MakeYourself
Structural
- Mar 5, 2012
- 2
I am designing a double angle fence post member that has a tension cable attached to its top. See the attached document for a graphical representation. The tension cable spans the width of a pedestrian pathway and is attached to double angle fence posts on either side of the pathway. The cable is only for aesthetic purposes, and thusly will be loaded only by its self-weight and a design ice thickness of approximately 10 lb/ft.
In order to arrive at the moments at the base of the post, I need to determine the amount of tension in the cable at the post's top. From what I can tell, there are a few complicating items:
1) The basic catenary tension/sag equation is T = wl^2/(8*d)
where
T=horizontal tension
w=uniform vertical load
l=undeflected cable span
d=mid-span cable sag
So from this equation, I need T to solve for d, and vice versa. Which variable is known? I can imagine 2 scenarios: the cable being installed to a limited maximum sag (in this case d is known and T can be derived) or the cable being pre-tensioned to a minimum tension value (in this case T is known and d is derived).
2) When the cable undergoes the design ice load, the post/cable system will deflect to reach a point of equilibrium. The cable will sag and the posts will bend inward (creating additional sag in the cable). In order to determine these forces, I have modeled the system in RISA.
Using the RISA manual's recommendations for modeling cable action, I've broken the cable up into 5 equal members and given the member joints an initial displacement downward (essentially a guess at the catenary shape). See second attached image. After running the analysis and recording the new displacements, I move the cable joints halfway between their initial location and the new displacements. After a few iterations, I have converged to an equilibrium state. This seems like a sensible way to arrive at a solution. Does anyone else have experience or suggestions on an analysis model?
I've used an E=12,000 ksi and an effective area Ae=0.5Ag which approximates the midrange of values listed in the Wire Rope Engineering Handbook. I've used a 1" diameter cable with Ae=0.393 in2.
Thanks guys; any and all help is appreciated.
In order to arrive at the moments at the base of the post, I need to determine the amount of tension in the cable at the post's top. From what I can tell, there are a few complicating items:
1) The basic catenary tension/sag equation is T = wl^2/(8*d)
where
T=horizontal tension
w=uniform vertical load
l=undeflected cable span
d=mid-span cable sag
So from this equation, I need T to solve for d, and vice versa. Which variable is known? I can imagine 2 scenarios: the cable being installed to a limited maximum sag (in this case d is known and T can be derived) or the cable being pre-tensioned to a minimum tension value (in this case T is known and d is derived).
2) When the cable undergoes the design ice load, the post/cable system will deflect to reach a point of equilibrium. The cable will sag and the posts will bend inward (creating additional sag in the cable). In order to determine these forces, I have modeled the system in RISA.
Using the RISA manual's recommendations for modeling cable action, I've broken the cable up into 5 equal members and given the member joints an initial displacement downward (essentially a guess at the catenary shape). See second attached image. After running the analysis and recording the new displacements, I move the cable joints halfway between their initial location and the new displacements. After a few iterations, I have converged to an equilibrium state. This seems like a sensible way to arrive at a solution. Does anyone else have experience or suggestions on an analysis model?
I've used an E=12,000 ksi and an effective area Ae=0.5Ag which approximates the midrange of values listed in the Wire Rope Engineering Handbook. I've used a 1" diameter cable with Ae=0.393 in2.
Thanks guys; any and all help is appreciated.