US Memorial Impact Dampers May2012 DanPowell

14 TheStructuralEngineerMay 2012

Project Focus

US Air Force Memorial

The United States Air Force Memorial Use of impact dampers to control wind induced vibrationsSynopsisThe United States Air Force Memorial (USAFM), overlooking the Pentagon in Washington DC, comprises three stainless steel spires which evoke an image of aircraft in a bomb-burst manoeuvre. The elegance and simplicity of their architectural form belies the complexity of their engineering design. Structurally they consist of a stiff ened stainless steel shell with the lower two thirds of each lled with concrete. A second component, essential to the integrity of the structure, is also hidden by the steel skin; a series of large, steel-coated spheres, free to roll in oversized padded boxes, are located inside each spire. The purpose of these impact dampers is to stabilise the motions of the spires in high winds. This article provides an overview of the spire structures and focuses on the challenges encountered during the design, development and test of the damping devices.

Project historySituated at the summit of a natural ridge overlooking the US Pentagon, and adjacent to Arlington National Cemetery in Washington DC, the Air Force Memorial evokes the spirit of ight through its stainless steel spires (Fig. 1). The memorial, conceived by the late James Ingo Freed of architects Pei, Cobb, Freed & Partners (PCF&P), was inspired by the US Air Force Thunderbird F-16s bomb burst ight manoeuvre (Fig. 2).

The road to the construction of a memorial to the United States Air Force was a long one. Arup began work with PCF&P on the design of the memorial in 1997. This original design was for a site just north of Arlington National Cemetery near the Marine Corps Iwo Jima Memorial.In 2001, Congress relocated the site to land adjacent to the Navy Annex buildings. The Air Force Memorial Foundation, a private organisation formed to lead the design and construction of the memorial, launched a second international competition; Arup again entered the competition with PCF&P and won the design commission for a second time.

From the earliest design meetings with Mr Freed, it was clear that the spires were to be as sleek and as slender as possible in order to maximise the impact on the observer. The

Air Force Memorial Foundation was led by retired Air Force Major General Edward F. Grillo Jr.

Overview of the structureThe spires range in height from 61 to 82m with the tallest spire only 4.2m wide at the base. The geometry of each spire was derived from the intersection of a horizontally oriented cylinder which forms the spires back surface and two opposing, horizontally oriented and intersecting cones. The resulting shape is a curved spire whose triangular section tapers towards its tip. The tapering triangular shape of the spires was formed by bending and welding 19mm stainless steel plates. As two faces of each spire are sculpted along conical surfaces, these surfaces are in fact warped out-of-plane, creating an added degree of complexity to the form. The pro le of the tallest spire was devised such that the combination of its slenderness, curvature, overhang, and the extent of internal reinforced concrete, serves to balance the structure about its base. This approach ensures that the foundation beneath the tallest spire is uniformly compressed under the structures self-weight, minimising the potential for diff erential settlement with time and, ultimately, reducing

TSE5_14-18_USairforce.indd 14TSE5_14-18_USairforce.indd 14 23/4/12 15:21:4623/4/12 15:21:46

Figure 1 The United States Air Force

Memorial, Washington DC

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the The United States Air Force memorial (USAFM), overlooking the Pentagon in Washington DC, comprises three stainless steel spires which evoke an image of aircraft in a bomb-burst manoeuvre. The elegance and simplicity of their architectural form belies the complexity of their engineering design. Structurally they consist of a stiff ened stainless steel shell with the lower two thirds of each lled with concrete. A second component, essential to the integrity of the structure, is also hidden by the steel skin; a series of large, steel-coated spheres, free to roll in oversized padded boxes, are located inside each spire. The purpose of these impact dampers is to stabilise the motions of the spires in high winds. This article provides an overview of the spire structures and focuses on the challenges encountered during the design, development and test of the damping devices.

Load demands on the foundations anchors, baseplates and caissons. Early in the evolution of the memorial it was decided that the spires would embody their true structural expression. No architectural cladding would shroud the monument. The stainless steel structural skin itself would instead be ground smooth and ush, bead-blasted, polished, and etched under an exacting litany of procedures to ultimately become the face of the monument with full penetration welds speci ed for all spire plate connections to improve fatigue performance.

