Tension at Midspan given Tension at Supports for UDL on Parabolic Cable Calculator

✖Tension at Supports is the tension due to loading on supports.ⓘ Tension at Supports [T_s]			+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 midspan is the total tension acting in cable at midpoint.ⓘ Tension at Midspan given Tension at Supports for UDL on Parabolic Cable [T_mid]

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Formula

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Tension at Midspan given Tension at Supports for UDL on Parabolic Cable

Formula

`"T"_{"mid"} = sqrt(("T"_{"s"}^2)-((("q"*"L"_{"span"})/2)^2))`

Example

`"196.1505kN"=sqrt((("210kN")^2)-((("10.0kN/m"*"15m")/2)^2))`

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Tension at Midspan given Tension at Supports for UDL on Parabolic Cable Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2))
T_mid = sqrt((T_s^2)-(((q*L_span)/2)^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 Midspan - (Measured in Newton) - Tension at midspan is the total tension acting in cable at midpoint.
Tension at Supports - (Measured in Newton) - Tension at Supports is the tension due to loading on supports.
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

Tension at Supports: 210 Kilonewton --> 210000 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_mid = sqrt((T_s^2)-(((q*L_span)/2)^2)) --> sqrt((210000^2)-(((10000*15)/2)^2))

Evaluating ... ...

T_mid = 196150.45245933

STEP 3: Convert Result to Output's Unit

196150.45245933 Newton -->196.15045245933 Kilonewton (Check conversion here)

FINAL ANSWER

196.15045245933 ≈ 196.1505 Kilonewton <-- Tension at Midspan

(Calculation completed in 00.004 seconds)

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< 12 Parabolic Cable Tension and Length Calculators

Tension at Midspan given Tension at Supports for UDL on Parabolic Cable

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

UDL given Tension at Supports for UDL on Parabolic Cable

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

Tension at Supports for UDL on Parabolic Cable

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

Span of Cable for Length of Cable for UDL on Parabolic Cable

Go Length of Cable Span = 1.5*Length of Cable-sqrt((2.25*Length of Cable^2)-8*(Maximum Sag^2))

Span of Cable given Tension at Supports for UDL on Parabolic Cable

Go Length of Cable Span = (sqrt((Tension at Supports^2)-(Midspan Tension^2))*2)/Total UDL

Span of Cable given Tension at Midspan for UDL on Parabolic Cable

Go Cable Span = sqrt(8*Tension at Midspan*Maximum Sag/Uniformly Distributed Load)

Parabolic Equation for Cable Slope

Go Y Co-ordinate = Uniformly Distributed Load*(Distance from Midpoint of Cable^2)/(2*Midspan Tension)

Maximum Sag given Length of Cable for UDL on Parabolic Cable

Go Maximum Sag = sqrt((Cable Length-Cable Span)*(3/8)*Cable Span)

Tension at Midspan for UDL on Parabolic Cable

Go Tension at Midspan = (Uniformly Distributed Load*(Cable Span^2))/(8*Maximum Sag)

Maximum Sag given Tension at Midspan for UDL on Parabolic Cable

Go Maximum Sag = Uniformly Distributed Load*(Cable Span^2)/(8*Tension at Midspan)

Length of Cable for UDL on Parabolic Cable

Go Cable Length = Cable Span+(8*(Maximum Sag^2)/(3*Cable Span))

Allowable Stress for Compression Elements for Highway Bridges

Go Allowable Stress = 0.44*Yield Strength of Steel

Tension at Midspan given Tension at Supports for UDL on Parabolic Cable Formula

Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2))
T_mid = sqrt((T_s^2)-(((q*L_span)/2)^2))

What is Parabolic Cable?

Parabolic Cable is a cable carrying a horizontally distributed load, then cable form a parabola or is called parabolic cable. Example: The cable carrying a bridge is a parabolic cable

How to Calculate Tension at Midspan given Tension at Supports for UDL on Parabolic Cable?

Tension at Midspan given Tension at Supports for UDL on Parabolic Cable calculator uses Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2)) to calculate the Tension at Midspan, The Tension at Midspan given Tension at Supports for UDL on Parabolic Cable formula is defined as maximum horizontal tension occurring in the cable due to uniform load at the midpoint of cable. Tension at Midspan is denoted by T_mid symbol.

How to calculate Tension at Midspan given Tension at Supports for UDL on Parabolic Cable using this online calculator? To use this online calculator for Tension at Midspan given Tension at Supports for UDL on Parabolic Cable, enter Tension at Supports (T_s), Uniformly Distributed Load (q) & Cable Span (L_span) and hit the calculate button. Here is how the Tension at Midspan given Tension at Supports for UDL on Parabolic Cable calculation can be explained with given input values -> 0.19615 = sqrt((210000^2)-(((10000*15)/2)^2)).

FAQ

What is Tension at Midspan given Tension at Supports for UDL on Parabolic Cable?

The Tension at Midspan given Tension at Supports for UDL on Parabolic Cable formula is defined as maximum horizontal tension occurring in the cable due to uniform load at the midpoint of cable and is represented as T_mid = sqrt((T_s^2)-(((q*L_span)/2)^2)) or Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2)). Tension at Supports is the tension due to loading on supports, 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 Midspan given Tension at Supports for UDL on Parabolic Cable?

The Tension at Midspan given Tension at Supports for UDL on Parabolic Cable formula is defined as maximum horizontal tension occurring in the cable due to uniform load at the midpoint of cable is calculated using Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2)). To calculate Tension at Midspan given Tension at Supports for UDL on Parabolic Cable, you need Tension at Supports (T_s), Uniformly Distributed Load (q) & Cable Span (L_span). With our tool, you need to enter the respective value for Tension at Supports, 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.

How many ways are there to calculate Tension at Midspan?

In this formula, Tension at Midspan uses Tension at Supports, Uniformly Distributed Load & Cable Span. We can use 1 other way(s) to calculate the same, which is/are as follows -

Tension at Midspan = (Uniformly Distributed Load*(Cable Span^2))/(8*Maximum Sag)

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