The effect of push-pull rod on the dynamic behavior of movable bridges

Abstract

In the Netherlands the design of a movable bridge and machinery part is based on the design standard NEN 6786:2001 (2001). When the bridge is in motion the calculations for the machinery part focus on the dynamic loads (torque) generating at the motor shaft. The calculation of these loads is carried out using tabulated formulas of the standard, which have been derived via a 2-DoF linear dynamic model. In this model the linear spring represents the total stiffness of the machinery part. For the calculation of the spring stiffness the push-pull rod component is excluded, assuming it as a rigid component of the system during the movement cycle of the bridge. The push-pull rod (also known as the buffer) is a component of the machinery of several bascule bridges that connects the leaf of the bridge with the drive mechanism. It consists of stacked disc springs and its stiffness varies based on the load acting on it.The main objectives of this thesis are to model the force deformation behavior of the buffer component, incorporate it in an update set of equations of motion of the bridge-machinery system, and study its effect on the decisive dynamic loads generated at the motor shaft during motion. First, the generalized force deformation diagram of the buffer is formulated with a piecewise function that is based on the force-deflection function for a stack of disc springs according to the standard DIN 2092:2006:03 (2006). Second, the damping of the buffer is modeled as Coulomb friction type, since friction is generated in various position in the stack of disc springs and is the main source of energy dissipation of the buffer component. The validity of the proposed modeling of the buffer component is evaluated via a SDoF model of it, performing a series of dynamic analyses and interpreting the results. Afterwards, the model of the buffer component is introduced in a new set of equations of motion for the bridge-machinery system, derived with the Lagrangian formalism technique. The resulting highly nonlinear set of equations of motion is implemented in the bascule bridge of the new Ramspol bridge located on N50. The analyses aim to the calculation of the torque generated at the motor shaft during an emergency stop at full speed. This loading case is the most decisive with respect to loads generating at the motor shaft.The resulted maximum torque from the dynamic analyses is compared with the torque calculated with the formulas of the standard NEN 6786:2001 (2001). The state of the buffer determines by which formula of the standard the comparison is carried out. A series of dynamic analyses is performed varying, the type of brake (constant or bilinear), the time the brake is applied, the duration of the emergency stop and the friction coefficient of the buffer. In case the buffer is not fully compressed, the calculations with the dynamic model result in lower maximum torque compared with the one according to the standard. In case the buffer is fully compressed the magnitude of the resulting maximum torque depends on the aforementioned variables, whilst the one calculated with the standard is independent of them. In general, the resulting maximum torque derived from the dynamic model decreases with the increase of the friction coefficient of the buffer and the bilinear modeling of the braking.Civil Engineering | Structural Engineerin