 3, and between Col. 1 and
Fig. 3. Peak tensile stresses for various wind directions for damping ratio of 1% (unit: kN/cm2). (a) SQ, (b) SB, (c) CC þ TPþ 360Hel, (d) SBþ 45RT.
CF
CC
TP
SB
90Hel
195
Col. 2 with wind direction. The variations of peak tensile stresses of the two helical models (90Hel and 180Hel) showed a quite similar tendency to the multiple modifications models, showing less variation of peak tensile stresses in Col. 1 and Col. 4 and not showing stress reversal for specific wind directions. Note that in this work, the dimensions of peak normal stresses themselves are not very meaningful. Thus, the largest peak tensile stresses were selected for the considered wind directions, and the ratios of stress for each model to that of SQ were calculated and shown in Fig. 4. The largest peak tensile stress in SQ was about 11 kN/cm2. The largest peak tensile stresses for the multiple modification models were generally smaller than those for the
Fig. 5. Peak normal stresses for various bending moments and axial forces for SQ wind damping ratio of 1%. (a) Peak normal stresses by bending moment MY, (b) peak normal stresses by bending moment MX, (c) peak normal stresses by axial force NZ.
180Hel
CV
CC+ 180Hel
TP+ CC+ 180Hel TP+ 180Hel
CC+ SB+ TP+ 45RT 360Hel
Fig. 4. Ratio of largest peak tensile stresses (The largest peak tensile stresses of SQ is about 11 kN/cm2).
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single modification models, and the largest peak tensile stresses for the single modification models were less than 90% of that of SQ, and those for the multiple modification models were about 70–80%. The smallest value was found for the CCþ TP þ360Hel model. The corner modification models (CF and CC) showed similar values, and it was found that setback was quite effective in reducing peak normal stresses in columns, showing superior characteristics to taper and helical shapes. The effects of corner cut and taper seemed to be negligible when they were added to the 180Hel model, showing similar values to the 180Hel model. Increasing helical angle resulted in smaller peak tensile stresses for single and multiple modification models but, as pointed out by Tanaka et al. (2012), the helical angle effect is small when the helical angle is larger than 1801. The ratios of peak tensile stresses of SB and SB þ45RT were similar, showing that the effect of rotation of each setback portion on peak normal stresses in the columns was very small. To examine the contributions of two bending moments (MY and MX) and axial force (NZ) to peak normal stresses, peak normal stresses were evaluated separately and the variations of peak normal stresses with MX, MY and NZ are shown in Fig. 5 for the square model (SQ) for a damping ratio of 1%. Peak normal stresses by bending moments were relatively small and showed less variation with wind direction and column position. But significant variations with wind direction and column position were found for axial force, and it was found that the peak normal stresses were greatly affected by axial force. The contributions of bending moments were approximately 20% when the wind directions were 01 and 901, and they increased when the wind directions were between 01 and 901 because the peak normal stresses decreased for these wind directions, as shown in Fig. 3(a). Similar trends were found for the other models. 3.2. Effects of damping ratios on peak normal stresses In the wind-resistant design of super-tall buildings, a damping ratio of 1% is recommended for safety design, and 70–80% of that damping ratio is recommended for serviceability design including habitability check. The results shown before were for the damping
Fig. 6. Effects of damping ratios on peak tensile stresses for square and 180 helical models (Q.S. means quasi-static). (a) SQ (wind direction of 01), (b) 180Hel (wind direction of 301).
Fig. 7. Variations of largest peak compressive stresses with damping ratio (Q.S. means quasi-static).
