Controlling movement and vibration in bridges suspended from a stadium roof
One of the world’s most famous sports and entertainment venues, Madison Square Garden is a large, round building with seating for about 20,000 spectators distributed around its perimeter. In 2009 the Garden’s owners decided to add additional fan capacity in an unusual location.
The owners planned to suspend the new viewing areas from the ceiling, installing two long bridges with seating along the length of the stadium – one on either side of the play surface. Suspending the bridges would avoid the need for support pillars, which could obstruct fan sightlines below.
Because Madison Square Garden’s roof is cable-supported and inherently flexible, hanging the bridges presented engineering challenges. The existing structures as designed could safely bear the required weight, but they’d be at risk of vibrating noticeably as people moved around on them, especially if fans were bouncing in time to music.
The new bridges themselves could be expected to move vertically and laterally, and also twist. Each moving part – roof, cables and bridges – had the potential to interact with the others multiple ways. The project’s engineers engaged us to help them understand this complex system and develop a mitigation strategy that would keep bridge movements at a comfortable level.
This was an unusual project for our damping systems specialists – and the tuned mass dampers (TMDs) we used to solve the problem were unlike any we’d built before. Having carefully assessed and quantified the problem, we installed five TMDs on each bridge: three closer to the middle of the building (center ice or center court) and two closer to the stadium’s perimeter.
Each TMD has an outer frame – a flat, rectangular case similar in shape to a longer-than-usual cereal box lying on its back – and a mass that moves inside. The mass is hinged at one end so it can only move up and down. Underneath the end that moves, we install six springs that are sized and placed to allow the mass to move at a specific frequency. We also add a mechanism that translates the vertical movement into lateral movement along the length of the TMD: as the hinged mass moves up and town, it engages a bellcrank system that translates the movement into two viscous damping devices (hydraulic shock absorbers).
The net effect of this system is to dissipate dynamic energy from the bridge’s structural system and prevent uncomfortable vibration. When spectators walk or jump and cause the bridge to start moving, the passive TMDs naturally lag behind the motion of the bridge and thus limit the bridge’s ability to build up any significant motion. They work together to absorb and dampen the movement caused by fans.
Because the bridges are thin and narrow, space constraints were a big factor in the design of the TMDs. For each damper, we needed five tons of mass to fit within a height of 14-1/2 inches – while leaving +/-2 inches’ clearance for the mass to move up and down. Although steel is often an economical choice in damping devices, in this case only a lead-filled box would give us enough mass in such a small space.
Our viscous-damper fabrication partners, ITT Enidine, also helped us meet the technical challenges associated with these space constraints. They were able to quickly adjust the properties of the fluid inside the hydraulic cylinders; being able to vary the fluid’s viscosity was vital to our ability to tune the TMDs so they’d have exactly the right amount of internal damping. The 10 TMDs are all similar devices, but each one is tuned to a slightly different frequency depending on its location in the system and the mode of vibration it’s intended to targeted.
Careful testing and monitoring before the facility reopened revealed that our TMDs were effective in controlling the bridges’ movements. Since Madison Square Garden reopened in 2013, spectators have comfortably enjoyed hundreds of sports and music events from unique vantage points on the new bridges overhanging the action. Soon after the renovated Garden opened, ESPN declared the suspended seating areas to be a hit with fans.