The spires were fabricated off -site in 12m segments. Each spire was pre-assembled in thefabrication shop to ensure satisfactory alignment prior to delivery to site (Fig. 3). During erection, the lower two-thirds of each spire were lled with high-strength (80MPa) concrete to increase their stiff ness (Fig. 4). The composite concrete sections are heavily reinforced to further increase their bending stiff ness; the total amount of internal reinforcement gradually reduces with the height of each spire. Each piece of internal reinforcing steel was mechanically spliced to provide the most secure and direct load path through the body of the spires. Above the concrete zone, there is a transition zone of concrete piers, or ngers, located in the corners. Above the transition zone, the segments are hollow with internal stiff eners.The spires are founded on deep belled caissons in order to evenly distribute their overturning forces. The caissons are grouped in pilecaps 10 caissons for the tall spire, eight for the medium spire, and six for the short spire. The three pilecaps are in turn joined together by triangulated grade beams that ensure that the foundation system is engaged as a monolithic whole. Each spire



Project Focus


terminates in a base plate with an anchor plate deeply embedded in the pilecap below.

Wind induced motionsTall slender structures such as the USAFM have an inherent susceptibility to wind induced vibrations. As the monuments function is purely aesthetic, provision in the design for controlling wind induced motions had to be particularly sympathetic to the structures appearance. In practice this meant there was little scope for reducing the slenderness to any signi cant degree or making a favourable adjustment to the aerodynamics.

The USAFM spires have a triangular cross section; such cross-sections have a vulnerability to the aeroelastic instability known as galloping. Across wind galloping is a phenomenon which occurs for non-circular sections in which, for certain oncoming wind directions, the uctuating transverse aerodynamic load (the lift) acts with structural motion rather than against it. Under such conditions, energy is added into the dynamic system by the wind with potential to develop large unstable de ections. The wind tunnel tests conducted at an early stage of the design con rmed that the spires could indeed gallop in their fundamental sway modes at winds well below the site design wind speed. This eff ect needed to be addressed to reduce the predicted de ections and associated loads on the structures. The galloping was predicted in a number of speci c oncoming wind directions. The spires have equal bending stiff ness about their two principal bending axes and were therefore predicted

to have the same fundamental natural frequencies in all sway directions.

The expectation was therefore that the galloping excitation would excite the same modal frequency for all the vulnerable wind directions. The large deformations resulting from galloping could result in strength or rapid fatigue failure of the structures. A common solution for structures with a potential galloping problem is to adjust their aerodynamic pro le such that the structure remains inherently stable.

However, given the constraints on the appearance and slenderness of the USAFM, galloping had to be countered by modifying the structural dynamics or, more speci cally, by increasing the damping. Although added damping was essential, the structural form of the spires restricted the number of damping options which could be implemented. For example, after installation, access to the voids in the top section of the spires would be restricted. Hence this precluded the use of tuned vibration absorbers as there would be no access for initial tuning or any subsequent maintenance. It is also questionable whether devices which rely on accurate, long-term tuning should be used to ensure structural integrity in concrete and composite structures where there is potential for long-term shifts in the natural periods. Similarly, there is limited scope for using viscous or friction dampers on monolithic structures such as the spires, where there is an absence

of points in close proximity which exhibit signi cant relative movement. Such dampers work by resisting the relative velocities between diff erent parts of the structure.

The USAFM solution was to design and install a set of impact dampers or ball-in-box dampers within each of the spires (Fig. 5). Each damper consists of a 750kg, 0.5m diameter sphere, free to roll in a steel box. The spheres are steel coated lead to provide enough mass but with reduced size, the internal vertical surfaces of the boxes are coated with synthetic rubber. When the spires vibrate, collisions occur between the inside of the box, which moves with the structure, and the free rolling ball. Each collision dissipates energy and thereby provides damping. The tallest, 80m, spire has a stack of six damper boxes, the middle spire four and the shortest spire three. The dampers are installed approximately three quarters of the way up each of the spires adjacent to the concrete transition zone.

