Uniformly distributed load w per unit length is suspended from a cable between points A and B. If points A and B are at the same level at distance l and the central sag of the cable is h, then the horizontal thrust developed of supports is
- Awl/2h
- Bwl²/4h
- Cwl/4h
- Dwl²/8hCorrect
Solution
Concept
Cable with UDL
Formula
H = w l² / 8h
Step-by-step solution
1. Moment at the centre of the cable: H h = w l²/8. 2. H = w l² / 8h.
Explanation
Taking moments of half the cable about the lowest point gives the horizontal thrust.
Why the other options are wrong
Other options have wrong constants.
Shortcut
H = wl²/8h (same as arch).
Common mistake
Using 4.
Correct answer: D) wl²/8h