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))
Px = PEnd*(1-(μfriction*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
Px = PEnd*(1-(μfriction*a)-(k*x)) --> 120*(1-(0.067*0.03490658503988)-(0.007*0.0101))
Evaluating ... ...
Px = 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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NSS College of Engineering (NSSCE), Palakkad
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7 Friction Loss Calculators

Coefficient of Friction given Px
Go Prestress Friction Coefficient = (1/Cumulative Angle)*(1-((Prestress Force at a Distance/End Prestress Force)+(Wobble Coefficient*Distance from Left End)))
Wobble Coefficient k given Px
Go Wobble Coefficient = (1/Distance from Left End)*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Prestress Force at a Distance/End Prestress Force))
Prestress Force at Stressing End using Taylor Series Expansion
Go End Prestress Force = Prestress Force at a Distance/((1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End)))
Prestress Force at Distance X by Taylor Series Expansion
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
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
Go Prestress Force at a Distance = Vertical Resultant/(2*sin(Subtended Angle in Degrees/2))
Resultant of Vertical Reaction from Concrete on Tendon
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

Prestress Force at a Distance = End Prestress Force*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Wobble Coefficient*Distance from Left End))
Px = PEnd*(1-(μfriction*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 Px 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 (PEnd), Prestress Friction Coefficient 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 Px = PEnd*(1-(μfriction*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 (PEnd), Prestress Friction Coefficient 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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