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Prestress Force at Stressing End using Taylor Series Expansion Calculator

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✖Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end.ⓘ Prestress Force at a Distance [P_x]			+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%

✖End Prestress Force refers to the applied prestressing force at the stretching end of tendon.ⓘ Prestress Force at Stressing End using Taylor Series Expansion [P_End]

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Prestress Force at Stressing End using Taylor Series Expansion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

End Prestress Force - (Measured in Newton) - End Prestress Force refers to the applied prestressing force at the stretching end of tendon.
Prestress Force at a Distance - (Measured in Newton) - Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end.
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

Prestress Force at a Distance: 96 Kilonewton --> 96000 Newton (Check conversion here)
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_End = P_x/((1-(μ_friction*a)-(k*x))) --> 96000/((1-(0.067*0.03490658503988)-(0.007*0.0101)))

Evaluating ... ...

P_End = 96231.8650201082

STEP 3: Convert Result to Output's Unit

96231.8650201082 Newton -->96.2318650201082 Kilonewton (Check conversion here)

FINAL ANSWER

96.2318650201082 ≈ 96.23187 Kilonewton <-- End Prestress Force

(Calculation completed in 00.020 seconds)

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< Friction Loss Calculators

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 Stressing End using Taylor Series Expansion Formula

LaTeX Go

End Prestress Force = Prestress Force at a Distance/((1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)))
P_End = P_x/((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 Stressing End using Taylor Series Expansion?

Prestress Force at Stressing End using Taylor Series Expansion calculator uses End Prestress Force = Prestress Force at a Distance/((1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))) to calculate 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 calculate Prestress Force at Stressing End using Taylor Series Expansion using this online calculator? To use this online calculator 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. Here is how the Prestress Force at Stressing End using Taylor Series Expansion calculation can be explained with given input values -> 0.096232 = 96000/((1-(0.067*0.03490658503988)-(0.007*0.0101))).

FAQ

What is Prestress Force at Stressing End using Taylor Series Expansion?

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 and is represented as P_End = P_x/((1-(μ_friction*a)-(k*x))) or End Prestress Force = Prestress Force at a Distance/((1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))). Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end, 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 Stressing End using Taylor Series Expansion?

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 is calculated using End Prestress Force = Prestress Force at a Distance/((1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))). To calculate Prestress Force at Stressing End using Taylor Series Expansion, you need Prestress Force at a Distance (P_x), 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 Prestress Force at a Distance, 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.

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