Bridges by David Blockley

Author:David Blockley [Blockley, David]
Language: eng
Format: mobi, epub
Publisher: OUP Oxford
Published: 2010-01-15T20:00:00+00:00

FIG 35. Deflections of tension cable

If the sag of the rope gets larger then the value of the horizontal reaction at the ends gets smaller. This is because the ends of the rope will be more vertical and will tend to pull down on the end more. This will increase the required vertical reaction. But what happens if the sag is zero? Theoretically the horizontal force required may become infinitely large. However, in practice this cannot happen. There will always be some sag under a lateral load because the rope cannot take any bending—it has no bending stiffness. A rope can only resist a lateral load by changing its shape.

Figure 35c has a second wiggly line over the right-hand part of the span. Instead of just one arrow as one truck in Figure 35b we now have a train of trucks all in a line—a queue of trucks—hence the new wiggly line. But a line like this can be of any length—how long should we make it? We want to find the answer for the worst case when the deflections of the cable are the largest. You could be forgiven for thinking that this worst case happens when the line of trucks covers the whole span—with a full wiggly line just like the dead load. That is so for a simple beam but a cable is different. The answer is a surprise. It turns out that the deflection of the cable at the centre of the span is largest when the train occupies the middle 40% of the span. The reason for this difference in behaviour between the simple beam and the cable is that there is axial tension in the cable but none in the beam, and the cable has no bending stiffness. Engineers call the stiffness created by the tension in the cable a geometric stiffness.

For most hanging bridges the first wiggly load, the dead load, is much larger than the second wiggly load, the live load. The bridge therefore settles down under the dead load and the changes, as the live loads move across, are smaller.

So far we have simply been talking about the cable. We haven’t yet introduced the bridge deck into our thinking and this will make a difference.

So let’s add a bridge deck. At the very least this increases the self-weight and hence the dead load of the bridge. In turn this increases the stiffness of the bridge.

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