b

CSTB, Nantes, France Ecole des Mines de Nantes, France c Potain, France

Abstract

An experimental method used to study the behaviour of tower cranes in strong winds exposed to the disturbed shear flow induced by the surrounding built environment is proposed. Wind tunnel tests on a tower crane model are described, the tower crane is considered as a rigid body slender structure equipped with a single degree of freedom part: the crane mobile jib allowing rotation with respect to the vertical axis. Geometrical and mechanical properties are simulated in order to reproduce realistic rotating part behavior. Instantaneous base overturning moments and rotating part positions are measured in a boundary layer wind tunnel able to simulate the turbulent wind characteristics. Improvements of the design of the crane in order to reduce the crane overturning moments, alleviate undesirable jib rotations and associated failure risks are investigated. Keywords: Tower crane, overturning risk, slender structures, wind loads, boundary layer wind tunnel, safety

1 INTRODUCTION In the last years, Europe was hit by several severe windstorms, which produced extensive damages. Among others, several tower cranes fell down. Strong windstorm and unfavourable erection site with surrounding buildings could result in an increase of overturning or failure risks. Those conditions usually appear on high-rise building sites during hurricanes. In previous studies related to cranes [1], the tower crane model had one degree of freedom. The rotating part was fixed in the wind direction and the only degree of freedom was the overturning angle around the tipping point. The objective was to characterize the influence of gust duration on overturning risk. Environmental effects were not taken into account this is to say that there were no special conditions of exposure or shelter. In engineering and standard practices [2,3,4], wind loads on cranes are estimated in the hypothesis of an optimized safety position during storms (i.e. with the lowest drag force). In a natural turbulent wind without any environmental effect, the rotating part of the crane moves automatically in the wind direction. This is representative if the crane is an isolated structure without any wind disturbances produced by surrounding buildings. However, due to its func_______________________________________

* Corresponding author: CSTB – 11 rue H. Picherit – BP 82341 – 44323 NANTES Cedex 3 – FRANCE Fax : 00 33 (0)2 40 37 20 60 - E-mail : [email protected]

tions, it is rarely the case. Because of the surrounding built environment, the wind flow around a tower crane may exhibit unexpected and dangerous aerodynamic phenomena. The aim of this research is to characterise the fluctuating loads induced on a tower crane by the disturbed approaching wind flow, more precisely the peak overturning moments for most actual configurations. As tower cranes are lattice structures and thus are porous, aerodynamic wind induced effects are mainly drag forces [5,6,7]. The wind overturning moment induced by the drag forces acting on the whole structure is function of the yaw angle between the wind direction and the rotating part of the crane. This yaw angle is governed directly by the differential wind moment produced by the drag forces acting on the jib and the counter jib. This is why the heterogeneity of the wind field at rotating part level plays an essential role for crane stability. The frequency of crane's fundamental vibration mode lies in the range 0.1 Hz to 0.5 Hz (higher is the crane, lower is the frequency). The jib rotation speed observed during storms is no faster than a few turns per minute, which corresponds to frequencies too low to excite the structure's natural modes. The porosity of the crane and the continuous motion of the rotating part which alleviates critical vibratory phenomenon are additional reasons to justify to neglect dynamic effects and to consider only the direct quasi-steady wind loads. Therefore the tower crane can be considered as a rigid body structure with a single degree of freedom: the crane mobile part rotating in respect to the vertical axis. Mast and jib deformations are neglected, as they are much smaller than the global crane motion. 2 MATHEMATICAL MODEL The equation of motion of the rotating part of the crane can be written as: ••

•

I θ + C Friction θ = CWind

(1)

where θ is the jib nose angular position, I is the mass moment of inertia of the whole rotating part about its rotating vertical axis, CWind is the instantaneous aerodynamic torque on acting on the rotating part (difference between jib and counter-jib aerodynamic loads) and CFriction the friction coefficient between the rotating part and the turntable tower head. The overall overturning moment is then expressed in SI units as: Centrifugal Inertial 47444 8 644 7448 644 •2

••

M Overturning (O) . y = − θ mRP lMast r sinθ − θ mRP lMast r cosθ

(2)

− a mMast g − [r cosθ + a ] mRP g + lCP FxWind →Mast + lMast FxWind →SP 144444244444 3 1444442444443 Gravity

