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Prestress Force at Stressing End using Taylor Series Expansion Formula

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

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

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

Prestress Force at Stressing End using Taylor Series Expansion Example

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Here is how the Prestress Force at Stressing End using Taylor Series Expansion equation looks like with Values.

Here is how the Prestress Force at Stressing End using Taylor Series Expansion equation looks like with Units.

Here is how the Prestress Force at Stressing End using Taylor Series Expansion equation looks like.

96.2319 = \frac{96}{(1 - (0.067 \cdot 2) - (0.007 \cdot 10.1))}

96.2319kN = \frac{96kN}{(1 - (0.067 \cdot 2°) - (0.007 \cdot 10.1mm))}

96.2319 = \frac{96}{(1 - (0.067 \cdot 2) - (0.007 \cdot 10.1))}

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Prestress Force at Stressing End using Taylor Series Expansion Solution

Follow our step by step solution on how to calculate Prestress Force at Stressing End using Taylor Series Expansion?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

P End = \frac{96kN}{(1 - (0.067 \cdot 2°) - (0.007 \cdot 10.1mm))}

Next Step Convert Units

∴

P End = \frac{96000N}{(1 - (0.067 \cdot 0.0349rad) - (0.007 \cdot 0.0101m))}

Next Step Prepare to Evaluate

∴

P End = \frac{96000}{(1 - (0.067 \cdot 0.0349) - (0.007 \cdot 0.0101))}

Next Step Evaluate

∴

P End = 96231.8650201082N

Next Step Convert to Output's Unit

∴

P End = 96.2318650201082kN

LAST Step Rounding Answer

∴

P End = 96.2319kN

Prestress Force at Stressing End using Taylor Series Expansion Formula Elements

Variables

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 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

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 in Friction Loss category

Go Resultant of Vertical Reaction from Concrete on Tendon

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

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

P x = \frac{N}{2 \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 Distance X by Taylor Series Expansion

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

How to Evaluate Prestress Force at Stressing End using Taylor Series Expansion?

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

How to evaluate Prestress Force at Stressing End using Taylor Series Expansion using this online evaluator? To use this online evaluator for Prestress Force at Stressing End using Taylor Series Expansion, enter Prestress Force at a Distance (P_x), 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 Stressing End using Taylor Series Expansion

What is the formula to find Prestress Force at Stressing End using Taylor Series Expansion?

The formula of Prestress Force at Stressing End using Taylor Series Expansion is expressed as End Prestress Force = Prestress Force at a Distance/((1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))). Here is an example- 0.096232 = 96000/((1-(0.067*0.03490658503988)-(0.007*0.0101))).

How to calculate Prestress Force at Stressing End using Taylor Series Expansion?

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

Can the Prestress Force at Stressing End using Taylor Series Expansion be negative?

No, the Prestress Force at Stressing End using Taylor Series Expansion, measured in Force cannot be negative.

Which unit is used to measure Prestress Force at Stressing End using Taylor Series Expansion?

Prestress Force at Stressing End using 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 Stressing End using Taylor Series Expansion can be measured.

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Prestress Force at Stressing End using Taylor Series Expansion Formula

Prestress Force at Stressing End using Taylor Series Expansion Example

Prestress Force at Stressing End using Taylor Series Expansion Solution

Prestress Force at Stressing End using Taylor Series Expansion Formula Elements

Other formulas in Friction Loss category

How to Evaluate Prestress Force at Stressing End using Taylor Series Expansion?

FAQs on Prestress Force at Stressing End using Taylor Series Expansion

Variable Name