Principal Investigator: Dr Ana Ruiz-Teran, Imperial College London

Research collaborators:

Dr Alfredo Camara, Imperial College London
Dr Peter J. Stafford, Imperial College London
Professor Angel C. Aparicio, Technical University of Catalonia

Background, context and methodology

Accidental and extreme loading (such as sudden breakage of stay cables, and seismic loading, etc.) may govern the design of cable-stayed bridges. Our research has been focussed on the response of cable-supported bridges under these two types of accidental loading.

Sudden breakage of stay cables

Verifying the capacity to sustain accidental breakage of stays is an essential requirement within design of cable-supported structures. In order to verify this requirement, codes and guidelines for the design of cable-supported structures have traditionally recommended the analysis of the sudden breakage, or loss, of a cable, through static analysis amplified by a dynamic amplification factor equal to two [1-4].

However, it has been demonstrated, analytically and numerically [5-7], that using equivalent static analysis with dynamic amplification factors equal to two provides an upper bound only for single degree of freedom systems, but not for multiple degree of freedom systems. For multiple degree of freedom systems, dynamic amplification factors larger than two occur, and consequently proper dynamic analyses are necessary in order to obtain the responses in an accurate and safe manner [5-7].

Fig 1. Comparison between the bending moment envelopes in the deck obtained with dynamic and pseudo-dynamic analysis. Case: breakage of one stay cable in the 2-strut bridge when the deviators have clamps and no traffic load is applied. The areas where the pseudo-dynamic analysis provides a smaller response than the dynamic one have been shaded [6]
Fig 1. Comparison between the bending moment envelopes in the deck obtained with dynamic and pseudo-dynamic analysis. Case: breakage of one stay cable in the 2-strut bridge when the deviators have clamps and no traffic load is applied. The areas where the pseudo-dynamic analysis provides a smaller response than the dynamic one have been shaded [6]

This contribution is applicable when comparing the dynamic and static application of loads in structures, and it is particularly valuable for the analysis of the sudden breakage of stay cables in cable-supported structures. Very detailed research studies, analysing the breakage of stay-cables using finite-element time-history analyses (realistically capturing the behaviour of the bridges in these accidental scenarios), and performing comprehensive parametric studies, have been performed [5,7].

This numerical work has been focussed on the sudden breakage of stay cables in under-deck cable-stayed bridges, demonstrating that pseudo-dynamic analyses (traditionally recommended by design guidelines worldwide, and used in industry and research) are inaccurate and unsafe. In addition, design criteria in order to enhance the resistance of this bridge type under the sudden breakage of stay cables have been provided.

Some design guidelines have subsequently modified their prescriptions related to the sudden loss of stay cables [8], and some include comments making the readers aware of the existence of recent research proving the inappropriateness of the traditional approach based on pseudo-dynamic analyses with dynamic amplification factors equal to two [9], suggesting the convenience of performing further numerical dynamic nonlinear analysis [8-9].

After this initial research (the first one that has demonstrated why the dynamic amplification factors are larger than two), other research groups have also produced publications analysing the sudden breakage of cables in conventional cable-stayed bridges and in other types of cable-supported structures.

Seismic response of cable-stayed bridges

Under-deck cable-stayed bridges are significantly lighter than other conventional schemes used for short and medium spans. Several footbridges with this structural type have been built in Japan and other areas where the seismic action is relevant.

Combining the different expertise in the bridge engineering research group and within the Structures section, the seismic response of under-deck cable-stayed bridges have been studied [10]. Through comprehensive parametric analyses using nonlinear finite-element models, the excellent performance of these bridges in comparison with conventional schemes has been demonstrated, opening a new research field in seismically-prone areas.

This latest contribution provides design guidance and accurate new intensity measures for bridges with significant multi-modal response.

Figure 2. Distribution of the extreme total strain [%] of the deck along its length (Earthquake (EQ) + Self-Weight (SW) + superimposed Dead-Load (DL) + 20% Live-Load (LL)) with each natural record included in the set of Eurocode 8 seismic action. Concrete cracking, elastic and ultimate limits strains are included. Two struts and LEB supports. [10]
Figure 2. Distribution of the extreme total strain [%] of the deck along its length (Earthquake (EQ) + Self-Weight (SW) + superimposed Dead-Load (DL) + 20% Live-Load (LL)) with each natural record included in the set of Eurocode 8 seismic action. Concrete cracking, elastic and ultimate limits strains are included. Two struts and LEB supports. [10]

References

[1] Eurocode 3: Design of steel structures. Part 1.11: Design of structures with tension components. Brussels (Belgium): European committee for standardization, CEN; 2006.

[2] Eurocode 1: Actions on structures. Part 1.7: Accidental actions. Brussels (Belgium): European committee for standardization, CEN; 2006.

[3] Recommendations for stay cable design. Testing and installation. Phoenix (Arizona): Post-Tensioning Institute, PTI; 2001

[4] HaubansRecomendations de la commission interministérielle de la précontrainte. Bagneux Cedex (France): Service d'Études Techniques des Routes et Autoroutes, SETRA; 2001 [in French].

[5] Ruiz-Teran AM (2005). Unconvential types of cable-stayed bridges. Structural response and design criteria. Doctoral thesis. University of Cantabria.

[6] Ruiz-Teran AM, Aparicio AC (2007). Dynamic amplification factors in cable-stayed structures. Journal of Sound and Vibration 300(1-2): 197-216

[7] Ruiz-Teran AM, Aparicio AC (2009). Response of under-deck cable-stayed bridges to the accidental breakage of stay cables. Engineering Structures, 31(7): 1425-1434

[8] Recommendations for stay cable design. Testing and installation. Phoenix (Arizona): Post-Tensioning Institute, PTI; 2007

[9] Manual of stay cables. Madrid (Spain): Asociación Científico-Técnica del Hormigón Estructural, ACHE; 2007 [in Spanish].

[10] Camara A, Ruiz-Teran AM, Stafford PJ (2013). Structural behaviour and design criteria of under-deck cable-stayed bridges subjected to seismic action. Earthquake engineering & structural dynamics, 42(6): 891-912