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Calculator Description
Catenary Calculator - Applied Load v1

Catenary - Applied Load

Calculator for the properties of a catenary

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 stand-alone 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, mid-length 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 (birds-eye), Face (front) and Side elevations of the resultant catenaries that update automatically each time Catenary+ recalculates. Catenary+ also provides the co-ordinates 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 point-load (‘F’) has two ends (End1 and End2) and hangs free. After applying your point-load the two consequent catenaries (Catenary1 and Catenary2) will be joined at Point3; (End31 of catenary1 and End32 of catenary2). All input and output data are labelled according to this convention.

You enter: and the catenary+ calculator will provide:
  • horizontal distance (x direction) from '1' to '2': x₂
  • vertical distance (y direction) from '1' to '2': y₂
  • total length of catenary: L
  • weight per unit length of catenary: w
  • distance along catenary from '1' to 'p': p
  • distance along catenary from '1' to '3': d
  • force applied to catenary at '3': F
  • angle of mid-length force 'F' about 'y' axis (α=0 @ x=0) [°]: α
  • angle of mid-length force 'F' about 'x,z' plane (β=0 @ plane x,z) [°]: β
  • horizontal component of 'F' in x-direction: Fx
  • vertical component of 'F' in x-direction: Fy
  • horizontal component of 'F' in z-direction: 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 y-axis (ACW) [°]: φ
  • rotation of catenary₂ about y-axis (CW) [°]: δ
  • iteration error: 'φε': φε
  • iteration error: 'y': yε
  • iteration error: 'Fh₁': Fh₁ε
  • milliseconds for iteration: ms

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