Applied Mechanics

Q1: Pick up the incorrect statement from the following. In case of suspension bridge due to rise in temperature,

A dip of the cable increases

B length of the cable increases

C dip of the cable decreases

D none of the these.

ANS:C - dip of the cable decreases

The "dip" of a cable refers to the amount of sag or curvature that the cable exhibits when suspended between two points, such as the towers of a suspension bridge. It's the distance between the lowest point of the cable and a hypothetical straight line drawn between the two anchor points. When a suspension bridge is subjected to a rise in temperature, several changes occur due to thermal expansion. The most significant change is the elongation of the cables. As the temperature increases, the metal cables comprising the bridge expand, causing their length to increase. Now, let's consider the effect of this increase in cable length on the dip of the cable:

  1. Increase in Length: As the cables expand due to the rise in temperature, their overall length increases. This increase in length affects the sagging profile of the cables.
  2. Reduction in Sag: The increase in cable length pulls the cable tauter. The additional length effectively reduces the amount of sag or dip that the cable exhibits between the towers. Essentially, the cables become more stretched out and less curved between the anchor points.
  3. Decrease in Dip: Therefore, due to the elongation of the cables and the resulting increase in tension, the dip of the cable decreases. The lowest point of the cable is pulled upward, closer to the straight line between the towers, resulting in less noticeable sag or dip.



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