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Bridge Girder Movements

Neighbouring structures can get damaged due to pounding if they are too close to one another. Even with the added research done and the extra recommendations recently included, the pounding damage in the bridge girders is still a major observation when earthquakes occur. The recent regulations have a recommendation that these adjacent structures need to be properly separated to avoid colliding the recommendation is made from the assumption of experience of similar ground excitation (Lee & Stuart, 2013). Also, their behaviors are produced form the study of structural properties. If one takes the case occurring in nearby buildings, the taken assumption regarding similar ground excitation can be justified. Caution needs to be taken on the various footing properties together with the non-uniform conditions on the ground. Interactions between the concerned subsoil and buildings. In the cases of many constructed bridges, the use pier supports is another reason that can lead to the production of the out-of-phase response of the adjacent spans of bridges. In cases that relate to the later, using current recommendations of designs can lead to an adverse effect (Sven, et al., 2013). The use of minimum spacing between structures is a major measure that allows avoidance of pounding damage. When bridges are concerned, using large spacing between neighboring girders will heavily affect the usage of traffic across them. The adjusting of fundamental frequencies in adjacent bridge structures could fail to be a good method that is sufficient or better suited to the approach to reducing out-of-phase responses. This is due to the feature of bridge structures to have the tendency of experiencing non-uniform spatial ground excitation (Parag, et al., 2001). This proposal aims at designing a new philosophy on the bridge girders.

Various sources induce movement relative to girders, they are; ground motion spatial vibration, uneven vibration properties in nearby structures of bridges and the variation of the interaction of soil structures due to the shifting properties of soil at the supports of bridges due to the variety of slenderness ratio and footings in neighboring bridge piers (National Research Council, 2006).

The forces of inertia are activated by the excitation vibration in the constructed structure. If say the structure put up is low, the footing of such a construction is most probably to move laterally from one side to another.  Movements like these initiate pressure waves at either footing sides together with the development of shear waves coming from the lowers interface of the structure footing. When such movements are experienced by tall structures, the concerned structure rocks at its footing due to the movement that leads to the whole structure bending (Jinrong, 2010). Movements in the footing mainly activate the pressure waves in either foot edges together with the development of shear waves in the same footings. Taking note that when a footing vibrates waves are produced, various footing movement lead to various wave propagation and also a variety of soil stiffness dynamics and damping in radiation will be developed (Anon., 2007).

Long-extended structures such as bridges are majorly influenced by the role of soil. Recalling that seismic waves require some duration to move from a footing bridge pier to the next support pier, exaction of grounds at the nearby support experience some delay. Also, the properties of soil in support of bridges are non-uniform and heterogeneous. This, therefore, means that the motions in the ground in the concerned support is incoherent (Teen-Hang, et al., 2013). Also, the structural response to the varying spatial ground excitation is not similar to the common ground motions that are uniform. Bridge structures have spatial variations that lead to a variety of relative response between the nearby bridges segments like the ones put under the assumption of bridge segments experiencing similar ground motion (M., et al., 1996).

Design Parameters

Taking note that any nearby bridge segment varies in slenderness, though they are from similar fundamentally fixed frequency base and are influenced by similar ground excitation with bridge pier subsoil being uniform in their properties, the response between the bridge segments will occur. Such a situation is due to the different interaction in the structure of a bridge with supporting soil. Each bridge structure can respond differently leading to relative movements individually. The soil influence on period Ti in the bridge system can be found using the equation below (Standards, 1968);

This where Ti has assumed fixed-base. The influence coming from the stiffness in vertical soil is set to be negligible. The actual situation is that soil stiffness is dependent on frequency thereby making the subsoil influence more complex. The equation and the diagram that is to follow indicate that even with both segments in a bridge having similar fixed-base in the fundamental period represented as T1 = T2 and similar ground support represented as k1x = k2x and k1Φ = k2Φ, a difference in height of structures will lead to a difference in system periods. Also, the bridge will react differently whether the ground excitation is similar or not (Standards, 2008).

Experiment.

Lately, there has been a cope in thermal contraction and expansion in long bridges and extra Modular Expansion Joints are being used. The diagram below shows a two-segmented bridge with an MEJ. 

The joint cross section of put in a longitudinal bridge direction. The segments of the bridge are connected using edge beams together with rubber bearings that transfer the traffic load from joints to nearby bridge girders. Water tightness is then ensured by installing rubber sealing between the beams. Using the bridge bearings will ensure that the concerned beams have a uniform movement (Mohiuddin, 2013).

The combination of the influence of SSI, the apparent velocity of the wave ca together with the coherent loss total mean minimum MEJ gap values are needed so as to prevent girder pounding (Publications, 2010).

