Question 13.11: A two span simply supported bridge is shown in Figure 13.47....
A two span simply supported bridge is shown in Figure 13.47. The left span is 6 m and the right span is 4 m. Height of piers is 3.5 m. Beam size is 30 × 50 cm and column size is 30 × 60 cm. Concrete is of grade M25. Left end of the beam in each span is hinged while the right end has a roller support between the beam and top of column. A 15 mm expansion gap is provided between the two spans. It is subjected to a sinusoidal ground motion. Plot the response across the gap and displacement and force in the gap element.
Period of the frame is 1.82 sec. The hinged end, roller end and gap elements were simulated using the link element in SAP2000 (CSI, Berkeley). R represents rigid link and simulates the gap between the center line of the super structure and bridge bearings.
Boundary conditions
At a hinged end: nodes 2 and 3
U_{1} of node 2 = U_{1} of node 3
U_{2} of node 2 = U_{2} of node 3
At a roller end: node 6
Node 6 between rigid elements 5-6 and 6-8 is split in two nodes. A link element having a zero length is introduced across this split node 6. The properties of the link element are set so that:
U_{2} of the both the split nodes 6 are same. The link element is represented by B_{1}.
At a hinged end: node 7
Node 7 between rigid elements 5-7 and 7-11 is split in two nodes. A link element having a zero length is introduced across this split node 7. The properties of the link element are set so that: U_{1} and U_{2} of both the split nodes 7 are the same. The link element is represented by B_{2}.
At a roller end: nodes 13 and 14
U_{2} of node 13 = U_{2} of node 14
The supports 1, 4 and 12 were fixed.
The gap element between nodes 9 and 10 was assigned the following properties:
Stiffness = 10^{7}kN/m, gap = 15 mm
Frequency of the sinusoidal ground motion was 2 Hz.
The absolute displacement time-history of nodes 8 and 11 are shown in Figure 13.48(a). The displacement time-history of the gap element is shown in Figure 13.48(b). It can be seen that it undergoes a maximum negative displacement (gap closing) of 15 mm, which was the gap, whereas, it undergoes a maximum positive displacement of about 110 mm (gap opening) due to the movement of the piers. The force time-history of the gap element in Figure 13.48(c) shows an impact when the gap is closed. Naturally, there will be no force when the gap is open. This information can be used to design bearing seat size, bearing connectors and stoppers. In real-time situations, the data needs to be assigned very carefully.
