# Load weight on a horizontal wireframe ladder

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

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