ratio of 1%. But examination of the effects of damping ratio on wind load effect is an issue of interest, and variations of peak compressive stresses with damping ratio are shown in Fig. 6 for the SQ and 180Hel models for the wind directions where the largest peak normal stresses occur. Q.S. in Fig. 6 indicates quasistatic condition. As expected, peak compressive stresses decrease with increasing damping ratios, approaching the quasi-static value. Decreasing ratios of peak compressive stress also decrease with increasing damping ratios. But there are clear discrepancies in trend for the SQ and 180Hel models. For the SQ model, the differences among peak compressive stresses in columns are large for extremely small damping ratios, even for columns located on the windward side (Col. 1 and Col. 3) or leeward side (Col. 2 and Col. 4). As the damping ratios increase, these differences for Col. 1 and Col. 3 or Col. 2 and Col. 4 decrease, and when the damping ratio is larger than approximately 3%, the difference is negligible. For the 180Hel model, the differences among peak compressive stresses in columns remains for large damping ratios, and decreasing ratios of peak compressive stresses with damping ratio are not significant compared with those for SQ. For the column on the windward side, i.e. Col. 1, the peak compressive stresses are negative when the damping ratio is larger than about 3%, which means that tensile forces are applied to Col. 1 at all time instants for these damping ratios. Fig. 7 shows the variations of the largest peak compressive stresses with damping ratios of the square (SQ), corner cut (CC), 180 helical (180Hel), and CCþ 180Hel models. The largest peak compressive stresses were defined as the largest value for considered wind directions. The largest peak compressive stresses for SQ is the largest, and those for 180Hel are the smallest. As mentioned before, the effect of corner cut is negligible, and when the damping ratio is less than 1%, corner cut has a negative effect on peak normal stresses, giving larger peak compressive stresses for CC þ180Hel than for 180Hel. The effects of damping ratio on phase-plane trajectories are shown in Fig. 8 for square (SQ) and cross void (CV) models for wind directions of 01 and 851, respectively. When the damping ratios are relatively small, the shapes of the envelopes are elliptic or parallelogram, but as the damping ratio increases, decreases of bending moments in the across-wind direction (MX for SQ and MY for CV) are significant, and the shapes of the envelopes change to semi-circular or semi-elliptic. The decreases of bending moments in the along-wind direction are not so noticeable, and the mean value of along-wind bending moments is almost the same. The envelopes of phase-plane trajectories in quasi-static conditions are similar to those of the phase-plane trajectory of alongand across-wind forces (Tamura et al. , 2012). Fig. 8 shows time histories of normal stresses by bending moments (MX and MY) for the square model (SQ) for wind direction 0° for different damping ratios. Fig. 8(a) shows the time histories with MX, which corresponds to across-wind direction. As damping ratios increase, a decrease in the resonant component is clearly observed. Some
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differences are admitted for the time histories with bending moments MY (Fig. 8(b)), which correspond to the along-wind direction, but the differences are not significant compared with those in the across-wind direction. The effects of damping ratio on phase-plane trajectories are shown in Fig. 9 for square (SQ) and cross void (CV) models for wind directions of 0° and 85°, respectively. When the damping ratios are relatively small, the shapes of the envelopes are elliptic
197
or parallelogram, but as the damping ratio increases, decreases of bending moments in the across-wind direction (MX for SQ and MY for CV) are significant, and the shapes of the envelopes change to semi-circular or semi-elliptic. The decreases of bending moments in the along-wind direction are not so noticeable, and the mean value of along-wind bending moments is almost the same. The envelopes of phase-plane trajectories in quasi-static conditions are similar to those of the phase-plane trajectory of along- and acrosswind forces (Tamura et al., 2012).
3.3. Effects of various loading conditions
Fig. 8. Effect of damping ratio on time history of bending moments for square (SQ) for wind direction 01. (a) Normal stress by MX, (b) normal stress by MY.
For the wind directions where the largest peak normal stresses occurred, the effects of various loading conditions were examined. Loading conditions included (i) ALL loads (FX þFY þMZ), (ii) FX only, (iii) FY only, (iv) MZ only, (v) FX and FY (FX þFY), (vi) FX and MZ (FX þ MZ), and (vii) FY and MZ (FY þMZ), i.e. 7 cases in total. The results are summarized in Tables 2–4 for the square model (SQ, wind direction 01), setback model (SB, wind direction 851), and SB þ45RT (wind direction 401). For SQ, the peak compressive stress in Col. 4 when FX and FY (FX þFY) are applied is almost the same as that for the ALL loading condition. Under the (FX þMZ) loading condition, the stresses are slightly larger than those under the FX only loading condition, and under the (FY þMZ) loading condition, they are slightly larger than those under the FY only loading condition. The results for the MZ only loading condition are very small, and can thus be ignored only when there are no eccentricities. For SB, the peak compressive stress under the FY only loading condition is larger than that under the FX only loading condition for wind direction 851. For this wind direction, FY roughly corresponds to along-wind force. Thus, the trends are very similar to those for SQ, i.e. for Col. 3, the (FX þFY) loading condition gives almost the same results as the ALL loading
Fig. 9. Effect of damping ratio on bending moments for square (SQ) and cross void model (CV). (a) SQ when damping ratio is 0.3% (left), 1% (center), and quasi-static (right) when wind direction of 01, (b) CV when damping ratio is 0.3% (left), 1% (center), and quasi-static (right)when wind direction of 851.
