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Subtended Angle given Resultant Reaction Calculator

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Loss due to Anchorage Slip, Friction Loss and General Geometric Properties Loss due to Elastic Shortening

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✖Vertical Resultant is the resultant of vertical reaction from concrete to tendons due to curvature of the tendon.ⓘ Vertical Resultant [N]			+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%

✖Subtended Angle in Degrees is the angle made by something from a given viewpoint.ⓘ Subtended Angle given Resultant Reaction [θ]

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Subtended Angle given Resultant Reaction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Subtended Angle in Degrees = 2*asin(Vertical Resultant/(2*Prestress Force at a Distance))
θ = 2*asin(N/(2*P_x))
This formula uses 2 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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

Subtended Angle in Degrees - (Measured in Radian) - Subtended Angle in Degrees is the angle made by something from a given viewpoint.
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.

STEP 1: Convert Input(s) to Base Unit

Vertical Resultant: 50 Kilonewton --> 50 Kilonewton No Conversion Required
Prestress Force at a Distance: 96 Kilonewton --> 96 Kilonewton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = 2*asin(N/(2*P_x)) --> 2*asin(50/(2*96))

Evaluating ... ...

θ = 0.526907469549188

STEP 3: Convert Result to Output's Unit

0.526907469549188 Radian -->30.1895741990921 Degree (Check conversion here)

FINAL ANSWER

30.1895741990921 ≈ 30.18957 Degree <-- Subtended Angle in Degrees

(Calculation completed in 00.035 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)

Subtended Angle given Resultant Reaction Formula

LaTeX Go

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

What are the Permissible Limits for Deflection?

(i)The final deflection due to all loads including the effects of temperature, creep & shrinkage should not normally exceed span / 250.
(ii) Deflections including the effects of temperature, creep & span / 350 or 20mm whichever is less
(iii)If finishes are to be applied to prestressed concrete members the total upward deflections should not exceed span.

How to Calculate Subtended Angle given Resultant Reaction?

Subtended Angle given Resultant Reaction calculator uses Subtended Angle in Degrees = 2*asin(Vertical Resultant/(2*Prestress Force at a Distance)) to calculate the Subtended Angle in Degrees, The Subtended Angle given Resultant Reaction is defined as the angle made by the curvature of tendon having radius R and arc length dx. Subtended Angle in Degrees is denoted by θ symbol.

How to calculate Subtended Angle given Resultant Reaction using this online calculator? To use this online calculator for Subtended Angle given Resultant Reaction, enter Vertical Resultant (N) & Prestress Force at a Distance (P_x) and hit the calculate button. Here is how the Subtended Angle given Resultant Reaction calculation can be explained with given input values -> 3437.747 = 2*asin(50000/(2*96000)).

FAQ

What is Subtended Angle given Resultant Reaction?

The Subtended Angle given Resultant Reaction is defined as the angle made by the curvature of tendon having radius R and arc length dx and is represented as θ = 2*asin(N/(2*P_x)) or Subtended Angle in Degrees = 2*asin(Vertical Resultant/(2*Prestress Force at a Distance)). Vertical Resultant is the resultant of vertical reaction from concrete to tendons due to curvature of the tendon & Prestress Force at a Distance refers to the force on prestressed section at a distance x from stretching end.

How to calculate Subtended Angle given Resultant Reaction?

The Subtended Angle given Resultant Reaction is defined as the angle made by the curvature of tendon having radius R and arc length dx is calculated using Subtended Angle in Degrees = 2*asin(Vertical Resultant/(2*Prestress Force at a Distance)). To calculate Subtended Angle given Resultant Reaction, you need Vertical Resultant (N) & Prestress Force at a Distance (P_x). With our tool, you need to enter the respective value for Vertical Resultant & Prestress Force at a Distance 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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