This paper presents a procedure for the response prediction and reduction in high-rise buildings under multidirectional wind loads. The procedure is applied to a very slender tall building that is instructive. The structure is exposed to both cross-wind and along-wind loads obtained from pressure measurements on a rigid model (scaled 1 : 100) that was tested in a wind tunnel with two different configurations of the surroundings. In the theoretical formulation, dynamic equations of the structure are introduced by finite element and 3D lumped mass modeling. The lateral responses of the building in the two directions are controlled at the same time using tuned mass dampers (TMDs) and active tuned mass dampers (ATMDs) commanded by LQR and fuzzy logic controllers, while the effects of the uncontrolled torsional response of the structure are simultaneously considered. Besides their simplicity, fuzzy logic controllers showed similar trend as LQR controllers under multidirectional wind loads. Nevertheless, the procedure presented in this study can help decision makers, involved in the design process, to choose among innovative solutions like structural control, different damping techniques, modifying geometry, or even changing materials.
Civil engineering structures are an integral part of our modern society. Traditionally, these structures are designed to resist static loads. However, they may be subjected to dynamic loads like earthquakes, winds, waves, and traffic. Such loads can cause severe and/or sustained vibratory motion, which can be detrimental to the structure and human occupants. Because of this, safer and more efficient designs are sought out to balance safety issues with the reality of limited resources. Wind-induced vibrations in buildings are of increasing importance, as the use of high-strength, lightweight materials, longer floor spans, and more flexible framing systems results in structures that are more prone to vibrations. In tall buildings, wind-induced vibrations may cause annoyance to the occupants (especially in the upper floors), impaired function of instruments, or structural damage.
Traditionally, wind-induced response of tall buildings in the along-wind direction are evaluated using some codes and formulas [
HFPI technique is based on simultaneous pressure measurements at several locations on a building’s outer surface. Pressure data can be used for the design of the claddings as well as the estimation of the overall design loads. The HFPI technique cancels out any inertial effects that may be included in the overall loads measured by the base balance if the HFBB technique was used. Time histories of wind forces at several levels of tall building models can be obtained in the wind tunnel with a multichannel pressure scanning system. This enables the building responses to be computed directly in the time domain for buildings with simple or complex mode shapes. Finite element models (FEMs) can be used for describing the dynamic behavior of the structures. HFPI with FEM have the advantages of considering complex shapes of structures with nonuniform mass distribution and can easily account for any required number of mode shapes to be considered in the response analysis.
Preliminary analysis of tall buildings in their preliminary design stages help the designer to make decision by modifying the design or adding passive, active, or semiactive control techniques. Structural control has recently been the subject of much discussion among structural designers. Structural control can potentially provide safer and more efficient structures. The concept of employing structural control to minimize structural vibrations was proposed in the 1970s [
McNamara [
The aim of this study is to present practical procedure for the response prediction and reduction in a very slender high-rise building under multidirectional wind loads. The procedure is schematically presented in Figure
Schematic representation of the proposed procedure for response prediction and reduction in tall buildings under wind loads.
A 48-strory steel tower proposed in Aly et al. [
Modal parameters of the FEM model.
Mode number* | Generalized mass × 107 (kg·m2) | Generalized stiffness × 109 (N·m) | Frequency (Hz) | Modal damping |
---|---|---|---|---|
1 | 1.2953 | 0.0147 | 0.1694 | 0.0102 |
2 | 0.9937 | 0.0178 | 0.2132 | 0.0112 |
3 | 0.4945 | 0.0222 | 0.3370 | 0.0150 |
4 | 0.8724 | 0.1115 | 0.5689 | 0.0234 |
5 | 0.8273 | 0.2153 | 0.8120 | 0.0326 |
6 | 0.3544 | 0.1600 | 1.0695 | 0.0426 |
*Modes 1 and 4 are lateral displacements in
Finite element model with the coordinate system and wind direction (
Equations of motion governing the behavior of the structure under wind loads are
Substituting by (
By assuming the damping matrix,
This means that once the time history of the pressures on the outer surfaces is calculated, the external forces acting on the nodes of the surface can be computed. The excitation forces acting on the internal nodes are of course equal to zero. The
For control purposes, a 3D lumped mass model is derived from the original FEM. In this model, the total mass of the building was assumed to be lumped at the positions of the floors, and it was assumed for the floors to perform a general 3D movement (each floor has two translations in the
Wind loading vectors (
Mean wind speed profile, turbulence intensity profiles, and wind spectra (
Two different configurations are used.
