11th

UK Conference on Wind Engineering, Birmingham, 2014

Experimental investigation of the aerodynamic performance of a long span

arch structure

Author Names: Stefano Cammelli1*

and Michael Clayton1

1BMT Fluid Mechanics, Teddington, UK

* E-mail: scammelli@bmtfm.com

ABSTRACT

Due to the novel design of the steel arch structure presented in this technical paper, available wind

codes and design guidelines were considered insufficient in terms of providing a reliable assessment of

its aerodynamic performance. A programme of detailed wind tunnel studies was therefore required by

the structural designers to validate the arch against potential aerodynamic instabilities – taking due

account of the fluid-structure interaction – as well as to derive an assessment of the wind loads.

The architectural form of the arch is highly three-dimensional and full aeroelastic model wind testing

was favoured over section model testing. The potential aerodynamic phenomena investigated during

the test campaign included resonant vortex-shedding excitation, primarily affecting the fatigue life of

the structure – and self-excited divergent aerodynamic instabilities such as galloping, potentially

leading to structural failure.

The derivation of peak design wind loads, which were obtained by combining wind tunnel data with

analytical models taking into account the effect of the atmospheric turbulence, will not be covered in

detail within this paper.

INTRODUCTION

The location of the site of the arch was a few kilometres from the Persian Gulf coastline, with the

immediate surrounding area consisting of mid- to low-rise sparse urban sprawl. The 50-yr return

period mean-hourly basic wind speed, based on a detailed extreme value analysis of the wind events in

the region, was ~23 m/s (10 m reference height in z0 = 0.03 m) and the characteristic product of the

wind climate ~5.4. The wind speed criteria for full model testing of divergent amplitude response of

the arch was derived in accordance with the methodology stipulated within [1]: the highest VWE speed

was found to be ~52 m/s (at 75 m above the local ground).

The height of the arch above the local ground was ~75 m and its span ~180 m. Its global orientation

was such that winds coming from ~70° and ~250° were parallel to the vertical plane of the arch. The

arch was entirely made by steel flange plates internally strengthened by a series of welded "T"

stiffeners. The structure had an equilateral triangle cross-section (side length ~3.5m at the base

reducing to ~2.2 m at the apex) twisting 120° along the entire development of the arch itself. The

overall geometrical slenderness of the structure was ~1:80.

The numerically predicted structural frequencies of the first lateral (out-of-plane) mode of vibration of

the arch was ~0.24 Hz; the second lateral (anti-symmetric) mode ~0.63 Hz; and the first vertical (in-

plane anti-symmetric) mode ~0.81 Hz.

With an equivalent mass per unit length in the first mode of vibration of ~2,800 kg/m (me) and an

inherent structural damping assumed by the design team of ~0.25% of critical (s), the expected

Scruton number [in the (4·∙s∙me)/(∙bref2) form] was ~12.

WIND ENGINEERING STUDIES

Initial wind tunnel testing

A 1:100 full aeroelastic wind tunnel model of the arch was designed to provide a best match to the key

mode shapes anticipated to dominate the aerodynamic stability of the arch (see Fig. 1). It was

constructed using a tubular steel spine as supporting structure and subsequently clad with 12 sections

of lightweight (balsa) wood. The wind tunnel model was instrumented with a series of strain-gauges

and biaxial micro-machined low-range high-resolution accelerometers (capable of recording both the

11th

UK Conference on Wind Engineering, Birmingham, 2014

in-plane and the out-of-plane wind-induced motion of the structure) and fully calibrated ahead of

testing. In addition, the model was also rigidly connected to two high-frequency force balances, one at

each end of the arch. The wind speed scales for the first three modes of vibration of the aeroelastic

model were ~3.1, ~3.6 and ~5.0 respectively, whilst the inherent damping levels of the model

respectively ~0.25%, ~0.41% and ~0.35% of critical.

Figure 1: Wind tunnel aeroelastic model (second quadrant) with associated mode shapes (‘mode 1’ in

the first quadrant, ‘mode 2’ in the third and ‘mode 3’ in the fourth).

The wind tunnel studies were carried out in BMT’s large wind tunnel in smooth flow conditions (level

of turbulence in the wind tunnel less than 0.3%). The cross-section of the facility is 4.8 m wide and 2.4

m high, while its fetch is 15 m long; it has a 4.4 m diameter multiple-plate turntable and an operating

wind speed range of 0.2 – 45 m/s.

The vortex-shedding and divergent responses of the arch were thoroughly investigated for a full range

of wind directions up to the required VWE speed.