Impact dampers are generally only practical for modest levels of additional damping; say a maximum 2 to 3% of critical. But by calculation, each of the spires required only in the order of 1% of critical damping to ensure stability (i.e. prevent build up of excessive de ections). Impact damper effi ciency, in terms of added damping per mass of damper, is lower than for a tuned vibration absorber and in addition the noise of impacts can be unattractive for some applications. However,

N Figure 2Thunderbird F-16s

executing bomb-burst manoeuvre

N Figure 3 Pre-assembly of spires during fabrication

E Figure 5 Schematic of impact damper and location in monument


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impact dampers have other characteristics which increased their suitability for the USAFM, principally:- Provided the metallic and elastomeric components are designed for fatigue, impactdampers should be service free for the design life of most structures.- Impact damper eff ectiveness is insensitive to shifts in the structures natural frequency.

Thus, the impact dampers could be pre-installed in the steel sections prior to erection and the subsequent restricted access could be managed by appropriate design.

Impact damper design considerationsThe performance of impact dampers depends principally on three dimensionless parameters:- The ratio between the damper ball mass and the mass associated with the structural mode/s of vibration being damped. The additional damping developed increases linearly with this ratio.- The coeffi cient of restitution describing the energy dissipation in each collision.- The gap ratio, which is the ratio of the amplitude of structure motion, at the location of the dampers, to the clearance between the ball and enclosing box in which it is free to roll.

The gap ratio has to be correctly sized if impact dampers are to work effi ciently. If the clearance is too great, collisions between the ball and box are intermittent and the energy dissipation per cycle of structural sway motion is relatively low. If the gap is under-sized, multiple collisions may occur

per cycle but the collision velocity, and consequently energy dissipation, is low. Optimum performance of impact damper is achieved by sizing the system so that, under design operating conditions, two collisions occur per cycle of structural oscillation and the ball and structure are approximately 90 out of phase as illustrated in Fig. 6. For operation in this mode, the gap is typically a half to three times the amplitude of motion of the structure at the location of the box. Maximum damping is achieved when this ratio is in the range two to three. The existence of these diff erent modes of operation means the damping off ered by impact dampers is highly non-linear i.e. it depends strongly on the amplitude of structural vibration. The theoretical variation of additional damping to amplitude of vibration is illustrated in Fig. 7. As a consequence of this speci c range of amplitudes for which impact dampers are most eff ective, it was important in the case of the USAFM to ensure structural stability was maintained at the peak spire displacements, which could be expected to precede galloping. These displacements were taken to be the peaks from buff eting of the spires derived from the wind tunnel test data. Buff eting is the build up of displacements due to sequential gust loading at a structures natural frequency.

Although the proportion of energy dissipation during each collision governs the damper performance to some degree, there is limited scope for tuning this as part of the design process because suitable commercially available elastomeric materials

tend to have a fairly narrow range of impact dissipation characteristics. The principal concern in designing the impact pads for the spires was limiting their peak strain to a level below which the elasticity of the synthetic rubber did not degrade. To assist, damper pad assemblies were clad with a stainless steel contact plate to prevent erosion or tearing of the synthetic rubber during collisions. For the fundamental modes of vibration of cantilever structures (such as the spires), damping devices operate more effi ciently if they are higher up the structure where the mode shape value and motions are greater. In the USAFM there was insuffi cient space for the dampers near the spire tips due to their taper. The dampers therefore had to be located at a lower elevation, approximately three quarters of the way up, with the reduction in eff ectiveness compensated for by additional damper mass. Moreover, the geometry did not allow suffi cient conservatism with steel spheres; hence, lead was favoured with a steel casing to prevent deformation during impact.

Theoretical predictions of impact damper performance can be derived for a few idealised cases. However to obtain a more complete understanding of the design sensitivities and ensure a robust system, a transient simulation of the structure and damper system was developed using rigid body dynamics and modal vibration theory. The simulation tool was used to nalise the geometry of the impact dampers prior to detailed mechanical design of the boxes and damper pads. This simulation represented

E Figure 6 Schematic of dampers

under mode of optimum

operation

W Figure 4 Overview of

structural scheme

E Figure 7Plot of

damping against

amplitude for impact

dampers on 82m spire

derived from laboratory

tests



Project Focus


the galloping eff ect by applying a negative damping constant to the structure. One phenomenon for which the simulation was particularly helpful was in assessing the eff ect of higher frequency modes on vibration of the whole system. When impacts occur in the dampers, energy is not only transferred to and from the fundamental mode for which the dampers are intended to be active, it is also transferred between the fundamental mode and higher modes. In the case of the USAFM, the modes above the fundamental (measured frequency = 0.57, 0.70 and 1.00Hz for the tall, medium and short spires, respectively) which receive energy from the impacts, are resistant to galloping as they have positive aerodynamic damping at high wind speeds. They therefore tend to dissipate the energy transferred to them adding to the overall stability of the spires.

