Catenary Calculator - Applied Load v1

Price: £51.00 (£51.00 Inc. VAT)

Calculator for the properties of a catenary with a point 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 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

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

Check minimum system requirements

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