Catenary  Applied Load
Subject
A catenary is the natural shape of a cable or cord with zero bending stiffness and infinite axial stiffness, the properties of which are fully described in CalQlata's technical help page for the Catenary calculator.
A point load, applied in any direction anywhere along the length of a single catenary will automatically generate two completely separate catenaries between the original ends and the point load. The problem is that you don’t know how the point load is split between the two catenaries, which is the purpose of Catenary+
Calculator
Catenary+ is a standalone calculator that determines the properties of ....
a) a single catenary (i.e. before a load is applied), and
b) both the catenaries generated after a load is applied
.... at; all supported ends, midlength loop and anywhere along its length.
CalQlata's policy of 'static' images (see How They Work) does not apply to this program. Catenary+ includes dynamic line displays of the Plan (birdseye), Face (front) and Side elevations of the resultant catenaries that update automatically each time Catenary+ recalculates. Catenary+ also provides the coordinates for both catenaries in the data listing page just in case the software system you are operating has a problem with the dynamic images in the program.
For help using this calculator, including an independent checking procedure, see Technical Help
Catenary Calculator for Applied Loads  Options
The unloaded catenary prior to your applying a pointload (‘F’) has two ends (End_{1} and End_{2}) and hangs free. After applying your pointload the two consequent catenaries (Catenary_{1} and Catenary_{2}) will be joined at Point_{3}; (End_{31} of catenary_{1} and End_{32} of catenary_{2}). All input and output data are labelled according to this convention.
You enter: 
and the catenary+ calculator will provide: 


horizontal component of 'F' in xdirection: Fx

vertical component of 'F' in xdirection: Fy

horizontal component of 'F' in zdirection: Fz

horizontal force in catenary₁: Fh₁

axial tension in catenary₁ at '1': F₁

horizontal force (x direction) in catenary₁ at '1': Fx₁

vertical force (y direction) in catenary₁ at '1': Fy₁

horizontal force (z direction) in catenary₁ at '1': Fz₁

horizontal force in catenary₂: Fh₂

axial tension in catenary₂ at '2': F₂

horizontal force (x direction) in catenary₂ at '2': Fx₂

vertical force (y direction) in catenary₂ at '2': Fy₂

horizontal force (z direction) in catenary₂ at '2': Fz₂

axial tension in catenary₁ at '3': F₃₁

vertical force (y direction) in catenary₁ at '3': Fy₃₁

axial tension in catenary₂ at '3': F₃₂

vertical force (y direction) in catenary₂ at '3': Fy₃₂

axial tension in catenary at 'p': Fᵨ

horizontal distance between '1' and 3': d₁

radius in catenary at '1': R₁

slope in catenary at '1' [°]: θ₁

horizontal distance between '2' and '3': d₂

radius in catenary at '2': R₂

slope in catenary at '2' [°]: θ₂

horizontal distance (x direction) between '1' and '3': x₃

vertical distance (y direction) between '1' and '3': y₃

horizontal distance (z direction) between '1' and '3': z₃

radius in catenary₁ at '3': R₃₁

slope in catenary₁ at '3' [°]: θ₃₁

radius in catenary₂ at '3': R₃₂

slope in catenary₂ at '3' [°]: θ₃₂

length of catenary between '1' and 'ℓ₁': Lℓ₁

horizontal distance (x direction) between '1' and 'ℓ₁': xℓ₁

vertical distance (y direction) between '1' and 'ℓ₁': yℓ₁

horizontal distance (z direction) between '1' and 'ℓ₁': zℓ₁

radius in catenary at 'ℓ₁': Rℓ₁

length of catenary between '1' and 'ℓ₂': Lℓ₂

horizontal distance (x direction) between '1' and 'ℓ₂': xℓ₂

vertical distance (y direction) between '1' and 'ℓ₂': yℓ₂

horizontal distance (z direction) between '1' and 'ℓ₂': zℓ₂

radius in catenary at 'ℓ₂': Rℓ₂

horizontal distance (x direction) between '1' and 'p': xᵨ

vertical distance (y direction) between '1' and 'p': yᵨ

horizontal distance (z direction) between '1' and 'p': zᵨ

radius in catenary at 'p': Rᵨ

slope in catenary at 'p' [°]: θᵨ

rotation of catenary₁ about yaxis (ACW) [°]: φ

rotation of catenary₂ about yaxis (CW) [°]: δ

iteration error: 'φε': φε

iteration error: 'y': yε

iteration error: 'Fh₁': Fh₁ε

milliseconds for iteration: ms

Check minimum system requirements