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Prestress Force at Distance X by Taylor Series Expansion Formula

GoPrestressing Force at Distance x from Stretching End for Known Resultant Formula

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Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end. Check FAQs

P x = P End \cdot (1 - (μ friction \cdot a) - (k \cdot x))

P_x - Prestress Force at a Distance?P_End - End Prestress Force?μ_friction - Prestress Friction Coefficient?a - Cumulative Angle?k - Wobble Coefficient?x - Distance from Left End?

Prestress Force at Distance X by Taylor Series Expansion Example

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Here is how the Prestress Force at Distance X by Taylor Series Expansion equation looks like with Values.

Here is how the Prestress Force at Distance X by Taylor Series Expansion equation looks like with Units.

Here is how the Prestress Force at Distance X by Taylor Series Expansion equation looks like.

119.7109 = 120 \cdot (1 - (0.067 \cdot 2) - (0.007 \cdot 10.1))

119.7109kN = 120kN \cdot (1 - (0.067 \cdot 2°) - (0.007 \cdot 10.1mm))

119.7109 = 120 \cdot (1 - (0.067 \cdot 2) - (0.007 \cdot 10.1))

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Prestress Force at Distance X by Taylor Series Expansion Solution

Follow our step by step solution on how to calculate Prestress Force at Distance X by Taylor Series Expansion?

FIRST Step Consider the formula

P x = P End \cdot (1 - (μ friction \cdot a) - (k \cdot x))

Next Step Substitute values of Variables

∴

P x = 120kN \cdot (1 - (0.067 \cdot 2°) - (0.007 \cdot 10.1mm))

Next Step Convert Units

∴

P x = 120kN \cdot (1 - (0.067 \cdot 0.0349rad) - (0.007 \cdot 0.0101m))

Next Step Prepare to Evaluate

∴

P x = 120 \cdot (1 - (0.067 \cdot 0.0349) - (0.007 \cdot 0.0101))

Next Step Evaluate

∴

P x = 119710.867056279N

Next Step Convert to Output's Unit

∴

P x = 119.710867056279kN

LAST Step Rounding Answer

∴

P x = 119.7109kN

Prestress Force at Distance X by Taylor Series Expansion Formula Elements

Variables

Prestress Force at a Distance

Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end.

Symbol: P_x

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Prestress Force at a Distance

End Prestress Force

End Prestress Force refers to the applied prestressing force at the stretching end of tendon.

Symbol: P_End

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find End Prestress Force

Prestress Friction Coefficient

The Prestress Friction Coefficient (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.

Symbol: μ_friction

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Prestress Friction Coefficient

Cumulative Angle

Cumulative Angle here refers to the angle in radian through which the tangent to the cable profile has turned between any two points under consideration.

Symbol: a

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Cumulative Angle

Wobble Coefficient

Wobble Coefficient is found by multiplying the jacking force at any distance from jacking end with the average of the intended angular deviation from the design profile.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wobble Coefficient

Distance from Left End

Distance from Left End is the distance considered from the left jacking end on a prestressed member.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Left End

Other Formulas to find Prestress Force at a Distance

Go Prestressing Force at Distance x from Stretching End for Known Resultant

P x = \frac{N}{2 \cdot \sin (\frac{θ}{2})}

Other formulas in Friction Loss category

Go Resultant of Vertical Reaction from Concrete on Tendon

N = 2 \cdot P x \cdot \sin (\frac{θ}{2})

Go Subtended Angle given Resultant Reaction

θ = 2 \cdot a \sin (\frac{N}{2 \cdot P x})

Go Prestress Force at Stressing End using Taylor Series Expansion

P End = \frac{P x}{(1 - (μ friction \cdot a) - (k \cdot x))}

Go Coefficient of Friction given Px

μ friction = (\frac{1}{a}) \cdot (1 - ((\frac{P x}{P End}) + (k \cdot x)))

How to Evaluate Prestress Force at Distance X by Taylor Series Expansion?

Prestress Force at Distance X by Taylor Series Expansion evaluator uses Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)) to evaluate the Prestress Force at a Distance, The Prestress Force at Distance X by Taylor Series Expansion is defined as the formula for finding the loss of prestress due to friction for small values of cumulative angle, wobble coefficient, distance from end and friction coefficient. Prestress Force at a Distance is denoted by P_x symbol.

How to evaluate Prestress Force at Distance X by Taylor Series Expansion using this online evaluator? To use this online evaluator for Prestress Force at Distance X by Taylor Series Expansion, enter End Prestress Force (P_End), Prestress Friction Coefficient (μ_friction), Cumulative Angle (a), Wobble Coefficient (k) & Distance from Left End (x) and hit the calculate button.

FAQs on Prestress Force at Distance X by Taylor Series Expansion

What is the formula to find Prestress Force at Distance X by Taylor Series Expansion?

The formula of Prestress Force at Distance X by Taylor Series Expansion is expressed as Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)). Here is an example- 0.119711 = 120000*(1-(0.067*0.03490658503988)-(0.007*0.0101)).

How to calculate Prestress Force at Distance X by Taylor Series Expansion?

With End Prestress Force (P_End), Prestress Friction Coefficient (μ_friction), Cumulative Angle (a), Wobble Coefficient (k) & Distance from Left End (x) we can find Prestress Force at Distance X by Taylor Series Expansion using the formula - Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)).

What are the other ways to Calculate Prestress Force at a Distance?

Here are the different ways to Calculate Prestress Force at a Distance-

Prestress Force at a Distance=Vertical Resultant/(2*sin(Subtended Angle in Degrees/2))

Can the Prestress Force at Distance X by Taylor Series Expansion be negative?

No, the Prestress Force at Distance X by Taylor Series Expansion, measured in Force cannot be negative.

Which unit is used to measure Prestress Force at Distance X by Taylor Series Expansion?

Prestress Force at Distance X by Taylor Series Expansion is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Prestress Force at Distance X by Taylor Series Expansion can be measured.

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Prestress Force at Distance X by Taylor Series Expansion Formula

​GoPrestressing Force at Distance x from Stretching End for Known Resultant Formula

Prestress Force at Distance X by Taylor Series Expansion Example

Prestress Force at Distance X by Taylor Series Expansion Solution

Prestress Force at Distance X by Taylor Series Expansion Formula Elements

Other Formulas to find Prestress Force at a Distance

Other formulas in Friction Loss category

How to Evaluate Prestress Force at Distance X by Taylor Series Expansion?

FAQs on Prestress Force at Distance X by Taylor Series Expansion

Variable Name

GoPrestressing Force at Distance x from Stretching End for Known Resultant Formula