Tension at any Point given Catenary Length of Simple Cable with UDL Calculator

✖Midspan Tension is the total tension acting in cable at midpoint.ⓘ Midspan Tension [T_m]			+10% -10%
✖Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.ⓘ Uniformly Distributed Load [q]			+10% -10%
✖Cable Span is total length of cable in horizontal direction.ⓘ Cable Span [L_span]			+10% -10%

✖Tension at Supports is the tension due to loading on supports.ⓘ Tension at any Point given Catenary Length of Simple Cable with UDL [T_s]

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Formula

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Tension at any Point given Catenary Length of Simple Cable with UDL

Formula

`"T"_{"s"} = sqrt(("T"_{"m"}^2)+("q"*"L"_{"span"})^2)`

Example

`"150.0533kN"=sqrt((("4kN")^2)+("10.0kN/m"*"15m")^2)`

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Tension at any Point given Catenary Length of Simple Cable with UDL Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2)
T_s = sqrt((T_m^2)+(q*L_span)^2)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Tension at Supports - (Measured in Newton) - Tension at Supports is the tension due to loading on supports.
Midspan Tension - (Measured in Newton) - Midspan Tension is the total tension acting in cable at midpoint.
Uniformly Distributed Load - (Measured in Newton per Meter) - Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.
Cable Span - (Measured in Meter) - Cable Span is total length of cable in horizontal direction.

STEP 1: Convert Input(s) to Base Unit

Midspan Tension: 4 Kilonewton --> 4000 Newton (Check conversion here)
Uniformly Distributed Load: 10 Kilonewton per Meter --> 10000 Newton per Meter (Check conversion here)
Cable Span: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_s = sqrt((T_m^2)+(q*L_span)^2) --> sqrt((4000^2)+(10000*15)^2)

Evaluating ... ...

T_s = 150053.323855222

STEP 3: Convert Result to Output's Unit

150053.323855222 Newton -->150.053323855222 Kilonewton (Check conversion here)

FINAL ANSWER

150.053323855222 ≈ 150.0533 Kilonewton <-- Tension at Supports

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Bridge and Suspension Cable » Suspension Cables » General Relation for Suspension Cables » Catenary » Tension at any Point given Catenary Length of Simple Cable with UDL

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< 4 Catenary Calculators

Catenary Length given Tension at any Point of Simple Cable with UDL

Go Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2))

UDL given Tension at any Point of Simple Cable with UDL

Go Uniformly Distributed Load = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Cable Span^2))

Horizontal Component given Tension at any Point of Simple Cable with UDL

Go Horizontal Tension = sqrt((Cable Tension^2)-((Total Load per Unit Length*Catenary Length)^2))

Tension at any Point given Catenary Length of Simple Cable with UDL

Go Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2)

Tension at any Point given Catenary Length of Simple Cable with UDL Formula

Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2)
T_s = sqrt((T_m^2)+(q*L_span)^2)

What is Tension in Cable?

The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension, T. When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object: T = mg.

How to Calculate Tension at any Point given Catenary Length of Simple Cable with UDL?

Tension at any Point given Catenary Length of Simple Cable with UDL calculator uses Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2) to calculate the Tension at Supports, The Tension at any Point given Catenary Length of Simple Cable with UDL formula is defined as the total force acting on the supports in both horizontal and vertical directions. Tension at Supports is denoted by T_s symbol.

How to calculate Tension at any Point given Catenary Length of Simple Cable with UDL using this online calculator? To use this online calculator for Tension at any Point given Catenary Length of Simple Cable with UDL, enter Midspan Tension (T_m), Uniformly Distributed Load (q) & Cable Span (L_span) and hit the calculate button. Here is how the Tension at any Point given Catenary Length of Simple Cable with UDL calculation can be explained with given input values -> 0.150053 = sqrt((4000^2)+(10000*15)^2).

FAQ

What is Tension at any Point given Catenary Length of Simple Cable with UDL?

The Tension at any Point given Catenary Length of Simple Cable with UDL formula is defined as the total force acting on the supports in both horizontal and vertical directions and is represented as T_s = sqrt((T_m^2)+(q*L_span)^2) or Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2). Midspan Tension is the total tension acting in cable at midpoint, Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element & Cable Span is total length of cable in horizontal direction.

How to calculate Tension at any Point given Catenary Length of Simple Cable with UDL?

The Tension at any Point given Catenary Length of Simple Cable with UDL formula is defined as the total force acting on the supports in both horizontal and vertical directions is calculated using Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2). To calculate Tension at any Point given Catenary Length of Simple Cable with UDL, you need Midspan Tension (T_m), Uniformly Distributed Load (q) & Cable Span (L_span). With our tool, you need to enter the respective value for Midspan Tension, Uniformly Distributed Load & Cable Span and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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