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Table 2 Effects of various loading conditions on peak compressive stress of square model (SQ) for ζ¼ 1% (wind direction of θ ¼01, kN/cm2). Peak compressive stress
ALL loadings
Only FX
Only FY
Only MZ
FX þ FY
FX þMZ
FY þ MZ
Col. 1
5.6
0.6
6.4
0.4
5.6
0.7
6.5
Col. 2
10.4
7.3
6.4
0.4
10.4
7.4
6.5
Col. 3
5.1
0.6
6.3
0.4
5.1
0.6
6.3
Col. 4
11.0
7.3
6.3
0.4
11.0
7.4
6.4
Table 3 Effects of various loading conditions on peak compressive stress of setback model (SB) for ζ¼ 1% (wind direction of θ ¼851, kN/cm2). ALL loadings
Only FX
Only FY
Only MZ
FX þ FY
FX þMZ
FY þ MZ
Col. 1
3.0
3.6
0.4
0.3
2.9
3.8
0.5
Col. 2
2.7
3.1
0.4
0.3
2.7
3.2
0.4
Col. 3
7.7
3.6
5.5
0.3
7.7
3.7
5.6
Col. 4
6.6
3.1
5.5
0.3
6.6
3.2
5.6
Peak compressive stress
Table 4 Effects of various loading conditions on peak compressive stress of SB þ 45RT model for ζ¼ 1% (wind direction of θ ¼401, kN/cm2). ALL loadings
Only FX
Only FY
Only MZ
FX þ FY
FX þMZ
FY þMZ
Col. 1
0.6
0.4
0.7
0.1
0.6
0.4
0.7
Col. 2
3.8
4.3
0.7
0.1
3.8
4.4
0.7
Col. 3
3.3
0.4
4.0
0.1
3.3
0.4
4.0
Col. 4
7.6
4.3
4.0
0.1
7.6
4.4
4.0
Peak compressive stress
condition, and (FY þMZ) gives slightly larger results than the FY only loading condition. Also, the results for the MZ only loading condition are negligible. For Col. 4 of SB þ 45RT, when the wind direction is 401, the contributions of the FX only and the FY only loading conditions are similar.
4. Concluding remarks Using wind pressures applied to 13 super-tall building models with atypical building shapes, time history analyses were conducted. Test models included 8 single modification models, and 5 multiple modification models. The primary purpose was to directly compare the peak normal stresses in columns of super-tall buildings. Comparison and discussion led to the following concluding remarks. The peak normal stresses for the square model were the largest among all the models tested. The CCþTP þ360Hel model showed the smallest peak normal stresses among the models tested, and the setback model showed the smallest peak normal stresses among the single modification models tested. The peak normal stresses of the two helical models and the multiple-modification models showed less variation with wind direction. Also, it was found that the effects of corner-cut and taper seemed to be negligible when they were added to the 180Hel model. The peak normal stresses under bending moments MX and MY were almost the same for the considered wind directions, and the
contributions of bending moments to total peak normal stresses were about 20% of the total. Most of the peak normal stresses were affected by axial force. This was because the frame model used in the present study was designed as bending type. As the damping ratio increases, the peak normal stress decreases and approaches the quasi-static value. The increase in bending moment for the across-wind direction became significant as the damping ratios decreased, and the sensitivity of the peak normal stresses for the helical and multiple modification models to damping ratio as well as wind directions was smaller than for the other models. The effects of damping ratio are also clearly seen in the time histories of normal stresses. From the analyses for the various loading conditions, it was found that the contribution of bending moment in the along-wind direction was larger than those of the other loading conditions and that of torsional moment was almost negligible.
Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A6A3A01064632). And this study was partly funded by the Ministry of Education, Culture, Sports, Science and Technology, Japan, through the Global Center of Excellence Program, 2008–2012.
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References Architectural Institution of Japan,2004. Recommendations for Loads on Buildings 2. Bandi, E.K., Tamura, Y., Yoshida, A., Kim, T.C., Yang, Q., 2013. Experimental investigation on aerodynamic characteristics of various triangular-section high-rise buildings. J. Wind Eng. Ind. Aerodyn. 112, 60–68. Cooper, K.R., Nakayama, M., Sasaki, Y., Fediw, A.A., Resende-Ide, S., Zan, S.J., 1997. Unsteady aerodynamic force measurements on a super-tall building with a tapered cross section. J. Wind Eng. Ind. Aerodyn. 72, 199–212. Hayashida, H., Iwasa, Y., 1990. Aerodynamic shape effects on tall building for vortex induced vibration. J. Wind Eng. Ind. Aerodyn. 33 (1–2), 237–242. Kawai, H., 1998. Effect of corner modifications on aeroelastic instabilities of tall buildings. J. Wind Eng. Ind. Aerodyn. 74–76, 719–729. Kim, Y.C., Kanda, J., 2010. Characteristics of aerodynamic forces and pressures on square plan buildings with height variations. J. Wind Eng. Ind. Aerodyn. 98, 449–465. Kim, Y.C., Kanda, J., Tamura, Y., 2011. Wind-induced coupled motion of tall buildings with varying square plan with height. J. Wind Eng. Ind. Aerodyn. 99 (5), 638–650.