Wind

where

M Overturning (O)

r y

Overturning moment at crane base level at tipping point O Unit vector perpendicular to wind direction

mRP

Mass of the rotating part

mMast

Mass of the mast

l Mast

Length of the mast

lCP

Height of the mast aerodynamic center

r

Rotating part barycenter to crane vertical axis length

a

Cross shaped-base spacing

g

Gravity acceleration

FxWind →Mast

Drag component of wind force on Mast

FxWind →SP

Drag component of wind force on rotating part Wind

r

TOP VIEW

Wind

••

r mRP g

In er tia

W &

Ce

nt ri

fu g

W

mMast

lMast

al F

in d

r g

in d

Fo r

ce

on

or ce s

Fo rc e

lCP y a

Iθ

on

M

Sl ew in

θ

Wind Force on Counter-jib

g

Pa rt

y x

•

CFriction θ

θ as t

Wind Force on Jib

Overturning Moment

O x

Fig. 1. Moments and forces schemes

The overturning moment at crane base level is the difference between restoring moment and overturning moment. It can be separated into four major components (Eq. 2): inertial and centrifugal rotating part moment, gravity moment and fluctuating wind moment. Gravity moment (resulting of the mass of the counter-weights on the counter jib used to balance the carried loads during service conditions) module is constant but its action is function of the angle θ. Overturning moment is mainly governed by the gravity moment and the fluctuating wind moment when the rotating part is steady or when the angular speed and acceleration of the rotating part of the crane are small.

3 DIMENSIONAL ANALYSIS AND SIMILARITY CONDITIONS In order to evaluate direct wind effects as well as the environmental effects on tower cranes a study on a reduced scale model in a boundary layer wind tunnel was initiated. The scale of the model is a compromise between similarity scales and the size of the wind tunnel test section. On one hand, to take into account a large built area surrounding the tower crane in the wind tunnel, the model scale needs to be small enough. But on the other hand, the model crane itself has to match geometrical and kinematic similarity conditions more easily satisfied if the geometrical scale of the model is large. The model geometrical scale factor was then chosen as λL=1/80 which represents an appropriate compromise between these two opposite conditions using a 9.2 m² cross section area wind tunnel.

3.1 Kinematic similarity The second step of the similarity study was then to satisfy the kinematics properties. To model the tower crane rotating part that moves into the air, we must ensure that the model rotation speed is similar to that of the prototype. This is achieved if the ratio of the acceleration of the structure to the acceleration of a fluid particle is the same for both model and prototype, Fay [8]. Thus, to model the behaviour of the tower crane rotating part which describes a disc of radius •

L with an angular velocity θ with a speed wind Vw we must check that the ratio of the cen•2

trifugal acceleration of the rotating part θ L to a typical acceleration of a fluid element

V . ∇V ≅Vw2 / L is the same for both model and prototype. In fact, kinematic similitude is ensured by the equality of the Strouhal number for both model and prototype (Eq. 3) •

⎛ θ• L ⎞ ⎛• ⎞ ⎜ ⎟ = ⎜ θ L ⎟ or (Vw / θ ) m = λ L • ⎜⎜ V ⎟⎟ ⎜⎜ V ⎟⎟ w w ( V / ) θ w p ⎝ ⎠m ⎝ ⎠p

(3)

In the present case, the crane model angular speed observed in wind tunnel (in strong environment effect conditions) for a 4.7 m/s wind speed can be around 2 rad/s (20 rpm), it corresponds to a crane prototype angular speed equals to 0.23 rad/s (2.2 rpm) in a 41.7 m/s wind speed (150 km/h). 3.2 Dynamic similarity Dynamic similarity exists between geometrically and kinematically similar systems if the ratios of all forces between the model and the prototype are the same. Therefore it is necessary to reproduce realistic rotating part behaviour to ensure that governing differential equation of motion (Eq. 1) and overturning moment equation at bases (Eq. 2) of the model and prototype are similar. The gravity term in Eq. 2 implies to reproduce a Froude number similarity. Consequently the square of the Froude number is relates to the ratio of inertial to gravity forces, it is used to define the wind speed similarity scale. Mass distribution, rotating part inertia and friction coefficient were reproduced at model scale in respect to similarity laws (Eq. 4, 5, 6).

M m = λ3L M p

(4)

I m = λ5L I p

(5)

CFriction m = λ4L λL CFriction p

(6)

Forcem = λ3L Forcep

(7)

Momentm = λ4L Momentp

(8)

This leads to very light model parts. For example 8000 kg of the model jib matched by 16 gr at model scale.

Linear wind surface distribution was respected all along the rotating part, this distribution generates an appropriate wind torque on the rotating part. In the wind tunnel velocity range of 0 to 10 m/s, the aerodynamic coefficients of the model proved to be constant, no Reynolds number effect were observed. A carbon tube used to reproduce the mast, it has similar drag characteristic than the full scale element. It has been verified that the mast wind surface S.Cx which is equal to 22.9 m2 at full scale (40 m/s) is reproduced by a 3 10-3 m2 at model scale (in wind tunnel velocity range of 0 to 10 m/s). 4 EXPERIMENTAL FACILITIES AND PROCESS