The numerical analysis was able to demonstrate that the proportion of input energy which transferred to higher modes during build up of the fundamental bending mode would only be of the order of 10%. Nevertheless, this level of transfer was suffi cient to increase conservatism in the design without leading to concerns about the stresses induced by any vibration in the higher modes.

TestingTwo programmes of testing were conducted on the impact dampers: laboratory tests were performed on a single damper unit prior to its

installation in the largest spire and site tests were performed on the completed structures to con rm that the required levels of damping had been achieved.

The laboratory tests, performed on a shake-table at State University of New York at Buff alo, were programmed to mimic the sway of the spires during high winds. The damper box was mounted on the shake table via load cells such that the forces the damper applied to the structure during sway motions could be recorded and the energy dissipated calculated. A photograph of the experimental set up is shown as Fig. 8. The accumulated energy dissipation from one of the laboratory tests and equivalent results predicted by the simulation tool are illustrated in Fig. 9. These, and other well correlated results, provided con dence in the design procedure which had been employed and in the robustness of the design. Acoustic tests were also conducted at the laboratory; these demonstrated that the noise of the impacts would be indiscernible over the background noise at the site. Site tests (summarised in Table 1) were conducted prior to the opening ceremony for the memorial when the spires were structurally complete. In these tests, the spires were dynamically excited in their fundamental nodding mode by a hydraulic system connected to the tip of each spire via a vertical steel cable. Once a prescribed amplitude of motion had been attained, equal to the maximum dynamic displacement which could precede galloping conditions, the loading was removed so allowing the oscillation of the spires to decay. Monitoring of the decay time histories then

W Figure 8 Laboratory test set up at State University New York

allowed calculation of the damping in the fundamental mode of each of the spires. In practice, the combination of inherent damping in the spires and damping provided by the impact dampers was observed to restrict the achievable amplitudes of motion of the spires. Nonetheless, the tests provided con dence that the design levels of damping were comfortably exceeded in all three spires.

ConclusionsThe slenderness and form of the United States Air Force Memorial provided considerable engineering challenges. The design and installation of impact dampers allowed the architects vision of the monument to be realised without compromise. The performance of the impact dampers was veri ed by site test and no abnormal wind induced behaviour of the structure has been observed over the last ve years. The result is a striking monument be tting its signi cance and location. The memorial was accepted by President George W. Bush on behalf of the USA in October 2006.

Daniel Powell, MA, MSc, CEng, MIMechEAssociate, Arup, London, UK

Patrick McCaff erty, BSc, MEng, PE, MASCEAssociate, Arup, Boston, USA

E 1 Simiu, E. and Scanlan, R. (1996) Wind Eff ects on Structures: Fundamentals and Applications to Design, 3rd ed. New York: John Wiley & Sons, pp. 230-236

E 2 Caughey, T. and Masri, S. (1966) On the stability of the impact damper, J. Appl.Mech., 33 (3), pp. 586-592

E 3 Argiris, L., Jackson, A., McCaff erty, P. and Powell, D. (2007) Engineering the United States Air Force Memorial Washington DC, Arup J., 41 (1), pp. 24-31

Bibliography

Spire height

Measured natural frequency (Hz)

Measured modal damping (% critical)

Target damping (% critical)[based on site measured mode shape]

61m 1.00 2.4 0.90

70m 0.79 1.8 0.95

82m 0.57 1.2 0.82

Table 1 Summary of site test measurements

E Figure 9 Plot of predicted upper and lower bound energy dissipation and energy dissipation recorded in laboratory tests


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US Memorial Impact Dampers May2012 DanPowell

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