Why Do Cables Use dx for Distributed Loads and ds for Weight?

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SUMMARY

The discussion centers on the distinction between using dx for distributed loads and ds for weight in cable mechanics. It highlights that dx represents an infinitesimal segment of the cable where distributed loads are applied, while ds refers to the arc length of the cable where weight is considered. The conversation emphasizes the importance of understanding these concepts in the context of statics and mechanics, particularly when analyzing forces and moments in cable systems.

PREREQUISITES
  • Understanding of basic mechanics and statics principles
  • Familiarity with distributed loads and their applications
  • Knowledge of cable dynamics and tension analysis
  • Concept of infinitesimal calculus in engineering contexts
NEXT STEPS
  • Research the principles of distributed loads in structural engineering
  • Study the mechanics of cables and their tension analysis
  • Learn about the application of infinitesimal calculus in engineering problems
  • Explore the differences between dx and ds in various engineering contexts
USEFUL FOR

Engineers, particularly those specializing in structural and mechanical engineering, students studying statics, and professionals involved in cable design and analysis will benefit from this discussion.

Cyrus
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First, on an unrelated note, I would like to share an anwser I think I found to be correct on a question I posted here a while back. I asked about how a smooth collar that was Not Pinned could prevent a moment. The problem I was faceing was the fact that in order to have "play" so that the collar is loose, there had to be some physical gap to allow for sliding. But if there is a gap, then when a moment is applied to the collar, it will move due to this gap a minute amount, which will result in some horrible complications. I think my resasoning in my gripe was correct, and if you actually did know the amount of gap/play or slop (whatever you want to call it) between the materials, you could calculate a moment and force that is prevented more accurately. (The amount of error in reality would depend on the geometry of the collar and the amount of play between it and the journal.) But the little devil here is the fact that there can be literally NO space between the collar and the journal, and yet it can still have the ability to slide, provided that the frictional force is zero! What a tricky little devilish detail! I guess that's why they call it an IDEAL CASE! :biggrin:

Anywho, My question is on distributed loads on cables. Why is a distributed load on a cable with respect to dx, but a distributed weight of a cable with resepct to arch length ds? (Oh yeah, and I've got a lot more questions on this subject to come!)
 
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Im 100% positive that someone here has dealt with statics of distributive loads on roaps.
 

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