Pressures on the outer surface of a scaled 1 : 100 model were obtained from a wind tunnel test: (a) pressure tap distribution (elevation and side view), (b) mean surface pressure coefficient distribution (for 292.5 deg).
Typical spectrum of measured pressure data (at model scale).
Wind load estimation from pressure data: the tributary area of floor
Due to the fact that the building’s mass is symmetrical, and the study is based on the assumption that the structure is responding in the linear region, the lateral and the torsional behavior of the building may be studied alone, then the response time histories may be combined simultaneously. In this study, the plane motion of the structure in the
The state reduction approach derived by Davison [
The state equation of the ROS that corresponds to the full order system (FOS) in (
The controlled output vector,
In this study, both TMDs and ATMDs are used for the reduction of the lateral responses of the building. However, in order to make the design of such control systems more realistic and applicable, the following restrictions and assumption are applied. The mass of the TMD in the The TMDs are tuned to the first vibrational mode in each corresponding lateral direction. The damping factor is taken to be 20% of the critical. This amount of damping is selected higher than the optimal value for the sake of restricting the stroke of the ATMDs. The maximum stroke of the actuators is restricted to 1.5 m. The maximum control force of the actuator in the The computational delay and the sampling rate of the digital controller are 0.001 s. Three acceleration measurements are available for each lateral direction (at floor 30, roof, and mass of the TMD).
Note that the tower required a TMD with heavier mass and ATMD with higher control force in one lateral direction than the other, which was basically attributed to geometry. A linear-quadratic regulator (LQR) design with output weighting is selected to give the desired control force using the MATLAB function (
For comparison reasons, fuzzy logic controllers are used in this study to command the actuators of the ATMDs (see Nguyen et al. [
The input variables to the fuzzy controller were selected as accelerations of floors 30 and 48 and the output as the control force. The membership functions for the inputs were defined and selected as seven triangles with overlaps as shown in Figure
Control rule base [
Acceleration of 48th floor | Acceleration of 30th floor | ||||||
NL | NM | NS | ZR | PS | PM | PL | |
NL | PVL | PVL | PL | PVS | ZR | ZR | ZR |
NM | PL | PL | PM | PVS | ZR | ZR | ZR |
NS | ZR | NVS | PM | PS | PVS | ZR | ZR |
ZR | ZR | ZR | NVS | ZR | PVS | ZR | ZR |
PS | ZR | ZR | NVS | NS | NM | PVS | ZR |
PM | ZR | ZR | ZR | NVS | NM | NL | NL |
PL | ZR | ZR | ZR | NVS | NL | NVL | NVL |
Membership functions for the input measured accelerations in the
Membership functions for the output control force in the
Table
Response of the top corner of the tower in the
Mode | RMS-disp. (m) | Max-disp. (m) | RMS-accel. (m/s2) | Max-accel. (m/s2) |
---|---|---|---|---|
1 | 0.000 (−100%) | 0.001 (−99.8%) | 0.000 (100%) | 0.001 (−99.9%) |
0.129 (−4.4%) | ||||
1 : 3 | 0.136 (0.7%) | 0.613 (1.5%) | 0.238 (−0.8%) | 0.980 (1.1%) |
1 : 4 | 0.136 (0.7%) | 0.613 (1.5%) | 0.238 (−0.8%) | 0.980 (1.1%) |
1 : 5 | 0.135 (0%) | 0.606 (0.3%) | 0.239 (−0.4%) | 0.966 (−0.3%) |
1 : 6 | 0.135 (0%) | 0.604 (0%) | 0.240 (0%) | 0.969 (0%) |
Response of the top corner of the tower in the
Mode | RMS-disp. (m) | Max-disp. (m) | RMS-accel. (m/s2) | Max-accel. (m/s2) |
---|---|---|---|---|
1 | ||||
1 : 2 | 0.188 (1.1%) | 0.646 ( | 0.203 ( | 0.654 ( |
1 : 3 | 0.187 (0.5%) | 0.648 ( | 0.204 (0%) | 0.653 ( |
1 : 4 | 0.186 (0%) | 0.649 (0%) | 0.204 (0%) | 0.676 ( |
1 : 5 | 0.186 (0%) | 0.649 (0%) | 0.204 (0%) | 0.676 ( |
1 : 6 | 0.186 (0%) | 0.649 (0%) | 0.204 (0%) | 0.678 (0%) |
Power spectra of the acceleration response of the top corner of the building in the two lateral directions.