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Kim, Y.C., Kanda, J., 2013. Wind pressures on tapered and set-back tall building. J. Fluids Struct. 39, 306–321. Kwok, K.C.S., Wilhelm, P.A., Wilkie, B.G., 1988. Effect of edge configuration on windinduced response of tall buildings. Eng. Struct. 10, 135–140. Tanaka, H., Tamura, Y., Ohtake, K., Nakai, M., Kim, Y.C., 2012. Experimental investigation of aerodynamic forces and wind pressures acting on tall buildings with various unconventional configurations. J. Wind Eng. Ind. Aerodyn. 107– 108, 179–191. Tanaka, H., Tamura, Y., Ohtake, K., Nakai, M., Kim, Y.C., 2013. Aerodynamic and flow characteristics of tall Buildings with various unconventional configurations. Int. J. High-Rise Buildings 2 (3), 213–288. Tamura, Y., Nakai, M., Ohtake, K., Koshika, N., Yamawaki, K., Hitomi, Y., 2011. Study on Wind Resistant Design Method of Super High-Rise Buildings with Various Unconventional Configurations, The Ministry of Land, Infrastructure. Transport and Tourism, Japan (in Japanese). Tamura, Y., 2012. Amplitude dependency of damping in buildings and critical tip drift ratio. Int. J. High-Rise Buildings 1 (1), 1–13. Tamura, Y., Kim, Y.C., Kumar, B.E., Tanaka, H, Ohtake, K., 2012. Aerodynamic characteristics of tall building models with unconventional configurations. Structures Congress.
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Wind-induced responses of super-tall buildings with various atypical building shapes Y.C. Kim a,n, Y. Tamura b,c, H. Tanaka d, K. Ohtake d, E.K. Bandi e, A. Yoshida c a
School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Republic of Korea Beijing Jiaotong University, China c Wind Engineering JURC, Tokyo Polytechnic University, Kanagawa, Japan d Research & Development Institute, Takenaka Corporation, Chiba, Japan e Department of Mechanical Engineering, Madanapalle Institute of Technology and Science (MITS), Madanapalle, Chittoor (Dt), Andhra Pradesh, India b
art ic l e i nf o
Keywords: Time history analysis Peak normal stress Damping ratio Loading condition
a b s t r a c t A wind tunnel tests were conducted on 13 super-tall building models with atypical building shapes under an urban area flow. The primary purpose of the present study was to directly compare the wind load effects on atypical super-tall buildings. Time history analyses were conducted using a frame model by inputting local wind forces at the center of each floor. The results show that the peak normal stresses on a square model are the largest among all the models tested, the setback model shows the smallest peak normal stresses of the single modification models tested, and CC þTPþ 360Hel shows the smallest peak normal stresses of the multiple modification models tested. The contributions of bending moments are about 20% of the total, and most of the peak normal stresses resulted from axial force. The increase in bending moment in the across-wind direction becomes significant as the damping ratio decreases, and the sensitivity of the peak normal stresses for the helical and multiple modification models to damping ratio is smaller than those of the other models. From the analyses for the various loading conditions, it was found that the contribution of bending moment in the along-wind direction is the largest and that of torsional moment is almost negligible. & 2014 Elsevier Ltd. All rights reserved.
1. Introduction According to Tamura et al. (2011), more than 50% of the 100 highest super-tall buildings have been completed since 2000, and many super-tall buildings higher than 600 m are under construction, including Ping An Finance Center (660 m, China), which will be completed in 2016, and Kingdom Tower (at least 1000 m, Saudi Arabia), which will be completed in 2019. As is well-known, as buildings become higher, wind loads become more important than earthquake loads in safety design as well as in serviceability design including occupants’ vibration perception. Thus, many attempts have been made to comprehensively suppress wind-induced responses by changing building shapes: so called aerodynamic modification. As wind forces largely depend on building shape regardless of structural system, studies on various aerodynamic modifications have been one of the most challenging issues in wind-resistant design. Aerodynamic modifications include taper,
n
Corresponding author. E-mail addresses: [email protected] (Y.C. Kim), [email protected] (Y. Tamura), [email protected] (H. Tanaka), [email protected] (K. Ohtake), [email protected] (E.K. Bandi), [email protected] (A. Yoshida). http://dx.doi.org/10.1016/j.jweia.2014.06.004 0167-6105/& 2014 Elsevier Ltd. All rights reserved.
set-back, helical twist, openings and combinations of them, and a comprehensive study on these aerodynamic characteristics was recently made by Tanaka et al. (2012). These atypical and unconventional building shapes are a resurrection of an old characteristic, but they have the advantage of suppressing across-wind responses, which is a major factor in safety and serviceability design of supertall buildings. The effectiveness of aerodynamic modification in reducing wind forces has been widely reported since the late 1980s (Kwok et al., 1988; Hayashida and Iwasa, 1990; Cooper et al., 1997; Kawai, 1998; Kim et al., 2011; Bandi et al., 2013; Kim and Kanda, 2013). Furthermore, Kim and Kanda (2010) reported that aerodynamic modifications such as taper and setback are also effective in suppressing mean along-wind forces, and Tanaka et al. (2013) showed high correlations between along- and across-wind forces. Wind pressure measurements were conducted on super-tall building models, which showed superior aerodynamic characteristics. Models tested included corner modifications, taper, setback, helical, cross void, and combinations of them (Tanaka et al., 2012). Following the previous report (Tanaka et al., 2012), time history analyses were conducted in the present study using wind pressures. First, time histories of local wind forces were obtained from the wind pressures, and the time histories of local wind forces
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Table 1 Test models for pressure measurements.
