Trillingen van betonnen voetgangersbruggen / Vibrations of concrete footbridges

Abstract

Nowadays more and more slender concrete footbridges are designed. Footbridges are designed thinner to increase esthetic value, as well as incorporate sustainability and to reduce building costs, with a consequence that the eigenfrequency of the bridge can drop so low that it may fall into a range of frequencies that is susceptible to vibrations caused by human beings who move along the bridge. When the eigenfrequency of the bridge is nearly the same as the stepfrequency of a person who moves along the deck this may lead to large displacements of the bridge. In this report the consideration of comfort of short-length concrete footbridges is investigated and checked whether this forms a decisive criteria for the determination of the slenderness of the bridge. Requirements of strength and usage are not taken into account. In order to prevent discomfort of users there are demands for comfort compiled for footbridges. The guidelines being compared in this report are: • Expired standard since April 2012: ‘NEN 6723: Guidelines Concrete – Bridges – Constructive Demands and Designmethods’ • National Attachment Eurocode The Netherlands: ‘EUR 23984 EN – Design of Lightweight Footbridges for Human Induced Vibrations’ o Single Degree of Freedom Method (SDOFM) o Response Spectra Method (RSM) • National Attachment Eurocode France: ‘SETRA Guide – Footbridges – Assessment of Vibrational Behaviour of Footbridges Under Pedestrian Loading’ • United States Guideline: ‘AASHTO – LRFD Guide Specifications for the Design of Pedestrian Bridges’ In this comparison it is found that the design calculations according to NEN 6723 and AASHTO are based upon the relation between the eigenfrequency- and a minimum prescribed weight of the bridge, in which the NEN 6723 is based on the concrete material while the AASHTO is independent of the material being used. The requirement for comfort in standard NEN 6723 must be used when the eigenfrequency of the footbridge is below 5 Hz. Besides the rule mentioned, there must also be a load taken into consideration of 1.5 kN, which is not allowed to cause a deformation of 0.25 mm of the deck. Contrary to the AASHTO which additionally requires that the eigenfrequency of the system is at least 3 Hz. The Eurocode proposes to check comfort when the eigenfrequency of the system is below 5 Hz. Where allowable bridge deck acceleration limits are the basis for design criteria, and the calculation method is independent of the material being used. In this report only the vertical direction is considered, because the other directions do not lead to low frequencies that may cause discomfort. The National Attachment of The Netherlands recommends EUR 23984 EN guideline that determines the occurring bridge deck acceleration based upon the amount of pedestrians and also so-called joggers (running persons) present on the deck. The design calculations in EUR 23984 EN are the SDOFM and the RSM, where the SDOFM takes both pedestrians and joggers into account, while the RSM only takes pedestrians into account. The SDOFM is based upon the usage of a mass-spring system and states comfort has to be checked when one of the eigenfrequencies falls into the critical range, which is between 1.25 Hz and 4.6 Hz. In contrary, the RSM calculates the occurring acceleration with an empirical formula in case one of the eigenfrequencies is below 5 Hz (as prescribed in the Eurocode). The guideline SETRA was released earlier than the EUR 23984 EN and also uses the SDOFM. Comfort has to be checked when one of the eigenfrequencies falls in between 1 Hz and 5 Hz, in which case only pedestrians are being taken into account. No joggers are considered because of the assumption that joggers will be present on the bridge for only a short amount of time, which does not lead to discomfort of other users, and the crossing time of a jogger is less than the time required to resonate the bridge. The guidelines mentioned above are applied to the case study Hoevebrug which is an existing bridge. The Hoevebrug is a clamped slab bridge constructed in concrete class B65. The results are summarized in the table below. *A table has to be made from the text below* Guideline Slenderness [-] Percentage [%] NEN 6723 1 op 44.2 100 EUR 23984 EN – SDOFM – Pedestrians 1 op 90.3 204.3 EUR 23984 EN – SDOFM – Pedestrians and Joggers 1 op 61.4 138.9 EUR 23984 EN – RSM 1 op 42.1 95.2 SETRA 1 op 84.2 190.5 AASHTO 1 op 70.2 158.8 Subsequently a separate study of parameters is conducted for short footbridges with the aid of the SDOFM of guideline EUR 23984 EN. The lengths considered vary between 10- and 30 meters. The influence and response of the bridge are considered with parameters of density, Young’s modulus, length, imposition, and height, where the quantity of pedestrians present on the deck is taken to be 0.5 persons/m2 as the Eurocode prescribes. It is found that the second harmonic of pedestrians (the EUR 23984 EN describes this as the stepfrequency between 2.3 Hz and 4.6 Hz) does not lead to discomfort because of the small load being excited by the pedestrian. So it can be stated the second harmonic of pedestrians is not a criteria for the determination of the height of the deck. Joggers however lead in all cases to extremely high values of acceleration of the deck, because the joggers may be assumed to be placed on the deck where the displacement is expected to be the largest. To check whether the response due to joggers can be reduced, a more detailed calculation is considered. The jogger is modeled as a moving harmonic load in time on a deck that is hinged on both sides. Next the differential equation of the continuous system is established and solved. Hereby creating a relation between stepfrequency, velocity, and load of the jogger. Allowing for a more accurate estimation of bridge response, multiple situations of joggers moving along the bridge as a group are then considered and in many cases show the response of the deck is not very similar to the result obtained from SDOFM. In the case of the calculation method of the moving harmonic, the response of the deck will only be significant when the stepfrequency almost equals the eigenfrequency of the system. The conclusion requires that joggers satisfy the condition that every jogger must run with the same frequency across the deck, as well as the interval between the joggers (if present) is equal to the period of the stepfrequency. Besides this the process of an occurring acceleration in vertical direction in case of a person moving along the bridge is ‘self-limiting’. This means that a person is not able to move along the bridge when the occurring acceleration in vertical direction is too large. Because the person stops moving there will no longer be a dynamic load excited any more so that the construction will damp out.