Wobble Coefficient k given Px Calculator

✖Distance from Left End is the distance considered from the left jacking end on a prestressed member.ⓘ Distance from Left End [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%
✖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%
✖End Prestress Force refers to the applied prestressing force at the stretching end of tendon.ⓘ End Prestress Force [P_End]			+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 given Px [k]

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Formula

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Wobble Coefficient k given Px

Formula

`"k" = (1/"x")*(1-("μ"_{"friction"}*"a")-("P"_{"x"}/"P"_{"End"}))`

Example

`"0.01957"=(1/"10.1mm")*(1-("0.067"*"2°")-("96kN"/"120kN"))`

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Download Loss due to Anchorage Slip, Friction Loss and General Geometric Properties Formulas PDF

Wobble Coefficient k given Px Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Distance from Left End: 10.1 Millimeter --> 10.1 Millimeter No Conversion Required
Prestress Friction Coefficient: 0.067 --> No Conversion Required
Cumulative Angle: 2 Degree --> 0.03490658503988 Radian (Check conversion here)
Prestress Force at a Distance: 96 Kilonewton --> 96 Kilonewton No Conversion Required
End Prestress Force: 120 Kilonewton --> 120 Kilonewton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = (1/x)*(1-(μ_friction*a)-(P_x/P_End)) --> (1/10.1)*(1-(0.067*0.03490658503988)-(96/120))

Evaluating ... ...

k = 0.0195704216635968

STEP 3: Convert Result to Output's Unit

0.0195704216635968 --> No Conversion Required

FINAL ANSWER

0.0195704216635968 ≈ 0.01957 <-- Wobble Coefficient

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Structural Engineering » Prestressed Concrete » Losses of Prestress » Loss due to Anchorage Slip, Friction Loss and General Geometric Properties » Friction Loss » Wobble Coefficient k given Px

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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National Institute of Technology Karnataka (NITK), Surathkal

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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)

Wobble Coefficient k given Px Formula

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

What is meant by Vertical or Transverse Prestressing?

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 Wobble Coefficient k given Px?

Wobble Coefficient k given Px calculator uses Wobble Coefficient = (1/Distance from Left End)*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Prestress Force at a Distance/End Prestress Force)) to calculate the Wobble Coefficient, The Wobble Coefficient k given Px is defined as the value of wobble coefficient or wave coefficient when values of cumulative angle and distance from end are considerably small. Wobble Coefficient is denoted by k symbol.

How to calculate Wobble Coefficient k given Px using this online calculator? To use this online calculator for Wobble Coefficient k given Px, enter Distance from Left End (x), Prestress Friction Coefficient (μ_friction), Cumulative Angle (a), Prestress Force at a Distance (P_x) & End Prestress Force (P_End) and hit the calculate button. Here is how the Wobble Coefficient k given Px calculation can be explained with given input values -> 0.01957 = (1/0.0101)*(1-(0.067*0.03490658503988)-(96000/120000)).

FAQ

What is Wobble Coefficient k given Px?

The Wobble Coefficient k given Px is defined as the value of wobble coefficient or wave coefficient when values of cumulative angle and distance from end are considerably small and is represented as k = (1/x)*(1-(μ_friction*a)-(P_x/P_End)) or Wobble Coefficient = (1/Distance from Left End)*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Prestress Force at a Distance/End Prestress Force)). Distance from Left End is the distance considered from the left jacking end on a prestressed member, 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, Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end & End Prestress Force refers to the applied prestressing force at the stretching end of tendon.

How to calculate Wobble Coefficient k given Px?

The Wobble Coefficient k given Px is defined as the value of wobble coefficient or wave coefficient when values of cumulative angle and distance from end are considerably small is calculated using Wobble Coefficient = (1/Distance from Left End)*(1-(Prestress Friction Coefficient*Cumulative Angle)-(Prestress Force at a Distance/End Prestress Force)). To calculate Wobble Coefficient k given Px, you need Distance from Left End (x), Prestress Friction Coefficient (μ_friction), Cumulative Angle (a), Prestress Force at a Distance (P_x) & End Prestress Force (P_End). With our tool, you need to enter the respective value for Distance from Left End, Prestress Friction Coefficient, Cumulative Angle, Prestress Force at a Distance & End Prestress Force 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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