4.1 Wind tunnel facility description The tests were conducted in one of the CSTB boundary layer return type wind tunnel whose cross-section is 2.3 m high × 4 m wide. The airflow velocity is adjustable in a range 0 to 10 m/s. Wind is simulated using calibrated roughness on the tunnel floor for scales ranging from 1/50 to 1/500. 4.2 Instrumentation The fluctuating wind loads acting on the rotating part of the crane, its angular position as well as the overall overturning moment at the base of the crane are the target parameters necessary to evaluate the crane behaviour. The Froude similarity criteria is associated to the matching of mass and inertia similarities of the rotating part and also of the mast of the tower crane model. This Froude condition implies also low wind velocity ranges (below 5 m/s) in the wind tunnel. Therefore the loads acting on the tower crane model are very small, estimates of the wind moment were 0.01 N.m for an along wind jib position and 0.1 N.m for a jib perpendicular to the wind. Thus the 15 m high (full scale) mast element of the model support of the rotating part was designed as a strain gauge balance. This balance is built using two aluminium stages fitted with gauges and connected to each other by the light 10 mm carbon tube (Fig. 2). The square cross sections of the upper and lower stages are respectively 2.5 × 2.5 mm2 and 3.5 × 3.5 mm2. Both mass and stiffness were properly tuned and the natural vibration frequency is high enough to not affect measurements. The strain gauges of the mast are wired into a Wheatstone bridge circuit, which gives a voltage output proportional to the overturning moment after preliminary calibration.

45 m full scale 0.56 m model 15 m full scale 0.19 m model

Strain gauge balance

Angular encoder

Fig. 2. 1/80 scale model of a Potain MD238 crane in CSTB boundary layer wind tunnel

The low friction torque at the taper roller bearing implies the use of a non-intrusive system of measurement of the angular position, which doesn't introduce additional friction. An incrementing angular encoder integrated into the tower crane model, consisting in three optoelectronic sensors and a reflecting surface, is used to measure the angular position. 4.3 Methodology Experimental results issued of the wind tunnel tests are the angular rotating part position, function of time, and the instantaneous overturning moment at the base of the crane. Angular speed and angular acceleration are obtained by time derivation of the angular rotating part position. Therefore inertial, centrifugal and gravity moments at the crane base can be easily calculated. Finally instantaneous wind moment at base crane level is deduced from the subtraction of instantaneous inertial, centrifugal and gravity moments (Eq. 2). 5 RESULTS AND DISCUSSION

5.1 Crane without surrounding built environment Preliminary to analyse the tower crane behaviour in a built surrounding environment, some preliminary experiments were carried out to simulate the model crane behaviour without any built environment. One of the former tests was to observe the rotating part motion initially perpendicular to the wind. The time delay T90°∏ 0° necessary for the rotating part initially in a perpendicular wind position to reach the along wind position can be estimated using a simplified wind torque hypothesis (i.e. the wind torque is constant in 90° to 45° angular sector and equals to its 90° value, and it is null between 45° to 0° angular sector) by integration of equation 1. So, the T90°∏ 0° estimation for the Potain MD238 real scale rotating part exposed to a 45m/s wind speed is close to 10.6s which corresponds to 1.19s at model scale. In the wind tunnel the measured corresponding time delay T90°∏ 0° is 1.42s (Fig. 4a). The 19% difference between estimates and wind tunnel tests is due to the integration hypotheses and the friction coefficient estimate. The rotating part motion describes only two oscillations before being steady. The maximum yaw angle observed during the counterflow period is less than 30°, and the total time delay for the crane to be in the alongwind safety position (in the wind direction) is 4.5 s. The friction part of the torque can be neglected (Fig. 4b), inertial torque contribution is predominant. Figure 4c illustrates overturning moment (y value) and its component moment at base crane level. The gravity component is null when the rotating part is perpendicular to the wind, inertia and centrifugal components are negligible. Compared to wind moment, gravity moment has an opposite sign. Opposed to wind effects, negative moments contribute to crane stability. Polar diagram (Fig. 4d) shows the resultant overturning moment decrease function to angular position.

Fig. 4. Crane without surrounding environment (a) Rotating part model angular position, speed and acceleration (b) Torques on rotating part around a vertical axis (c) Moments at base level (d) Polar representation of the overturning moment function to angular position. (Results at model scale)

5.2 Crane in turbulent flow and in a built environment Surrounding built environment can generate heterogeneous and unbalanced wind flow around the crane. This kind of flow may be found in the wake and in the shear layer of a building sensibly higher and/or larger than the crane (Fig. 5). But, it is interesting to notice that if the crane is a third higher than the building the phenomenon does not occur any more as the sensitive part of the crane is out of the perturbed flow. To reproduce and estimate the effects of such built environment effects, a 0.87 m high, 0.16 m wide and 0.48 m long model of building was set upwind to the crane, 0.6 m front of the rotation axis crane. Wind velocity and crane characteristics were the same than the former uniform flow test. Heterogeneous

