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Prestress Force at Distance X by Taylor Series Expansion Calculator

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✖End Prestress Force refers to the applied prestressing force at the stretching end of tendon.ⓘ End Prestress Force [P_End]			+10% -10%
✖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.ⓘ Prestress Friction Coefficient [μ_friction]			+10% -10%
✖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.ⓘ Cumulative Angle [a]			+10% -10%
✖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.ⓘ Wobble Coefficient [k]			+10% -10%
✖Distance from Left End is the distance considered from the left jacking end on a prestressed member.ⓘ Distance from Left End [x]			+10% -10%

✖Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end.ⓘ Prestress Force at Distance X by Taylor Series Expansion [P_x]

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Prestress Force at Distance X by Taylor Series Expansion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))
P_x = P_End*(1-(μ_friction*a)-(k*x))
This formula uses 6 Variables

Variables Used

Prestress Force at a Distance - (Measured in Kilonewton) - Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end.
End Prestress Force - (Measured in Kilonewton) - End Prestress Force refers to the applied prestressing force at the stretching end of tendon.
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.
Cumulative Angle - (Measured in Radian) - 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.
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.
Distance from Left End - (Measured in Meter) - Distance from Left End is the distance considered from the left jacking end on a prestressed member.

STEP 1: Convert Input(s) to Base Unit

End Prestress Force: 120 Kilonewton --> 120 Kilonewton No Conversion Required
Prestress Friction Coefficient: 0.067 --> No Conversion Required
Cumulative Angle: 2 Degree --> 0.03490658503988 Radian (Check conversion here)
Wobble Coefficient: 0.007 --> No Conversion Required
Distance from Left End: 10.1 Millimeter --> 0.0101 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_x = P_End*(1-(μ_friction*a)-(k*x)) --> 120*(1-(0.067*0.03490658503988)-(0.007*0.0101))

Evaluating ... ...

P_x = 119.710867056279

STEP 3: Convert Result to Output's Unit

119710.867056279 Newton -->119.710867056279 Kilonewton (Check conversion here)

FINAL ANSWER

119.710867056279 ≈ 119.7109 Kilonewton <-- Prestress Force at a Distance

(Calculation completed in 00.004 seconds)

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Prestress Force at Distance X by Taylor Series Expansion

LaTeX Go Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))

Subtended Angle given Resultant Reaction

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

Prestressing Force at Distance x from Stretching End for Known Resultant

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

Resultant of Vertical Reaction from Concrete on Tendon

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

Prestress Force at Distance X by Taylor Series Expansion Formula

LaTeX Go

Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))
P_x = P_End*(1-(μ_friction*a)-(k*x))

What is meant by Vertical or Transverse Prestresisng?

Besides the longitudinal prestressing sometimes it may be desirable to provide vertical prestresisng to reduce or eliminate the principal tensile stress. Vertical prestressing is done by providing high tension vertical steel wires of small diameter at suitable pitch & stressed adequately.

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

Prestress Force at Distance X by Taylor Series Expansion calculator uses Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)) to calculate 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 calculate Prestress Force at Distance X by Taylor Series Expansion using this online calculator? To use this online calculator 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. Here is how the Prestress Force at Distance X by Taylor Series Expansion calculation can be explained with given input values -> 0.119711 = 120000*(1-(0.067*0.03490658503988)-(0.007*0.0101)).

FAQ

What is Prestress Force at Distance X by Taylor Series Expansion?

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 and is represented as P_x = P_End*(1-(μ_friction*a)-(k*x)) or Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)). End Prestress Force refers to the applied prestressing force at the stretching end of tendon, 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, 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, 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 & Distance from Left End is the distance considered from the left jacking end on a prestressed member.

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

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 is calculated using Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)). To calculate Prestress Force at Distance X by Taylor Series Expansion, you need End Prestress Force (P_End), Prestress Friction Coefficient (μ_friction), Cumulative Angle (a), Wobble Coefficient (k) & Distance from Left End (x). With our tool, you need to enter the respective value for End Prestress Force, Prestress Friction Coefficient, Cumulative Angle, Wobble Coefficient & Distance from Left End 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 Prestress Force at a Distance?

In this formula, Prestress Force at a Distance uses End Prestress Force, Prestress Friction Coefficient, Cumulative Angle, Wobble Coefficient & Distance from Left End. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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