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*Px))
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*Px)) --> 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 00.020 seconds)

Credits

Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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National Institute Of Technology (NIT), Hamirpur
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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)

Subtended Angle given Resultant Reaction Formula

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

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 (Px) 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*Px)) 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 (Px). 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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