Square (SQ)
Chamfered (CF)
Corner cut (CC)
90 helical (90Hel)
180 helical (180Hel)
Cross void (CV)
CC+180Hel
TP+180Hel
CC+TP+180Hel
were input at the center of each floor of the frame model to investigate the wind load effects. The purpose of the present study was to directly compare the wind load effects on super-tall
Taper (TP)
CC+TP+360Hel
Setback (SB)
SB+45RT
buildings with various atypical building shapes, focusing on peak normal stresses in columns. These comparisons can advise the structural designers regarding the effectiveness of each aero-
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dynamic modification and provide them with comprehensive information that can be used in the preliminary design stage. Also, it would be helpful to evaluate the most effective structural shape in wind-resistant design of atypical super-tall buildings.
2. Outlines of experiments 2.1. Test models The test models used for the pressure measurements are listed in Table 1. The width B of the square (SQ) model is 0.05 m, which is used as the representative width in this work, and the height H is 0.4 m, giving an aspect ratio H/B of 8. The geometric scale of the wind tunnel tests is 1/1000, so the height of the super-tall buildings is 400 m in full scale. The total volumes of the super-tall buildings are set to be the same: about 106 m3 in full scale. Eight different single modification models were used. For corner modifications, chamfered (CF) and corner-cut (CC) were focused on, and the modification length was set at 0.1B, where B is the building width. This modification length was determined considering the previous result (Kawai, 1998) which showed that the optimistic modification length is 0.1B. For the tapered model (TP), although models with larger tapering ratios show better aerodynamic characteristics (Kim and Kanda, 2010), a taper ratio of about 10% was used considering practicality. Taper ratio is defined as (base width roof width)/height 100, and the taper ratio of the John Hancock Center on its long side is about 9.1%. The taper ratio of 10% roughly corresponds to an area ratio of the top floor to the bottom floor of 1/6. A 4-layer setback (SB) is used, and the area ratio of the roof floor to the base floor is also set at 1/6. Two helical models were used, whose helical angles between roof floor and base floor were 901 (90Hel) and 1801 (180Hel).
Turbulence intensity Iu 0
0.1
0.2
193
A cross-void model whose void was provided at the top-center was used. The void size was set at 5H/24. Five multiple modification models were also used, which combined the above aerodynamic modifications, i.e. corner-cut (CC), taper (TP), setback (SB), and two helical angles (90Hel and 180Hel). Multiple modification models included corner-cutþ180 helical (CCþ180Hel), taperþ 180 helical (TPþ180Hel), corner-cutþtaperþ 180 helical (CCþ TPþ180Hel), and corner-cutþtaperþ180 helical (CCþTPþ 360Hel). Besides, the effects of rotation of each portion of setback shape on load effect characteristics were also examined (SBþ 45RT). 2.2. Wind pressure measurement Wind tunnel experiments were performed in a closed-circuit boundary-layer wind tunnel whose working section was 1.8 m high by 2.0 m wide. Fig. 1 shows the condition of the approaching turbulent boundary layer flow with a power-law index of 0.27, which represents an urban area flow. The wind speed and turbulence intensity at the top of the model were about UH E11.8 m/s and Iu,H E0.09%, respectively. The turbulence scale near the model tip was about 0.360 m, and that of Architectural Institution of Japan (2004) is 365 m. Therefore, when considering a length scale of 1/1000, the flow conditions of the present work are thought to be appropriately simulated. The fluctuating wind pressures of each pressure tap were measured and recorded simultaneously using a vinyl tube 80 cm long through a multi-channel pressure transducer. The sampling frequency was 1 kHz with a low-pass filter of 500 Hz. The total number of data was 32,768. The fluctuating wind pressures were revised considering the transfer function of the vinyl tube. There were about 20 measurement points on one level on four surfaces, and the measurement points were instrumented at 10 levels, giving about 200 measurement points. The local wind force coefficients were obtained for the structural axes by considering the dynamic velocity at model height qH and the building width of the square model B regardless of building shape.
0.3
1
2.3. Frame model for time history analyses
U/UH
0.8
The frame model for the time history analyses and the first three mode shapes are shown in Fig. 2. Building dimensions (B D H) are 50 50 400 in common, and all beams were assumed to be rigid (Fig. 2(a)). Square tube columns were used and column sizes were adjusted such that the first translational natural period becomes about H/50 (Tamura , 2012) assuming steel buildings. Local wind force coefficients were converted into fullscale local wind forces, and input at the center of each floor. A design wind speed of 70 m/s was used, corresponding to a 500year return period wind speed in Tokyo. In the frame model, no eccentricities were considered, and dead and live loads were not applied, so that only the effects of various building shapes on load effect were evaluated. For mode shapes, as no eccentricities were considered, there was no coupled motion, as shown in Fig. 2(b). The frame model was designed approximately as bending type.
h0.27
0.6 Height (m)
Iu
0.4 Model height
0.2 3. Results and discussion 3.1. Variations of peak normal stresses with wind direction
0 0
0.5 1 Mean wind speed U/UH
1.5
Fig. 1. Profiles of mean wind speed U/UH and turbulence intensity Iu.
