Resultant of Vertical Reaction from Concrete on Tendon Calculator

✖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%
✖Subtended Angle in Degrees is the angle made by something from a given viewpoint.ⓘ Subtended Angle in Degrees [θ]			+10% -10%

✖Vertical Resultant is the resultant of vertical reaction from concrete to tendons due to curvature of the tendon.ⓘ Resultant of Vertical Reaction from Concrete on Tendon [N]

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Formula

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Resultant of Vertical Reaction from Concrete on Tendon

Formula

`"N" = 2*"P"_{"x"}*sin("θ"/2)`

Example

`"49.69326kN"=2*"96kN"*sin("30°"/2)`

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

Resultant of Vertical Reaction from Concrete on Tendon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vertical Resultant = 2*Prestress Force at a Distance*sin(Subtended Angle in Degrees/2)
N = 2*P_x*sin(θ/2)
This formula uses 1 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Vertical Resultant - (Measured in Kilonewton) - Vertical Resultant is the resultant of vertical reaction from concrete to tendons due to curvature of the tendon.
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.
Subtended Angle in Degrees - (Measured in Radian) - Subtended Angle in Degrees is the angle made by something from a given viewpoint.

STEP 1: Convert Input(s) to Base Unit

Prestress Force at a Distance: 96 Kilonewton --> 96 Kilonewton No Conversion Required
Subtended Angle in Degrees: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = 2*P_x*sin(θ/2) --> 2*96*sin(0.5235987755982/2)

Evaluating ... ...

N = 49.6932566596748

STEP 3: Convert Result to Output's Unit

49693.2566596748 Newton -->49.6932566596748 Kilonewton (Check conversion here)

FINAL ANSWER

49.6932566596748 ≈ 49.69326 Kilonewton <-- Vertical Resultant

(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 » Resultant of Vertical Reaction from Concrete on Tendon

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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)

Resultant of Vertical Reaction from Concrete on Tendon Formula

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

Name the hoo effects due to which friction loss occur?

(i)Loss of stress due to the curvature effect : Curvature effect is caused by the friction due to designed curvature of the cable.
(ii) Loss of stress due to the wobble effect : If the profile of cable is linear, the loss will be due to straightening or stretching of the cables called Wobble Effect.

How to Calculate Resultant of Vertical Reaction from Concrete on Tendon?

Resultant of Vertical Reaction from Concrete on Tendon calculator uses Vertical Resultant = 2*Prestress Force at a Distance*sin(Subtended Angle in Degrees/2) to calculate the Vertical Resultant, The Resultant of Vertical Reaction from Concrete on Tendon is defined as an infinitesimal length of tendon is considered. Vertical Resultant is denoted by N symbol.

How to calculate Resultant of Vertical Reaction from Concrete on Tendon using this online calculator? To use this online calculator for Resultant of Vertical Reaction from Concrete on Tendon, enter Prestress Force at a Distance (P_x) & Subtended Angle in Degrees (θ) and hit the calculate button. Here is how the Resultant of Vertical Reaction from Concrete on Tendon calculation can be explained with given input values -> 0.025882 = 2*96000*sin(0.5235987755982/2).

FAQ

What is Resultant of Vertical Reaction from Concrete on Tendon?

The Resultant of Vertical Reaction from Concrete on Tendon is defined as an infinitesimal length of tendon is considered and is represented as N = 2*P_x*sin(θ/2) or Vertical Resultant = 2*Prestress Force at a Distance*sin(Subtended Angle in Degrees/2). Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end & Subtended Angle in Degrees is the angle made by something from a given viewpoint.

How to calculate Resultant of Vertical Reaction from Concrete on Tendon?

The Resultant of Vertical Reaction from Concrete on Tendon is defined as an infinitesimal length of tendon is considered is calculated using Vertical Resultant = 2*Prestress Force at a Distance*sin(Subtended Angle in Degrees/2). To calculate Resultant of Vertical Reaction from Concrete on Tendon, you need Prestress Force at a Distance (P_x) & Subtended Angle in Degrees (θ). With our tool, you need to enter the respective value for Prestress Force at a Distance & Subtended Angle in Degrees 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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