In building construction, the structural system generally takes the form of a single-span beam, whose vibration behaviour can, in simple terms, be described by a single degree of freedom system (Figure 1: dynamic model). In typical composite structures, inherent damping (logarithmic decrement) is only δ = 0.06.
Given this relatively low self-damping factor, the natural frequency of the system must be increased to avoid perceptible vibrations. Load-bearing structures beneath assembly rooms and dance, sports or exhibition halls should have a natural frequency f of at least 5 Hz, without additional vibration-damping measures. One way of meeting this requirement would be to weld heavy steel reinforcing plates to the bottom flange of wide-span steel beams (Figure 1).
However, rather than increasing the system’s natural frequency f, a far more efficient approach would be to dampen the perceptible vibrations by reducing the acceleration amplitude az.
According to the literature, the maximum acceleration amplitude az in a normal workplace setting is 0.03 m/s².
In order to reduce the acceleration amplitude az, the damping δ must be substantially increased. This can be achieved with vibration dampers (Figure 2). These improve the vibration behaviour significantly and permit smaller natural frequencies f. However, additional vibration dampers come with increased costs, require extra space and are visually disruptive.
The idea behind the vibration-damped composite girders (Figure 3) is that they rely on the steel weight already present within the structure itself to provide additional vibration damping.
The structural system of a vibration-damped composite girder corresponds to an underspanned beam. The ends of the tie bar are welded to the beam, so the bar is involved in load bearing. The tie bar is attached to springs connected to the beam at intermediate points, which are themselves damped. The bar thus acts as a damper mass, significantly increasing the vibration damping δ of the system with the aid of the springs.
Vibration-damped composite girders can take various forms:
During the second construction phase of the two-storey Exhibition Hall A in Berlin, we constructed 229 beams as vibration-damped composite truss girders.
To increase the natural frequency to 5 Hz, the bottom chord of the girder was reinforced with an additional cover plate during the first construction phase, increasing the weight of steel to approximately 18 tonnes per girder. Despite achieving a natural frequency of 5.2 Hz, the vibration behaviour was not ideal – people experienced discomfort due to the low self-damping.
So we adopted a different approach during the second phase of construction and used the vibration-damped composite beams for the first time.
Due to the increased system damping, the optimised beams achieved a natural frequency of 3.8 Hz, resulting in optimal dynamic behaviour without perceptible vibrations. This solution also decreased the weight of steel by around 45 percent to approximately 10 tonnes per beam.
Solid-web beams may be constructed with architectural appeal, such as the gently curved ‘fish belly’ beams used in the Rudower Straße construction project in Berlin, or as normal welded beams with parallel flanges. The tie bar can run below the bottom flanges or on either side of the web. With the second option, it is easy to fasten box-shaped fire protection boards to the entire beam cross-section.
The vibration-damped composite girder system can be tailored to suit the aesthetic or economic requirements of the project.
Our vibration-damped composite girders are protected by patent law.