Fig. 3 shows the variations of peak tensile stresses with wind direction for two single modification models (square (SQ) and setback (SB)) and two multiple modification models (CC þTP þ 360Hel and SB þ 45RT). For SQ, the largest peak tensile stress was
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D
B
H
B×D×H=50m×50m×400m
1st mode
2nd mode
3rd mode
Fig. 2. Schematic view of frame model and first three mode shapes. (a) Frame model, (b) first three mode shapes.
observed for wind directions of 01 and 901. The peak tensile stresses of Col. 1 were generally large and those of Col. 4 were generally small in the ranges between 01 and 901. Col. 3, which was on the windward side, showed a large peak tensile stress, but the peak tensile stresses decreased with increasing wind directions because Col. 3 was located on the leeward side for large wind directions. The opposite trend was found for Col. 2. One thing to be noted is that when the wind direction ranged from 01 to about 201, the peak tensile stresses in Col. 3 were larger than those in Col. 1.
This seems to be because, for these wind directions, as the separated shear layer approached the side surface of Col. 1 and Col. 2, relatively large peak tensile stresses occurred at Col. 3. Similarly, relatively large peak tensile stresses were found in Col. 2 for wind directions from 701 to 851. Similar discussions can be made for SB, although the peak normal stresses were smaller than those for SQ for the considered wind directions. For the multiple modification models, the peak tensile stresses in Col. 1 were the largest for the considered wind directions, and the variations with
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wind direction for Col. 1 and Col. 4 were small compared with those for SQ and SB. One more difference was that there were no stress reversals between Col. 1 and Col. 3, and between Col. 1 and
Fig. 3. Peak tensile stresses for various wind directions for damping ratio of 1% (unit: kN/cm2). (a) SQ, (b) SB, (c) CC þ TPþ 360Hel, (d) SBþ 45RT.
CF
CC
TP
SB
90Hel
195
Col. 2 with wind direction. The variations of peak tensile stresses of the two helical models (90Hel and 180Hel) showed a quite similar tendency to the multiple modifications models, showing less variation of peak tensile stresses in Col. 1 and Col. 4 and not showing stress reversal for specific wind directions. Note that in this work, the dimensions of peak normal stresses themselves are not very meaningful. Thus, the largest peak tensile stresses were selected for the considered wind directions, and the ratios of stress for each model to that of SQ were calculated and shown in Fig. 4. The largest peak tensile stress in SQ was about 11 kN/cm2. The largest peak tensile stresses for the multiple modification models were generally smaller than those for the
Fig. 5. Peak normal stresses for various bending moments and axial forces for SQ wind damping ratio of 1%. (a) Peak normal stresses by bending moment MY, (b) peak normal stresses by bending moment MX, (c) peak normal stresses by axial force NZ.
180Hel
CV
CC+ 180Hel
TP+ CC+ 180Hel TP+ 180Hel
CC+ SB+ TP+ 45RT 360Hel
Fig. 4. Ratio of largest peak tensile stresses (The largest peak tensile stresses of SQ is about 11 kN/cm2).
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single modification models, and the largest peak tensile stresses for the single modification models were less than 90% of that of SQ, and those for the multiple modification models were about 70–80%. The smallest value was found for the CCþ TP þ360Hel model. The corner modification models (CF and CC) showed similar values, and it was found that setback was quite effective in reducing peak normal stresses in columns, showing superior characteristics to taper and helical shapes. The effects of corner cut and taper seemed to be negligible when they were added to the 180Hel model, showing similar values to the 180Hel model. Increasing helical angle resulted in smaller peak tensile stresses for single and multiple modification models but, as pointed out by Tanaka et al. (2012), the helical angle effect is small when the helical angle is larger than 1801. The ratios of peak tensile stresses of SB and SB þ45RT were similar, showing that the effect of rotation of each setback portion on peak normal stresses in the columns was very small. To examine the contributions of two bending moments (MY and MX) and axial force (NZ) to peak normal stresses, peak normal stresses were evaluated separately and the variations of peak normal stresses with MX, MY and NZ are shown in Fig. 5 for the square model (SQ) for a damping ratio of 1%. Peak normal stresses by bending moments were relatively small and showed less variation with wind direction and column position. But significant variations with wind direction and column position were found for axial force, and it was found that the peak normal stresses were greatly affected by axial force. The contributions of bending moments were approximately 20% when the wind directions were 01 and 901, and they increased when the wind directions were between 01 and 901 because the peak normal stresses decreased for these wind directions, as shown in Fig. 3(a). Similar trends were found for the other models. 3.2. Effects of damping ratios on peak normal stresses In the wind-resistant design of super-tall buildings, a damping ratio of 1% is recommended for safety design, and 70–80% of that damping ratio is recommended for serviceability design including habitability check. The results shown before were for the damping
Fig. 6. Effects of damping ratios on peak tensile stresses for square and 180 helical models (Q.S. means quasi-static). (a) SQ (wind direction of 01), (b) 180Hel (wind direction of 301).
