Bridge Analysis Simplified By Bakht Jaeger Pdf 29

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The present numerical investigation aims at estimating the loading capacity of grillage structures for out-of-plane loads by adopting a simple numerical procedure. The analysis is based on the computation of the maximum moment carried by the beams and the dimensions of the grillage. The numerical procedure employs the beam grillage analogy [7], to which we refer as “grillage structural approach”. It consists in the adoption of the beam grillage structural analogy in order to model the mechanical behavior of the structural beams of a grillage (i.e., M and T beams in Fig. 1). Such approach allows the straightforward calculation of the critical moment of the system and it can be shown to be equivalent to the failure of the support itself. Actually, it is possible to estimate the moment capacity of a grillage by calculating the maximum value of moment carried by any beam in the system. For this purpose, the beams in grillage are modeled as beams of length l (in Fig. 1, the main beam is named as L, while the transverse beams are named as T1, T2 and T3), with their length and width having the values l, w, w and 2w respectively. The beam width is assumed to be much larger than the beam depth; thus, the beam thickness is neglected. The beam weight is assumed to be proportional to the width and is assumed to have a value of mg. An arbitrary load is applied by the main beam. The beam grillage structural analogy is then applied to the system to calculate its maximum moment. If the maximum moment value calculated by the grillage structural analogy is lower than the critical moment of the grillage, the system has a capacity of carrying the applied load and the grillage structure is said to be “safe”. Otherwise, the system fails. If the maximum moment calculated by the grillage structural analogy is equal to the critical moment of the grillage, the beam grillage structural analogy does not give any useful information on the loadability of the system and the grillage structure is said to be “unsafe”. Both “safe” and “unsafe” solutions are obtained as the result of the grillage structural approach application.

The size of the grillage and the distribution of the loads, when the grillage is adopted in a bridge deck, depend on the application and the loads. In the present analysis, the size of the grillage is equal to the length of the main beams, and the loads are uniformly distributed along the system. The main loads are considered as vertical normal forces, while the transverse ones are simulated as vertical shear forces. The analysis has been made with standard beam finite elements. The distribution of the loads along the main beams is illustrated in Fig. 2. In Fig. 2, the shear force q is concentrated in the center of the beam, and the normal force p is uniformly distributed along the entire length of the beam. The numerical analysis has been carried out by the Discretization, Numerical Modeling and Analysis (DNM4) code [14]. 827ec27edc