Suspension bridges - Computational Analysis and Design of Bridge Structures - page 387

12.3.5 consideration of cable tangent changes
Unlike a free node of any component or element whose movement com-
pletely depends on stiffness and forces, nodes of cable ends that connect
to saddles are restrained by the shape of the saddle. When cable deforms,
the displacements at cable ends fall in the cable slots on top of the saddles
(Figure 12.13). In the iteration of large displacement analysis, any incre-
mental displacements at the ends of main cables should be adjusted to
reflect that the trace of the displacement is on the arc of the saddle.
Considering that the load step is small enough and the incremental dis-
placement in each of many iterations for one load step is sufficiently small,
the adjustment to the incremental displacement of the cable end at saddle
can be simplified as follows:

1. Assume the deformed saddle center is S c , which will be derived from
the new position of the rigid body that is used to simulate the saddle;
the saddle radius is R ; the deformed cable end at saddle is N 0 , the
other end is N 1 ; and the adjusted cable end at saddle is N 0 ′ .

2. Construct a tangent line from N 1 to an arc of radius R , centered at S c
with a tangent angle as the same as line N 0 1 . The tangent point is
the adjusted cable end N 0 ′ . The offset from N 0 ′ to N 0 is the adjustment
to the incremental displacements of the cable end at saddle.

This process shows that a general-purpose FEA package with nonlin-
ear analysis feature may not be sufficient in suspension bridge analyses.
Additional displacement constraints to the cable ends due to the saddle slot
have to be built into the analysis package.
However, it should be noted that the consideration of saddle slot con-
straint to the cable ends does not affect the analysis of internal forces and

Trace of cable end

Trace of cable end

Saddle

Cable center

Cable center

Displaced cable Displaced cable

Top of pylon

Figure 12.13 Displacements at cable ends fall in slot on top of saddles.