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

GoTension at Midspan for UDL on Parabolic Cable Formula

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Tension at midspan is the total tension acting in cable at midpoint. Check FAQs

T mid = \sqrt{({T s}^{2}) - ({(\frac{q \cdot L span}{2})}^{2})}

T_mid - Tension at Midspan?T_s - Tension at Supports?q - Uniformly Distributed Load?L_span - Cable Span?

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

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Here is how the Tension at Midspan given Tension at Supports for UDL on Parabolic Cable equation looks like with Values.

Here is how the Tension at Midspan given Tension at Supports for UDL on Parabolic Cable equation looks like with Units.

Here is how the Tension at Midspan given Tension at Supports for UDL on Parabolic Cable equation looks like.

196.1505 = \sqrt{(210^{2}) - ({(\frac{10 \cdot 15}{2})}^{2})}

196.1505kN = \sqrt{({210kN}^{2}) - ({(\frac{10kN/m \cdot 15m}{2})}^{2})}

196.1505 = \sqrt{(210^{2}) - ({(\frac{10 \cdot 15}{2})}^{2})}

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

Follow our step by step solution on how to calculate Tension at Midspan given Tension at Supports for UDL on Parabolic Cable?

FIRST Step Consider the formula

T mid = \sqrt{({T s}^{2}) - ({(\frac{q \cdot L span}{2})}^{2})}

Next Step Substitute values of Variables

∴

T mid = \sqrt{({210kN}^{2}) - ({(\frac{10kN/m \cdot 15m}{2})}^{2})}

Next Step Convert Units

∴

T mid = \sqrt{({210000N}^{2}) - ({(\frac{10000N/m \cdot 15m}{2})}^{2})}

Next Step Prepare to Evaluate

∴

T mid = \sqrt{(210000^{2}) - ({(\frac{10000 \cdot 15}{2})}^{2})}

Next Step Evaluate

∴

T mid = 196150.45245933N

Next Step Convert to Output's Unit

∴

T mid = 196.15045245933kN

LAST Step Rounding Answer

∴

T mid = 196.1505kN

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

Variables

Functions

Tension at Midspan

Tension at midspan is the total tension acting in cable at midpoint.

Symbol: T_mid

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Tension at Midspan

Tension at Supports

Tension at Supports is the tension due to loading on supports.

Symbol: T_s

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Tension at Supports

Uniformly Distributed Load

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.

Symbol: q

Measurement: Surface TensionUnit: kN/m

Note: Value can be positive or negative.

Formulas to find Uniformly Distributed Load

Cable Span

Cable Span is total length of cable in horizontal direction.

Symbol: L_span

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cable Span

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.

Syntax: sqrt(Number)

Other Formulas to find Tension at Midspan

Go Tension at Midspan for UDL on Parabolic Cable

T mid = \frac{q \cdot ({L span}^{2})}{8 \cdot d}

Other formulas in Parabolic Cable Tension and Length category

Go Maximum Sag given Tension at Midspan for UDL on Parabolic Cable

d = q \cdot \frac{{L span}^{2}}{8 \cdot T mid}

Go Tension at Supports for UDL on Parabolic Cable

T s = \sqrt{({T mid}^{2}) + {(q \cdot \frac{L span}{2})}^{2}}

Go UDL given Tension at Supports for UDL on Parabolic Cable

q = \frac{\sqrt{({T s}^{2}) - ({T mid}^{2})} \cdot 2}{L span}

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

L cable_span = \frac{\sqrt{({T s}^{2}) - ({T m}^{2})} \cdot 2}{W}

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

Tension at Midspan given Tension at Supports for UDL on Parabolic Cable evaluator uses Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2)) to evaluate 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 evaluate Tension at Midspan given Tension at Supports for UDL on Parabolic Cable using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Tension at Midspan given Tension at Supports for UDL on Parabolic Cable?

The formula of Tension at Midspan given Tension at Supports for UDL on Parabolic Cable is expressed as Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2)). Here is an example- 0.19615 = sqrt((210000^2)-(((10000*15)/2)^2)).

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

With Tension at Supports (T_s), Uniformly Distributed Load (q) & Cable Span (L_span) we can find Tension at Midspan given Tension at Supports for UDL on Parabolic Cable using the formula - Tension at Midspan = sqrt((Tension at Supports^2)-(((Uniformly Distributed Load*Cable Span)/2)^2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Tension at Midspan?

Here are the different ways to Calculate Tension at Midspan-

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

Can the Tension at Midspan given Tension at Supports for UDL on Parabolic Cable be negative?

No, the Tension at Midspan given Tension at Supports for UDL on Parabolic Cable, measured in Force cannot be negative.

Which unit is used to measure Tension at Midspan given Tension at Supports for UDL on Parabolic Cable?

Tension at Midspan given Tension at Supports for UDL on Parabolic Cable is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Tension at Midspan given Tension at Supports for UDL on Parabolic Cable can be measured.

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

​GoTension at Midspan for UDL on Parabolic Cable Formula

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

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

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

Other Formulas to find Tension at Midspan

Other formulas in Parabolic Cable Tension and Length category

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

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

Variable Name

GoTension at Midspan for UDL on Parabolic Cable Formula