Barrier Cable Deflection Formula 1

[JohnRwals]

Hi!

PTI technical note shows barrier cable deflection formula.
Can anybody explain how to get this deflection formula a?

John R.

 

[jayrod12]

Literally trigonometry with the additional length due to stretching of the cable.

They assume that once you load the cable it no longer has any sag in adjacent spans and no curvature in the span under review.

So delta is the expected elongation of the cable which will make the actual length of each hypotenuse longer than l/2 by half of delta. Then they use trig to solve for a.

 

[phamENG]

Check out this thread: thread507-388481

There's a reference to what looks like a table from Roark's that will help you with the derivation. The difference is that your calculation a has to account for the elastic lengthening of the entire L of the cable.

 

[jayrod12]

Oh, yeah I also forgot to mention that it is an iterative process, the P load downwards is not the same load used for the elongation calculation. The downward load P creates a tension in the cable, it is that tension in the cable that you use to determine the elongation, and then calculate was the "a" depth is using trig. Re-iterate until your "a" depth used to determine the tension in the cable matches the "a" depth you calculate at the end using trig.

 

[HTURKAK]

An a pink star for this post...

The mentioned system is typical geometric non-linear system and the exact solution is iterative..

Assuming the cable is pin supported at both ends and free to slide at intermediate supports,

Steps ;

1- Choose an ( a 1) value, and calculate the tension force developing at the cable,

2- Calculate the elongation with the new tension force and calculate the new ( a 2) value,

3- choose the new ( a ) value ( a1+a2 )/2 and repeat step 2 until the last( a) value does not chage substantially..

The procedure is convergent and after 3-4 steps, one can find a precise ( a ) value ...