Fig. 7. Variations of largest peak compressive stresses with damping ratio (Q.S. means quasi-static).
ratio of 1%. But examination of the effects of damping ratio on wind load effect is an issue of interest, and variations of peak compressive stresses with damping ratio are shown in Fig. 6 for the SQ and 180Hel models for the wind directions where the largest peak normal stresses occur. Q.S. in Fig. 6 indicates quasistatic condition. As expected, peak compressive stresses decrease with increasing damping ratios, approaching the quasi-static value. Decreasing ratios of peak compressive stress also decrease with increasing damping ratios. But there are clear discrepancies in trend for the SQ and 180Hel models. For the SQ model, the differences among peak compressive stresses in columns are large for extremely small damping ratios, even for columns located on the windward side (Col. 1 and Col. 3) or leeward side (Col. 2 and Col. 4). As the damping ratios increase, these differences for Col. 1 and Col. 3 or Col. 2 and Col. 4 decrease, and when the damping ratio is larger than approximately 3%, the difference is negligible. For the 180Hel model, the differences among peak compressive stresses in columns remains for large damping ratios, and decreasing ratios of peak compressive stresses with damping ratio are not significant compared with those for SQ. For the column on the windward side, i.e. Col. 1, the peak compressive stresses are negative when the damping ratio is larger than about 3%, which means that tensile forces are applied to Col. 1 at all time instants for these damping ratios. Fig. 7 shows the variations of the largest peak compressive stresses with damping ratios of the square (SQ), corner cut (CC), 180 helical (180Hel), and CCþ 180Hel models. The largest peak compressive stresses were defined as the largest value for considered wind directions. The largest peak compressive stresses for SQ is the largest, and those for 180Hel are the smallest. As mentioned before, the effect of corner cut is negligible, and when the damping ratio is less than 1%, corner cut has a negative effect on peak normal stresses, giving larger peak compressive stresses for CC þ180Hel than for 180Hel. The effects of damping ratio on phase-plane trajectories are shown in Fig. 8 for square (SQ) and cross void (CV) models for wind directions of 01 and 851, respectively. When the damping ratios are relatively small, the shapes of the envelopes are elliptic or parallelogram, but as the damping ratio increases, decreases of bending moments in the across-wind direction (MX for SQ and MY for CV) are significant, and the shapes of the envelopes change to semi-circular or semi-elliptic. The decreases of bending moments in the along-wind direction are not so noticeable, and the mean value of along-wind bending moments is almost the same. The envelopes of phase-plane trajectories in quasi-static conditions are similar to those of the phase-plane trajectory of alongand across-wind forces (Tamura et al. , 2012). Fig. 8 shows time histories of normal stresses by bending moments (MX and MY) for the square model (SQ) for wind direction 0° for different damping ratios. Fig. 8(a) shows the time histories with MX, which corresponds to across-wind direction. As damping ratios increase, a decrease in the resonant component is clearly observed. Some
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differences are admitted for the time histories with bending moments MY (Fig. 8(b)), which correspond to the along-wind direction, but the differences are not significant compared with those in the across-wind direction. The effects of damping ratio on phase-plane trajectories are shown in Fig. 9 for square (SQ) and cross void (CV) models for wind directions of 0° and 85°, respectively. When the damping ratios are relatively small, the shapes of the envelopes are elliptic
197
or parallelogram, but as the damping ratio increases, decreases of bending moments in the across-wind direction (MX for SQ and MY for CV) are significant, and the shapes of the envelopes change to semi-circular or semi-elliptic. The decreases of bending moments in the along-wind direction are not so noticeable, and the mean value of along-wind bending moments is almost the same. The envelopes of phase-plane trajectories in quasi-static conditions are similar to those of the phase-plane trajectory of along- and acrosswind forces (Tamura et al., 2012).
3.3. Effects of various loading conditions
Fig. 8. Effect of damping ratio on time history of bending moments for square (SQ) for wind direction 01. (a) Normal stress by MX, (b) normal stress by MY.
