Analysis of a parabolic cable subjected to UDL


I was running a very simple analysis, of a parabolic cable (subjected to a UDL of 10kN/m) hanging from two supports. 

(a) sir, initially I gave the material density of cable, hangers, and deck as zero and applied just udl , and we know these are standard cases. but the result of horizontal forces coming different by a value of 11.1kN.
(H= wl^2/8h)  sir, may I know, why this difference is occurring? do I need to run some specific analysis for the exact results? 

(b) sir, when I changed the element type from cable to truss. the difference of value reduced to 9.8kN. 

Length = 216m
udl = 10kN/m
h= 27m 

thank you sir.


There could be some reasons why the results are not coming exactly:
1. The Geometric non-linearity of the analysis type changes the result of the forces and reactions with the change in deformation.
2. There is always a possibility that the nodes defined are not exactly forming a parabolic 2 degree curve.

 For verification, I took Length as 200m, udl as 25 kN/m and h =35m. For this Fx for hand calculated value will be 3571.43 kN and value obtained from the software is 3570.7 which are approximately equal. 
Further, the cable type element were used for cables where the unstrained cable length(Lu) was provided. Hanger were converted to truss element types.
Midas converts cable elements to truss elements whose stiffness depends upon usual elastic stiffness and stiffness resulting from sag.
Model has been attached for review.

Creation date: 5/31/2021 4:20 PM      Updated: 5/7/2023 11:42 PM
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