Question 13.9: A frame has a length of 6 m and height of 3.5 m. Beam size i...

The frame represents a simply supported bridge. The centre line of the beam is assumed to be 500 mm above the top of column. It is represented through rigid links. It is assumed that there is no lateral pressure on the columns. Period of the frame is 1.9 sec. The hinged end, roller end and viscous damper were simulated using link elements having a finite length in SAP2000.

Boundary conditions:
At a hinge 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
U_{1} = lateral displacement (along x) and U_{2} = vertical displacement (along z)
At a roller end: nodes 5 and 6
U_{2}  of node 5 = U_{2} of node 6
The viscous damper between nodes 5 and 7 was assigned the following properties:
Stiffness = 10^{6} kN/m, damping coefficient = 100, damping exponent = 1.0.
Nodes 7 and 8 were connected through a rigid link. Thus, viscous damper was connected between the beam and the column.
Supports 1 and 4 were fixed.
Period of the sinusoidal ground motion was 0.5 sec.
The response of the roller end of the beam and viscous damper are shown in Figures 13.45(a) and (b). The hysteresis behaviour of the viscous damper is shown in Figure 13.45(c).

The seismic response of such structures is influenced by the characteristics of the
ground motion. It means its response will vary with each different ground motion. In such a situation, it becomes difficult to isolate the effect of the viscous damper from that of the ground motion. The characteristics of a sine curve are well known. Therefore, a sine curve was used as a ground motion in this example for illustration.
The effect of viscous damper is to reduce the maximum lateral displacement of the
roller end by 10 mm.