Notable interaction between the vortices shed by the arch and the vertical (in-plane) structural modes

of vibration was apparent at wind angles spanning between ~180° and ~200°. For winds blowing from

180° (South) the vortex-shedding primarily interacted with ‘mode 3’, generating a full scale modal

standard deviation resonant displacement of ~0.18 m at a full scale wind speed of ~10 m/s (referenced

to 75 m above local ground). For winds blowing from 190° and 200° the vortex-shedding primarily

interacted with ‘mode 5’ (another vertical mode of the arch, in-plane anti-symmetric), generating in

this case a full scale modal standard deviation resonant displacement of ~0.15 m at a full scale wind

speed of ~22 m/s (referenced to 75 m above local ground). It should be noted that no vortex-shedding

resonant behaviour of ‘mode 1’, for which a critical wind speed of ~4 m/s at 75 m above local ground

was originally estimated (Strouhal number ~0.15) by the authors of this technical paper, was observed

during the tests.

A divergent instability developing in ‘mode 1’ was observed for winds blowing from 60° and 70°. The

critical on-set wind speed for divergent response was ~32 m/s (referenced to 75 m above local

ground), significantly lower than the required VWE. Interestingly, due to the unsymmetrical nature of

the shape of the arch, no divergent instability was detected for winds blowing from 250° (see Fig. 2;

reduced wind speed defined using n1 = 0.24 Hz and D = 2.5 m). It should be noted that the largest

lateral standard deviation displacement recorded during the experiments was approximately of the

same size as the width of the cross-section of the structure at its apex.

11th

UK Conference on Wind Engineering, Birmingham, 2014

Figure 2: Full scale lateral standard deviation modal displacement vs. reduced wind speed.

The wind-induced acceleration time-histories were also analysed making use of the so-called random

decrement (RD) technique, as described in [2]; the RD signatures were then treated using modal

identification techniques, as presented in [3], in order to identify the total damping of the wind tunnel

aeroelastic model undergoing different wind speeds (see Fig. 3). Fig. 3 also shows the decreasing trend

of the response peak factor (‘mode 1’) with increasing speed.

Figure 3: ‘Mode 1’ total damping (left-hand side, secondary axis) and response peak factor (right-

hand side, secondary axis) at 70deg wind direction vs. reduced wind speed.

As a result of these findings, the shape of the arch was modified in order to prevent galloping to occur

and the new developed shape tested to verify its aerodynamic stability.

Developing an aerodynamically stable shape

A close examination of the two views presented within Fig. 2 highlighted two main aerodynamic

features of the shape of the arch: a) the far more regular aerodynamic shape offered to winds

approaching the site from 70° has the potential to enhance the level of correlation of any wind loading

mechanism driving the response of the arch; and b) although the mean aerodynamic drag force

associated to the West half of the arch for winds approaching the site from 70° is relatively high, the

rate of change of the mean aerodynamic lateral force coefficient has the potential to be even higher,

increasing significantly the risk for galloping instability to occur.

With the two above in mind, a number of options were developed, proposed and discussed with the

architect and the structural engineering team; these included: i) a more pronounced overall twist of the

entire arch (180° as opposed to the initial 120°); and ii) mirroring the West half of the arch in order to

generate a shape symmetric about the apex.

Arch viewed

from 70°

(unstable)

Arch viewed

from 250°

(stable)

11th

UK Conference on Wind Engineering, Birmingham, 2014

Although the authors of this technical papers were fully aware that the mechanism behind the

galloping instability was not only driven by the aerodynamic shape of the upstream half of the

structure, it was felt that the option of mirroring the West half of the arch was, on balance, the one

most likely to succeed. The project moved forward on this basis.

Investigation of the aerodynamically improved shape

The existing wind tunnel aeroelastic model had at this stage to be modified: the internal supporting

structure was retained whilst only the external balsa cladding was changed to replicate the new form.

A great degree of care had to be put in this process in order to ensure that the structural properties of

the modified wind tunnel aeroelastic model were fully aligned with the slightly revised ones of the full

scale structure; in particular, ensuring that in this process the inherent damping level of the model

remained unchanged was paramount.

The aerodynamically improved shape of the arch was found to be stable with regard to divergent

instability for the full range of wind directions investigated and up to the VWE speed (see Fig. 4).

For winds blowing from 65° and 260°, a high dynamic response of the arch in ‘mode 1’ near the end

of the design wind speed range of interest was observed (see Fig.4).

Figure 4: Full scale lateral standard deviation modal displacement vs. reduced wind speed.

CONCLUSIONS

After an initial campaign of aeroelastic wind tunnel studies, a divergent instability (galloping) was

found to be developing well within the design wind speed range.

A number of alternative shapes were studied and discussed with the different members of the design

team.

The aerodynamically improved shape of the arch was then tested for a full range of wind directions

and wind speeds and found to be stable with regard to divergent instability.

REFERENCES

[1] BD 49/01 (2001). Design Rules for Aerodynamic Effects on Bridges. The Highways Agency.

[2] Tamura, Y., Suda, K., Sasaki, A. (2000). “Damping in Buildings for Wind Resistant Design”,

Proc. International Symposium on Wind and Structures for the 21st Century, Cheju, Korea,

26-28 Jan.

[3] Tamura Y. (2005). “Damping in buildings and estimation techniques”, Proceedings of

APCWE-VI, Seoul, Korea.