4.1 General
Finite element (FE) models are widely used to predict the dynamic characteristics of structures. The Jamuna Multipurpose Bridge is a prestressed box girder bridge. The depths of boxes vary along the length of the bridge. In this chapter, steps and assumptions of modelling of the bridge using SAP2000 are presented.
4.2 Finite Element Modelling of the Bridge
The Jamuna Multipurpose Bridge has seven 695.625 m long modules, which have identical superstructures. These modules separated by expansion joints are longitudinally free and fixed in transverse and up-down direction with respect to adjacent module. Superstructure of the module, second from the west bank of the river, has been modelled using SAP2000 (Rahman, 2008a). The module starts from the expansion joint before pier number 7th and ends at the expansion joint beyond pier number 14th which is shown in Figure 4.1. This portion is divided into six equal spans with seven piers and two extended portions. The 26.325m extended portion is directed towards west-side (Shirajgonj side) and the 73.05 extended portions is directed towards east-side (Tangail side).
Figure 4.1 :.Longitudinal profile of the model
The following are the important features of the modelling of the bridge-
• The structural behaviour of the bridge was assumed to be linear ignoring material nonlinearity.
• Only nonlinearity of the isolator was considered.
• Both longitudinal and vertical curvature of the bridge was considered.
• The variation In the depth of the deck along its length was considered parabolic as per the actual condition.
• The variation in the width of the box girder along its length was considered parabolic as per the actual condition
4.2.1 Bridge layout line
The modules of the bridge have curvature in both horizontal and vertical directions, shown in Figure 4.2. There is a circular curve of radius of 12000 meter in the horizontal direction. On the other hand the curvature in vertical direction is combination of 1460 meter straight line of 0.05 percent gradient and then a circular curve which has a length of 1880 meter. and then again a straight line of same length and same gradient as mentioned before. Studied portion of the bridge is the second module from the western side, which lies on the vertical gradient.
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Figure 4.2: Side view of the Jamuna Multipurpose Bridge
4.2.2 Deck section
The cross-sectional characteristics and dimensional properties are shown in the Figure 4.3 (a) and 4.3 (b).
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The deck section has three variations in parameters. These are as follows 1. Parabolic variation in depth (5.5m. at pier and 3.05 m. at mid span)
2. Parabolic variation in the thickness of bottom slab (.65 m. at pier and.2 m.
at mid span)
3. Parabolic variation in bottom slab width (6.4 m. at pier and 8.604 m. at mid span)
The above three variation was considered in the modelling of deck section and also the thickness in the various part of the deck section is not uniform which also has been considered in the model. A 3D view of the bridge deck is shown in Figure 4.4.
4.2.3 Pier, diaphragm, exterior rail girder
The pier is 6 m. in width and 2.5 m. thick. One of the most challenging parts of the model was to model the pier as it has a notch in the top (.54 m.) and at bottom it is solid (3 m.) but in the mid of the two the pier is hollow and it varies linearly .298 m.
at the first pier of the module and 0 m. at the end pier of the module. (Figure 4.5) There are an exterior rail girder and a diaphragm at the each pier above. \
Figure 4.4: 3D view of bridge deck with piers
Figure 4.5: 3d view of only pier, diaphragm and exterior rail girder.
The diaphragm girder is 2.5 m. thick, its top portion is 1 m, the bottom portion is .5 m and the side portion is 1.5 m in depth. The exterior rail girder is 2.5 m. thick and it starts at a depth of 1.11 m. and end at a depth of .75 m. The diaphragm and exterior rail girder was modelled using shell and frame element.
4.2.4 Bearing and restraint
There are seven piers in a module. Each of the piers has three bearing points. One is at the mid point of the pier and the other two are at the edges which are shown in Figure 4.6. In the edges of the pier the bearings are multi directional and the mid point bearings are of two types, the three piers of the each sides of the span has horizontal restraint with shock transmission device and the one at the centre is horizontal restraint without shock transmission device. Mid points at the top of all piers, except the 4th, has a horizontal restraint with a shock transmission device, which is modelled as multi linear plastic link, as shown in Figure 4.6( c). These points are free to move in the vertical direction. The mid point at the top of the 4th pier (Pll) is fixed.
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linear plastic model of shock transmission device.
4.2.5 Lateral prestressing in the deck
To apply prestress one needs to consider the following criteria as follows
• The average spacing of the prestress is 0.665m and our module is 695.625 m. it means we need 1046 tendon to apply.
• The adjacent two tendons are different that is if one has a dead end to the right then the other has dead end to the left and the variation is all through the same.
Considering these three complexities a small software was written (coordinate calculator) in visual basic to make the difference of coordinate between each of the tendons. Then half of the tendon to the zero point was produced and moved all along the bridge with spacing of 1.330 m for right side dead end and again do the same thing for left side dead end. (Figure 4.7)
For applying prestressing the data have been taken from as built drawing are as follows,
}>- Area of the tendon is 0.7258 sq. mm
}>- Applied load is from one end and that is 755kN.
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Figure 4.7: Lateral prestressing layout for deck section from as built drawing.
4.3 Different Models
Four different FE models were developed (Rahman,2008). Descriptions of the modelling are given bellow.
Model-I
The model does not consider prestrl;:ssing in the deck. Pier system is modeled with solid elements. Hollow sections at the top of the piers are also considered. Internal diaphragm and exterior rail girder are modeled with shell elements.
Model-II
The model does not consider prestressing in the deck. Pier system is modeled with shell elements Hollow sections at the top of the piers are not considered. Internal diaphragm and exterior rail girder are modeled with shell elements.
Model-III
The model does not consider lateral prestressing in the deck. Pier system is modeled with solid element. A hollow section at the top of the piers is also modeled. Internal diaphragm lIfd exterior rail girder are modeled with beam-column-element.
Model-IV
The model considers lateral prestressing in the deck. Pier system is modeled with solid element. A hollow section at the top of the piers is also modeled. Internal diaphragm and exterior rail girder are modeled with shell element.
Model-III is a simplified model, since its exterior rail girder was modelled with frame element. Model-IV is the most sophisticated model among these four models. A 3-D view of Model-IV is shown in Figure 4.8.
Figure 4.8: Three dimensional model of Model-IV of second module of the bridge.