I'm wondering about the following scenario. A wire cable ladder is mounted horizontally and a person uses the rungs to navigate from one end to the other (imagine monkey bars).

If the wire cable is ~15 metres in length and supported in the middle by another top down wire to prevent sagging and offer some tension (from a roof), how much strain/weight/load could a person possibly cause, if for example the person was 90kg, 100kg, 110kg

Alternative would be two ~7metre ladders joined and suspended in the middle. • Do a free body diagram and balance the forces. If the middle support can swing then make the swing reaction force angle an unknown. Apr 9 '18 at 13:23
• The answer depends on the elastic properties of the wire ladder, and the support cable. The reason being is that the tension depends on the amount of sag and sag depends on stretching of the parts. Apr 9 '18 at 13:40
• Sorry but no idea what that diagram is or how i'd make it and i'd prefer not to use my own math.. Apr 10 '18 at 13:00

I don't have any formulas for you, but I can mostly answer your question. If both the 15 meter and 2 7 meter ladders were both the same distance they would experience the same strain, weight and load as each other.(unless the connection between the 2 7 meter ladders was weaker than that of the middle of the 15 meter ladder) A person would cause the most strain on the ladders when they are in the middle of them, and the least the farther away from the center they are. I don't know how much load the ladders can take A, because I don't know how strong the ladders are and the supports keeping them up, and B, I don't even have an equation to calculate that. I hope this answers you general question even if I can't give you any formulas.

• It just reaffirms my thoughts, i'm just hoping for more of a '100kg person can cause 100-115kg of tension on the ladder' style of answer. Supports btw, are reinforced wall mounted brackets, and normal load for the slimmer ladder as example is 120kg. I'm looking to clarify if that is wire load or wire ends (connectors). Apr 9 '18 at 10:42

The problem is complex enough to need computer simulation for a reasonable answer.

As a first stab at it you can look at the wire ladder (black lines) spanning a distance $S$ between points A and B below: The middle support (blue line) connects to the ladder at C and to the ceiling at D. The load $W$ is at point G a distance $x$ from A.

If the angle $\varphi$ is near zero, then the support forces $F_A$ and $F_B$ need to be really large to counteract the weight $W$. The angle increases as the ladder and/or the supports stretch. The higher the load the more stretch

The solution will be found when the elastic forces match the forces from the sketch above 