Why is a beam supported by two cables more stable than one?

[Tom Lever]

Imagine a steel I-girder lifted by a single wire rope. If the rope is not perfectly centered along the girder length, the girder will rotate about a horizontal latitudinal axis through its centroid.

Imagine a girder pair lifted by two wire ropes, with one rope on each side of the girder centroid, each about five percent of the length of the girder away from the centroid. If ropes are not perfectly equidistant from the centroid, the girder will rotate.

Imagine a girder pair lifted by two wire ropes, each about five percent of the length of the girder away from an end. If the ropes are not perfectly equidistant from the ends, there will be a net moment / torque about the latitudinal axis, equal to the net moments above, but this situation will be more stable. Why?

Additionally, for a rigid girder, cables at the ends would be most stable (stability score of 50), cables at the centroid would be least stable (stability score of -50), and cables each halfway between centroid and end would be stable in an intermediate way (stability score of 0). Why is this a linear relationship?

 

[cjl]

In your second case, there will be zero net moment on the girder, which will be enabled by a slightly different tension in each of the two ropes. It's more stable because slight asymmetries in geometry can be compensated with slight asymmetries in cable tension to enable an overall zero net moment across a range of cable locations, while the first scenario has no margin for error in cable positioning before you start to have an applied moment.

 

[FactChecker]

The stability is directly related to the restoring force. When there is a slight disturbance, is there a restoring force that opposes the disturbance? In each case that you mention, you can understand the answer by describing the sign and magnitude of the restoring force.

PS. If this is a class exercise, there is a format that you should use.