The overall gap gc is an addition of every gap between the beams of MEJ. When a uniform excitation in the ground and structures have fixed bases, the least gap gc will be 059 cm. the result is an expectation from the fact that the structures have fixed bases with same fundamental frequencies (Helmut, 2008). Subsoil effect can be considered meaning that the gap that is needed is not equal to the expected value. Though the structures in exclusion of the SSI have similar frequencies and they experience equal ground excitation, these bridge structures differently interact with the ground. Unevenness in the SSI effect leads to relative movements and causes greater minimum required in the total MEJ gap as 10.42 cm. the results indicate an assumed uniform excitation in the ground that underestimates the least total MEJ gap needed so as to prevent pounding, critical if this structure has a fixed base. In the wave, apparent velocity case that has a value 500 m/s the least total gap does not reduce with low coherency loss that might have been expected. These results, therefore, make it practical that the least gap in MEJ needs not to be related to one influencing factor since there is a combined influence that dominates (Dina & Enrico, 2008).

One factor that is not considered is the ratio fII/fI in fundamental frequencies fixed bases in closed structures. The feature of such a factor is influential in relative girder response as in the diagram below;

Enabling clear interpretation of factors that are considered makes the slenderness of the structure to be neglected. The adjacent structures are put to have the same height of 9 m. therefore, the girder movement that comes from the uneven interaction between the soil and the put up structures are not to be considered. The reference case structures having assumed base that is fixed is shown in the immediate diagram above on the left side. The results that come after directly indicate that the recommended current design regulation avoids relative movement of the girders by developing structures having similar fundamental frequencies that are not adequate. Actually, the fixed base ratio of frequency is not to be used as the only existing parameter in designing (Jean-Paul, 2007).

When frequency ratio is 1.0 the minimum overall gap needs not to be the smallest and should not be equal to a value zero. This design investigation takes the assumption that varying spatial ground motion is heavily correlated. Using a higher ratio of fII/fI higher than 1.15 influences the apparent wave velocity can be dominant. An expected minimum total gap in MEJ is therefore reduced as the wave speed increases (Administration, 2011).

Taking a range of low-frequency ratios makes no direct influence on the apparent wave velocity. The existence of high wave speed does not mean that the gap required is smaller since varying spatial ground motions induce dynamic and quasistatic responses. Structures that are relatively stiff, the dominating response is the quasi-static response. Hence making the frequency ratio to be higher than the 1.15 is made possible by increasing the bridge structure stiffness on the right and making no changes in the left structure of the bridge. However, if the structure in concern is flexible with a dynamic response domination, that’s heavily influenced by dynamic bridge properties and content of frequency ground motion. Comparing the results with the SSI or without the SSI indicates that an increase in effect from the SSI leads to an increase in the minimum gap in the MEJ gap that will ensure that pounding will not take place. This is a resulting indication of the importance of the combination of SSI, variation in spatial ground excitation and the fundamental frequency ratio of nearby structures in bridges (X.L. & R.H., 2000).

An insurance of good function of the MEJ, every seal between the beams of MEJ need not be overstretched during the opening of relative movement in the bridge girders. So as to achieve the intended goal, the MEJ should have a design with adequate centered beams to accommodate the relative movement without damaging the covering seals.

The diagram above displays the combined influence of the SSI together with the spatial variation in the ground excitation concerning mean values expected to be large in the opening movement go existing between girders in the bridge. When one assumes uniformity in ground excitation, a theoretical explanation is that there is no opening in a relative movement that will occur. This is due to the existence of both structural makeups having almost similar fundamental frequencies of about 0.99 each. However, the practical structures have different height and the subsoil vary in the influence on every structure. Also, there is unequal soil-structure interaction causing opening movement that is relative of about 10.4 cm. The diagram above shows a display of a solid line that is horizontal clearly indicating the importance of the effect of unequal soil structure (R.B., 2012).

Considering the influence of the apparent wave velocity, there is a large relative movement of girders that increase to 12.5 cm taking the value of ca be 500 m/s. This is similar to the total gap required in an MEJ to prevent pounding. The movement of girders does not increase the speed of wave indicating that there is a strong influence.

The results coming from the case entailing Ca = 500 m/s is a confirmation of the involvement of numerous factors in the development of the movement of girders. Contrasting to the expected large opening having relative movement of go being 12.5 cm is present. Taking the spatial varying excitation in ground produces the highest correlation. The weakly correlation in the ground motion does not cause the largest opening that is relative to the movement of girders but the 11.75 cm value, whereas an intermediate ground motion correlation produces smaller relative opening movement about 10.72 cm.

Focusing on the combined influence of SSI, the variation in spatial ground motions and ratio in the fundamental frequencies in adjacent structures leads to an assumption that both structures of bridges have an equal height of about 9 m with the motions in the ground having a high correlation. The combination of effect on large opening with a relative movement that is expected in MEJ is displayed on the diagram below. If there is a neglect in SSI effect, apparent velocity in spatial varying ground motion is dominating factor when the ratio of frequency is greater than 1. Though there is a decrease in the high-frequency ratio given the opening relative movement with the respective apparent velocity that is similar to gap required in avoiding girder pounding, the smaller opening relative movement does not happen when both the neighboring structures possess equal fundamental frequency ((U.S.), 1977).

