Bridge Analysis Simplified By Bakht Jaeger Pdf Download
Distribution factors (DFs) for one typical cross-section as specified in the AASHTO LRFD specification can be varied when the bridge parameters such as span length, loading lanes and skew are changed. The diversity between design and actual DFs may be varied as the bridge parameters changed. To study this diversity, this paper presents an evaluation of lateral load DFs for prefabricated hollow slab bridges. The response of the bridge was recorded during the field test. This field test was divided into two stages: a concentrated force loading test on the prefabricated girder that settled on the bridge supports before the girders were connected transversely and a vehicle loading test after the girders were connected transversely. The instruments used to record the response of the bridge were strain gauges and dial indicators. The measured data in the multi-stages of the field test could be used to calibrate the support condition of the bridge and transverse connection between adjacent girders in the finite element model (FEM) using beam and plate elements. From the FEM, DFs for this hollow slab bridge were determined and compared with the DFs in the AASHTO LRFD specification. A parametric study using the calibrated FEM was then used to investigate the effect of various parameters including span length, skew and bridge deck thickness on the DFs. It was found that AASHTO LRFD specification is conservative compared with the analysis in the FEM, while this conservatism decreased as the span length and skew of the hollow slab bridge increased.
Bridge Analysis Simplified By Bakht Jaeger Pdf Download
This loading phase was performed after the prefabricated girders were installed and the adjacent girders had not been connected transversely. Before this loading test, a preloading test was carried out on the tested girders to ensure the accuracy of the instruments. G1 (exterior girder), G4 (interior girder) and G7 (medium girder) girders were selected to be the test girders. The loading girder, which weighed 160.44 kN, was also a prefabricated hollow slab girder. One end of the loading girder was simply supported on the bearings in the mid-span of the two tested girders and the other end of the loading girder was simply supported outside the abutment (Fig. 3). As a result, the analysis of the tested girder could be simplified to be a prefabricated girder with a concentrated force on the mid-span. So the concentrated force applied on the mid-span of each tested girder was 80.22 kN. The concentrated force loading tests were performed on the G1 and G4, G4 and G7, respectively. The dimension of the girder and material properties were measured in this loading phrase.
Elastic spring elements were used to simulate actual behavior of supports as shown in Fig. 10 (Eom and Nowak 2001). To model this kind of connection, general connection options in elastic connection were selected in MIDAS CIVIL, while the combin14 elements were modeled in ANSYS model. In this calibrating process, main girders were not connected transversely. Elastic spring elements were added to restrict the horizontal movement of the bridge on the base of the simply support condition according to the design plan. The stiffness of the spring elements was represented by K values. The suitable K values were found by comparing the deflections at the mid-span from FEM analysis with those from the concentrated force loading test by trial and error analysis. The K values used in the analysis are shown in Table 1, in which, girder 1 and 13 had different K values with the other girders because of their different section from the others. The K values that acquired from different FE models were the same.
The structural behavior of T-frame bridges is particularly complicated and it is difficult using a general analytical method to directly acquire the internal forces in the structure. This paper presents a spatial grillage model for analysis of such bridges. The proposed model is validated by comparison with results obtained from field testing. It is shown that analysis of T-frame bridges may be conveniently performed using the spatial grillage model.
Typically, the design of highway bridges in China must conform to the General Code for Design of Highway Bridges and Culverts (JTG D60-2004) specifications. The analysis and design of any highway bridge must consider truck and lane loadings. However, the structural behavior of T-frame bridge is particularly complicated, and many rigorous methods for analysis of T-frame bridges are quite tedious and often difficult.
Pan et al. [1] carried out uncertainty analysis of creep and shrinkage effects in long-span continuous rigid frame of Sutong Bridge. Azizi et al. [4] used spectral element method for analyzing continuous beams and bridges subjected to a moving load. Wang et al. [5] analyzed dynamic behavior of slant-legged rigid-frame Highway Bridge. Dicleli [6] presented a computer-aided approach of integral-abutment bridges, and an analysis procedure and a simplified structure model were proposed for the design of integral-abutment bridges considering their actual behavior and load distribution among their various components [7, 8]. There were several approximate analysis methods for bridge decks, which include the grillage method and the orthotropic plate theory [9]. Yoshikawa et al. [10] investigated construction of Benten Viaduct, rigid-frame bridge with seismic isolators at the foot of piers. Kalantari and Amjadian [11] reported a 3DOFs analytical model an approximate hand method was presented for dynamic analysis of continuous rigid deck.