Figure
displacement and acceleration responses of a point at the top corner for FEM, 3D full order system (3D-FOS), and 3D reduced order system (3D-ROS).
The building required a TMD with heavier mass and ATMD with higher control force in one lateral direction than the other. This may be attributed to geometry. Figures
RMS-displacements of the top corner of the tower.
Maximum displacements of the top corner of the tower.
RMS accelerations of the top corner of the tower.
Figures
Figures
Maximum accelerations of the top corner of the tower.
Generally, TMDs are able to give good reduction in the rms displacements in both the
As a general comment on Figures
The paper presents practical procedure for the response prediction and reduction in high-rise buildings under wind loads. To show the applicability of the procedure, aerodynamic loads acting on a quasirectangular high-rise building based on an experimental approach (surface pressure measurement) are used with a mathematical model of the structure for the response prediction and reduction. The building represents a case study of an engineered design of a very slender tower that is instructive. The contributions of this paper can be summarized as follows. The methodology based on HFPI and FEM proposed for the estimation of the response of high-rise buildings under wind loads has the advantage of combining lateral along-wind, lateral cross-wind, and torsional responses altogether. The technique allows for the consideration of any number of modes. Results show that the responses of tall buildings under winds are dominated by the first few modes. Consequently, FEM, 3D lumped mass modeling, and reduced order 3D modeling of tall buildings under wind loads give an accurate assessment of the response provided that the first dominant modes are retained. Results show that the response of tall buildings in the cross-wind direction (lateral response combined simultaneously with torsion) can be higher than the response in the along-wind direction. This reveals the importance of the procedure proposed in this study as many design codes and formula may provide accurate estimate of the along-wind response but less guidance for the estimation of the critical cross-wind and torsional response. The building represents an engineered steel design of a structure that is very much vulnerable to wind loads. This may be due to its low weight as well as high flexibility related to the low dominant frequencies and the high aspect ratio. The building demands TMD with heavier mass and ATMD with higher control force in one lateral direction than the other. This may be attributed to geometry. For the purpose of the use of active control, LQR and fuzzy logic controllers are shown to be effective in enhancing the response reduction over the TMD. ATMDs with fuzzy logic controllers show similar trend like LQR controllers under multidirectional wind loads. In addition, from a design point of view, fuzzy logic controllers do not require the complexity of traditional control systems. The procedure presented in this paper permits the response of tall buildings to be assessed and controlled in the preliminary design stages. This can help decision makers, involved in the design process, to choose among innovative design solutions like structural control, considering several damping techniques, modifying geometry, or even changing materials.
The authors would like to express appreciation to the work team at the Wind Tunnel of Politecnico di Milano, Milan, Italy. The first author wishes to thank Ms Corey Ginsberg, Florida International University, for her helpful comments.