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| Air Force Memorial |
Engineering the United States Air Force Memorial, Washington DC
"Building this Memorial took a lot of talent and creativity and determination. Like the aircraft whose flight it represents, this Memorial is an incredible feat of engineering"
President George W Bush
Perched high atop a natural ridge overlooking the Pentagon and adjacent to Arlington National Cemetery in Washington DC, the Air Force Memorial evokes the spirit of flight as its three glimmering stainless steel spires appear to soar to the heavens. Designed by the late James Ingo Freed of Pei Cobb Freed & Partners and engineered by Arup, the Memorial was inspired by the US Air Force Thunderbird F-16 fighter jets' "bomb burst" flight manoeuvre.
Structural Form
Limited by the maximum height restrictions mandated by the Federal Aviation Authority due to the Memorial's close proximity to Reagan National Airport, the spires vary in height from 270ft (82.3m) to 200ft (61m) - the tallest is only 13ft 9in (4.19m) wide at its base.
The geometry of the tallest spire derives from the intersection of a horizontally-orientated cylinder (which forms the spire's back surface) and two horizontally-orientated and intersecting cones that oppose each other (the intersection of which forms the spire's leading edge). The resulting shape is a curved spire whose triangular section tapers towards its tip. Each of the two smaller spires is formed by the successive rotation of the tallest about its conical axis by specified angles.
The three spires are founded on a common triangular grade beam bearing on groups of caissons. This system ensures monolithic behaviour of the structure under lateral loads.
Superstructure Design
The curving, tapering shape of the spires is formed by bending and welding 3/4in (19mm) stainless steel plates into the tapering triangular shape. 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 nuanced form.
The spires were fabricated off-site in 40ft (12.2m) segments. In the lower two-thirds of the each spire, the segments are filled with high-strength (12ksi / 80MPa) reinforced concrete for increased stiffness. Above the concrete zone, there is a transition zone with concrete piers, or "fingers", located in the corners. Dampers were included in this section to reduce the spires' susceptibility to galloping wind excitations. Above this the segments transition to hollow stainless steel with internal stiffeners.
At every turn during the design process, the engineers were challenged to make the spires ever more slender. Conscious that every inch shaved from their profiles served to push the monument ever nearer the precipice of instability, the Arup team was nonetheless able to demonstrate through advanced non-linear structural analysis, dynamic computation, rigorous laboratory testing, and ultimately field testing that the intended slenderness was in fact achievable.
Structural Analysis
The spires' curved shape makes them tend to flex and slightly compress under their own self weight, stresses that are exacerbated at times by wind loads. When the bending stresses exceed the axial compressive stresses, the internal concrete cracks slightly. The orientation and degree of this cracking directly impacts the spires' effective stiffness along their height.
The magnitude of dynamic wind load the structure experiences is a direct function of its natural frequency, which is proportional to its mass and stiffness. Since the shape and materials of each spire establish its mass, the wind loads are a function of its stiffness.
The spire's stiffness is a function of the degree of cracking within the internal reinforced concrete, which in turn is influenced by the total effective wind load imposed on the structure. A degree of iteration was therefore required to properly assess the true structural response of the spires to wind load.
The iterative analytical procedure was thus to:
- create a GSA analytical model of the whole spire based on the assumed cracked cross-sectional stiffness at discrete segments along the height
- compute the spire's natural frequency based on the assumed cross-sectional stiffness
- calculate the anticipated magnitude of wind pressure acting on the spire as a function of the spire's assumed natural frequency
- apply the wind pressure to the GSA stick model and obtain internal axial and flexural forces at discrete segments along the spire's height
- perform non-linear computational structural analyses on GSA 3D cross-sectional models of each spire segment (comprising of concrete struts and steel bars), applying the axial and flexural forces determined in (4) to each segment in turn; using first principles of structural mechanics and Euclidean geometry, determine the effective bending stiffness of each cross-section under each wind load case
- modify the analytical stick model with the revised cracked cross-sectional stiffnesses
- repeat from (2) until the process converges on the calculated spire natural frequency, wind load, and resulting internal stiffness.
Regarding the 3D cross-sectional model analysis, Project Manager Patrick McCafferty said "I wish that we had AdSec at the time. It would have made our lives a lot easier".
This procedure was repeated to determine the internal forces acting on all three spires. Once identified, these forces were then used to size and detail all aspects of the spires, including final skin thickness, internal reinforcement quantities, and anchor bolts.
Conclusion
The simple elegance of the Air Force Memorial belies the complex engineering mechanics that describe its behaviour and response to the environment. The intended aesthetic of the monument was preserved through the combination of advanced structural analysis applied to an innovative solution of custom-designed passive impact dampers. In so doing, the architect's vision of a soaring memorial to the United States Air Force was achieved.