Low Speed Area

Wind Field

Wind Acceleration Area

Fig. 5. Example of environment wind effect: Heterogeneous wind field

Fig. 6. Crane in heterogeneous wind field (a) Rotating part model angular position, speed and acceleration (b) Torques on rotating part (c) Moments at crane base level (d) Polar representation of the overturning moment function to angular position. (Results at model scale)

Starting the test, the wind tunnel is off, the initial rotating part position is parallel to the wind tunnel longitudinal axis. Then, starting the propeller, wind velocity increases from 0 to 5 m/s in approximately 4 s before being steady at 5 m/s. An auto-rotating phenomena arises, the rotating part revolved six times during 30 s. For each turn the angular speed is in a range of – 70 deg/s to –180 deg/s and the maximum angular acceleration value is –270 deg/s2 (Fig. 6a). As previously mentioned, inertial torque contribution is predominant compared to friction torque in the estimation of the wind torque (Fig. 6b). At the beginning of the test, the overturning moment is equal to the gravity moment -0.027 N.m, the tower crane stay in safety position. 5 to 10 s later, wind moment increases as wind speed increases but the rotating part is not moving significantly before starting to rotate. During the first half turn, overturning moment increases to a maximum of 0.08 N.m. Then, when rotating, the overturning moment is in a range from -0.01 N.m to 0.08 N.m. Figure 6d shows that overturning moment maximum values correspond to -240° to 120° angular sectors and minimum values to 60° to 300°. Inertial and centrifugal moment module values are less than 0.01 N. In comparison with the crane without any built environment, the rotating part behaviour is tremendously different: it does not stop to turnaround. Consequences on moments at the crane base level are their large amplitude variation function of the angle of attack and angular speed and acceleration (Fig.6c). Most important variations are due to the gravity moment with respect to the position of rotating part's barycenter and the aerodynamic wind moment depending of the wind angle of attack. Thus, the overturning moment of the crane in this heterogeneous wind field is strongly fluctuating and its maximum value is more than twice higher than in the case without any built environment.

6 CONCLUSION Measurements of overturning moments at crane base level and angular rotating part position were carried out on a 1/80 scaled tower crane model. Two environment conditions (with and without an upwind surrounding building) were tested in a boundary layer wind tunnel to analyse the wind field influence on the tower crane behaviour. Overturning moments at base crane level were identified and evaluated. It was observed that inertial and centrifugal moments are much smaller in comparison to gravity and wind moments. Concerning the role of the friction coefficient on rotating part motion in storm wind conditions, it appears that its contribution to wind torque on rotating part is not predominant compared to the inertial torque contribution. This model crane is an efficient tool to study any unsuspected surrounding built environment effect on tower cranes submitted to strong winds. Also, it will be essential to test improvements of the tower cranes designs in order to reduce environmental effect on overturning crane moment and alleviate undesirable rotating part auto-rotating phenomenon. Tests on reduced drag cranes and various differential jib/counter-jib aerodynamics weightings are in progress. 7 ACKNOWLEGMENTS Potain S.A. acts as sponsor on this study. The assistance and co-operation of the sponsor are gratefully acknowledged. In particular the authors would like to extend thanks to Guy Galand who is following this research. REFERENCES [1] Eden J.F., the late Iny A. and Butler A.J. (1981) Cranes in storm winds. Eng. Struct.,1981, Vol. 3, july [2] Eden J.F., Butler A.J. and Patient J.(1983) Wind tunnel tests on model crane structures. Eng. Struct.,1983, Vol. 5, October Building Reseach Establishment, Garston, Watforf WD2 7JR, UK [3] Fetizon F., Jouannet J.C., Watremetz M. (1979) Tower crane in turbulent wind. Pratical experiences with flow induced vibrations Symposium, Karlsruhe 3-6/september 1979 [4] Vreugdenhll J. (1995) Out-of-service Wind-Loading of cranes gusts. Bulk Solids Handling/Volume15/No.1/January-March 1995 [5] Eden J.F., Butler A.J. and Patient J. (1985) A new approach to the calculation of wind forces on latticed structures. Building Research Institut The Structural Engineer/ Volume 63 A/No. 6/June 1985 [6] ESDU (1988) Lattice structures Part 1 : mean fluid forces on single and multiple plane frames. Engineering Sciences Data Unit - Wind Engineering Sub-Series, Data Item 81027, London, 1988. [7] ESDU (1988) Lattice structures Part 2 : mean fluid forces on tower-like space frames. Engineering Sciences Data Unit - Wind Engineering Sub-Series, Data Item 81028, London, 1988. [8] James A. Fay, N. Sonwalkar A fluid mechanics hypercourse Massachusetts Institute of Technology 1991 http://www.mas.ncl.ac.uk/~sbrooks/book/nish.mit.edu/2006/Textbook/Nodes/chap10/node1.html