Taking additional SSI consideration changes the result evidently. Generally, there are observations that amplify in averagely all cases in opening relative movement. In the higher frequency ratios higher than, with apparent velocity ca that is higher than the value 500 m/s did not reduce the opening relative movement that is constant at 7.6 cm. During low ratio in frequencies, the difference occurring in fundamental frequencies in neighboring structures of bridges have a significant influence on the developing large opening relative movement that is to be considered in designing of MEJ. The resulting SSI effect indicates that the recent design recommendation in using the existing frequency ratio as only design factor is very insufficient.

Designing MEJ, the least total gap needed and large opening relative movement are important. The middle beam number in MEJ need to be chosen to make the overall seals that are available amongst the MEJ beams together with total seals available to cover the gaps can shift with the closing and opening relative movement within the girders of the bridge structure.

Conclusion

The new design for preventing girders in bridges from pounding due to the earthquake is introduced in this project. Contrasting to the conventional bridge design having expansion joint that is characterized with small gap centimeters, the design in the discussion has Modular Expansion Joints that are installed to enable the adjacent girders in bridges can be featured with bog relative movement with lacking pounding that can lead to damage of the girders. The important specification is the use of minimum total gap joint. The design of MEJ gaps is such that the total gap in MEJ can shift with the expected largest closing relative movement. Another important specification is the highest opening movement that is relative that can be expected in the MEJ. The design is to make the bridge have the ability to shift with the movements without leading to causing damage to the seal existing the MEJ beams. The influence of the spatial ground motion, SSI and combination effect are discussed in the project. The recommendation in the current design regulation in adjusting fundamental frequencies in the adjacent structures of bridges does not mean production of small minimum gap required in MEJ when there in non-uniform ground motions with soft soil.

References

(U.S.), G. S., 1977. Geological Survey Professional Paper. 1 ed. Wagga Wagga: U.S. Government Printing Office.

Administration, U. S. F. H., 2011. SR 520 Bridge Replacement and HOV Project: Environmental Impact Statement. 1 ed. Melbourne: Northwestern University.

Anon., 2007. Seismic Bridge Design and Retrofit -- Structural Solutions: State-of-the-art Report. 1 ed. Sydney: FIB - Féd. Int. du Béton.

Dina, D. & Enrico, F., 2008. Structural Analysis of Historic Construction: Preserving Safety and Significance, Two Volume Set: Proceedings of the VI International Conference on Structural Analysis of Historic Construction, SAHC08, 2-4 July 2008, Bath, United Kingdom, Volume 1. 1 ed. Wollongong: CRC Press.

Helmut, W., 2008. Health Monitoring of Bridges. 1 ed. Adelaide: John Wiley & Sons.

Jean-Paul, K., 2007. Dictionary of Civil Engineering: English-French. illustrated ed. Perth: Springer Science & Business Media.

Jinrong, Z., 2010. Modelling and Computation in Engineering. 1 ed. Brsibane: CRC Press,.

Lee, M. & Stuart, J., 2013. Performance-based Seismic Bridge Design. illustrated ed. Sydney: Transportation Research Board.

M., J., Priestley, F., S. & G., C., 1996. Seismic Design and Retrofit of Bridges. illustrated ed. Cairns: John Wiley & Sons.

Mohiuddin, A., 2013. Earthquake-Resistant Structures: Design, Build, and Retrofit. 1 ed. Brsibane: Butterworth-Heinemann.

National Research Council, D. o. E. a. L. S. B. o. E. S. a. R. C. o. S. a. G. C. o. t. E. B. o. I. S. M., 2006. Improved Seismic Monitoring - Improved Decision-Making: Assessing the Value of Reduced Uncertainty. 1 ed. Sydney: National Academies Press.

Parag, D., Engineers, I. o. C. & Dan, F., 2001. Current and Future Trends in Bridge Design, Construction and Maintenance: Safety, Economy, Sustainability, and Aesthetics, Volume 2. 1 ed. Sydney: Thomas Telford.

Publications, U., 2010. Earthquake! Beyond Duck, Cover, and Hold. 1 ed. Darwin: UCANR Publications.

R.B., J., 2012. Advanced Dam Engineering for Design, Construction, and Rehabilitation. illustrated ed. Bendigo: Springer Science & Business Media.

Standards, U. S. N. B. o., 1968. NBS Special Publication, Issue 342. 1 ed. Sydney: The Bureau.

Standards, U. S. N. B. o., 2008. Publications of the National Bureau of Standards ... Catalog. 1 ed. Sydney: U.S. Department of Commerce, National Bureau of Standards, 1979.

Sven, K., Christoph, B., Gao, L. & Britta, H., 2013. Seismic Design of Industrial Facilities: Proceedings of the International Conference on Seismic Design of Industrial Facilities (SeDIF-Conference). illustrated ed. Brsibane: Springer Science & Business Media.

Teen-Hang, M., Stephen, P. & Artde, D., 2013. Innovation, Communication and Engineering. 1 ed. Cairns: CRC Press.

X.L., Z. & R.H., G., 2000. Structural Failure and Plasticity: IMPLAST 2000: 4-6 October 2000, Melbourne, Australia. 1 ed. Mackay: Elsevier.

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