For the wind directions where the largest peak normal stresses occurred, the effects of various loading conditions were examined. Loading conditions included (i) ALL loads (FX þFY þMZ), (ii) FX only, (iii) FY only, (iv) MZ only, (v) FX and FY (FX þFY), (vi) FX and MZ (FX þ MZ), and (vii) FY and MZ (FY þMZ), i.e. 7 cases in total. The results are summarized in Tables 2–4 for the square model (SQ, wind direction 01), setback model (SB, wind direction 851), and SB þ45RT (wind direction 401). For SQ, the peak compressive stress in Col. 4 when FX and FY (FX þFY) are applied is almost the same as that for the ALL loading condition. Under the (FX þMZ) loading condition, the stresses are slightly larger than those under the FX only loading condition, and under the (FY þMZ) loading condition, they are slightly larger than those under the FY only loading condition. The results for the MZ only loading condition are very small, and can thus be ignored only when there are no eccentricities. For SB, the peak compressive stress under the FY only loading condition is larger than that under the FX only loading condition for wind direction 851. For this wind direction, FY roughly corresponds to along-wind force. Thus, the trends are very similar to those for SQ, i.e. for Col. 3, the (FX þFY) loading condition gives almost the same results as the ALL loading
Fig. 9. Effect of damping ratio on bending moments for square (SQ) and cross void model (CV). (a) SQ when damping ratio is 0.3% (left), 1% (center), and quasi-static (right) when wind direction of 01, (b) CV when damping ratio is 0.3% (left), 1% (center), and quasi-static (right)when wind direction of 851.
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Table 2 Effects of various loading conditions on peak compressive stress of square model (SQ) for ζ¼ 1% (wind direction of θ ¼01, kN/cm2). Peak compressive stress
ALL loadings
Only FX
Only FY
Only MZ
FX þ FY
FX þMZ
FY þ MZ
Col. 1
5.6
0.6
6.4
0.4
5.6
0.7
6.5
Col. 2
10.4
7.3
6.4
0.4
10.4
7.4
6.5
Col. 3
5.1
0.6
6.3
0.4
5.1
0.6
6.3
Col. 4
11.0
7.3
6.3
0.4
11.0
7.4
6.4
Table 3 Effects of various loading conditions on peak compressive stress of setback model (SB) for ζ¼ 1% (wind direction of θ ¼851, kN/cm2). ALL loadings
Only FX
Only FY
Only MZ
FX þ FY
FX þMZ
FY þ MZ
Col. 1
3.0
3.6
0.4
0.3
2.9
3.8
0.5
Col. 2
2.7
3.1
0.4
0.3
2.7
3.2
0.4
Col. 3
7.7
3.6
5.5
0.3
7.7
3.7
5.6
Col. 4
6.6
3.1
5.5
0.3
6.6
3.2
5.6
Peak compressive stress
Table 4 Effects of various loading conditions on peak compressive stress of SB þ 45RT model for ζ¼ 1% (wind direction of θ ¼401, kN/cm2). ALL loadings
Only FX
Only FY
Only MZ
FX þ FY
FX þMZ
FY þMZ
Col. 1
0.6
0.4
0.7
0.1
0.6
0.4
0.7
Col. 2
3.8
4.3
0.7
0.1
3.8
4.4
0.7
Col. 3
3.3
0.4
4.0
0.1
3.3
0.4
4.0
Col. 4
7.6
4.3
4.0
0.1
7.6
4.4
4.0
Peak compressive stress
condition, and (FY þMZ) gives slightly larger results than the FY only loading condition. Also, the results for the MZ only loading condition are negligible. For Col. 4 of SB þ 45RT, when the wind direction is 401, the contributions of the FX only and the FY only loading conditions are similar.
4. Concluding remarks Using wind pressures applied to 13 super-tall building models with atypical building shapes, time history analyses were conducted. Test models included 8 single modification models, and 5 multiple modification models. The primary purpose was to directly compare the peak normal stresses in columns of super-tall buildings. Comparison and discussion led to the following concluding remarks. The peak normal stresses for the square model were the largest among all the models tested. The CCþTP þ360Hel model showed the smallest peak normal stresses among the models tested, and the setback model showed the smallest peak normal stresses among the single modification models tested. The peak normal stresses of the two helical models and the multiple-modification models showed less variation with wind direction. Also, it was found that the effects of corner-cut and taper seemed to be negligible when they were added to the 180Hel model. The peak normal stresses under bending moments MX and MY were almost the same for the considered wind directions, and the
contributions of bending moments to total peak normal stresses were about 20% of the total. Most of the peak normal stresses were affected by axial force. This was because the frame model used in the present study was designed as bending type. As the damping ratio increases, the peak normal stress decreases and approaches the quasi-static value. The increase in bending moment for the across-wind direction became significant as the damping ratios decreased, and the sensitivity of the peak normal stresses for the helical and multiple modification models to damping ratio as well as wind directions was smaller than for the other models. The effects of damping ratio are also clearly seen in the time histories of normal stresses. From the analyses for the various loading conditions, it was found that the contribution of bending moment in the along-wind direction was larger than those of the other loading conditions and that of torsional moment was almost negligible.
Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A6A3A01064632). And this study was partly funded by the Ministry of Education, Culture, Sports, Science and Technology, Japan, through the Global Center of Excellence Program, 2008–2012.
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