I have used this method on a number of projects and situations and never had an issue with it. The basic assumption is that once it buckles – or AS is buckles/bends – the pin-pin situation creates tension in the system, at which point it is acting like a cable… no need to define a limit or standard, just logic. This would even work for say a ladder rung that is only 18” long – though in this case you’re counting on it forming a plastic hinge in the center… but still, if it isn’t going break while someone is standing on it, then it is safe – correct? So if the rod is capable of taking the tension, and the connections at each end are capable of sustaining the tension reaction, then I don’t see where he has room to take issue with this one.
From: Michael Gregory [mailto:tsemike@ida.net]
Sent: Tuesday, June 23, 2009 8:02 AM
To:
Subject: Flexure vs. Cable Action in a solid rod.
A contractor has used a ½” diameter solid rod (50 ksi) for railing on a bicycle bridge. The railing spans 6’-0” and has about a 4” fillet weld at each end attaching it to the vertical uprights which are heavy HSS sections. The specifications required the rod to carry a 50 plf horizontal and vertical load simultaneously. Using standard flexure equations, it fails. However, it appears to act as a cable in that it only delfects about ½” with a 500 lbs point load (2 big guys standing on it).
I performed cable calculations showing that it works since it appears to act as a cable. The EOR has rejected my calculations as “a leap of faith” and contends since the element is a sold rod, it has to act as a bending member and be analzyed using standard flexure calculations and cannot be reasonably analyzed as a cable. Specifically he has asked to show something from an “industry standard” that shows exactly where it stops acting as a beam and starts acting as a cable. As he pointed out, if the rod were only 6” long, it would definitely act as a beam – I agree. But if the rod were 20’ long and fixed at both ends, it would most certainly act as a cable, which he agreed.
My calculations are based on the book Cable Structures by Max Irvine which was copyrighted by MIT in 1981. I am confident that my calculations and assumptions are correct but I’m dealing with a Civil Engineering firm and the EOR admits that he doesn’t know anything about cable calculations (he asked me to send him my book). The research I’ve done indicates that there is not an exact point at which an element quits acting as a flexural element and begins behaving as a cable element.
Any help? Is there someone or some other reference that I can turn to? I have searched the internet and have not turned up any good leads. Is there any software available that will analyze a catenary shaped member? Are there any references, research papers or other documents that indicates at what point a solid element may begin to behave as a cable? Thanks!!
Michael Gregory, PE
208-357-2420 Office
208-357-2419 Fax