Mabsout et al. [12] reported the results of parametric investigation using the finite-element analysis of straight, single-span, simply supported reinforced concrete slab bridges. The study considered various span lengths and slab widths, number of lanes, and live loading conditions for bridges with and without shoulders. Longitudinal bending moments and deflections in the slab were evaluated and compared with procedures recommended by AASHTO [13].
This paper presents a spatial grillage model for the analysis of a T-frame bridge. Static and dynamic analysis results of spatial grillage model for the T-frame bridge are compared with results based on results obtained from field testing. The research results shown that analysis of T-frame bridges may be conveniently performed using the spatial grillage model.
Spatial grillage model is a convenient method for analysis of box-girder bridges. In the model, the box-girder slab is represented by an equivalent grid of beams whose longitudinal and transverse stiffnesses are approximately the same as the local plate stiffnesses of the box-girder slab.
In the spatial grillage model analysis, the orientation of the longitudinal members should be always parallel to the free edges while the orientation of transverse members can be either parallel to the supports or orthogonal to the longitudinal beams. According to the grillage model, the output internal force resultants can be used directly. The grillage model involves a plane grillage of discrete interconnected beams. The representation of a bridge as a grillage is ideally suited for carrying out the necessary calculations associated with analysis and design on a digital computer and it gives the designer an idea about the structural behavior of the bridge.
Determination of a suitable grillage mesh for a box-girder of rigid frame bridge is, as for a slab deck, best approached from a consideration of the structural behavior of the particular deck rather than from the application of a set of rules. Since the average longitudinal and transverse bending stiffness are comparable, the distribution of load is somewhat similar to that of a torsionally flexible slab, but with forces locally concentrated. The grillage simulates the prototype closely by having its members coincident with the centre lines of the prototypes beams. In addition, there is a diaphragm in the prototype such as over a support, and then a grillage member should be coincident. Based on section shape of the rigid frame bridge and support arrangements, a spatial grillage mesh should be represented by the above mentioned spatial grillage method. At the same time, according to the grillage equivalent theory, the following three important aspects have to be noted: according to mechanical behavior of a rigid frame bridge, one should place the grillage beams along the lines of designed strength; the longitudinal and transverse member spacing should be reasonably similar to permit sensible static distribution of loads; in addition, virtual longitudinal and transverse members are often employed for the sake of convenience in the analysis. The virtual members only offer stiffness, but its weight must be ignored.
Three-dimensional linear elastic finite element models of the spatial grillage model of the Quhai Bridge have been constructed using SAP2000 finite element analysis software. In the finite-element model, 3D beam4 elements were adopted to create the grillage model that will be used to determine the internal stress resultants, natural frequencies, and corresponding mode shapes. The spatial grillage model was shown in Figure 3, and the virtual beams only offer stiffness. In the finite-element model of the bridge, 3D 1104 elements (beam 4) and 817 nodes were used. The spatial grillage model of the bridge as a whole is shown in Figure 4.
Dynamic properties can be obtained by measurement of vibrations produced by ambient loads and vehicle bump. The experimental program includes dynamic characterization of the structure in normal conditions and when a half of the bridge is covered by traffic. The response of the structure was measured at 7 selected points using accelerometers. Preliminary results obtained from an FE dynamic analysis were used to determine the optimum location of the sensors. The first mode shapes of the bridge according to field dynamic test and theoretical value are presented in Table 3. The results of measured dynamic properties show that the test values of fundamental frequency for T-frame is bigger than theoretic values, but the test values of fundamental frequency for middle-span hang beam is smaller than theoretic values. This indicates that middle-span stiffness is relatively weak.